Using fuzzy measures and habitual domains to analyze the public attitude and apply to the gas taxi policy

Decision Aiding

Using fuzzy measures and habitual domains to analyze

the public attitude and apply to the gas taxi policy

Ting-Yu Chen

, Hsin-Li Chang

, Gwo-Hshiung Tzeng

a_{Department of Business Administration, College of Management, Chang Gung University,}

259, Wen-Hwa 1st Road, Kwei-Shan, Taoyuan 333, Taiwan, ROC

b_{Department of Transportation Engineering and Management, College of Management,}

National Chiao Tung University, 1001, Ta Hsueh Rd., Hsinchu 300, Taiwan, ROC

c_{Institute of Management of Technology, College of Management, National Chiao Tung University,}

1001, Ta Hsueh Rd., Hsinchu 300, Taiwan, ROC Received 2 February 1998; accepted 27 March 2001

Abstract

Public acceptance and support are the crucial keys for implementing public policies successfully. Thus, the under-standing of public acceptance or rejection towards the policy, as well as the important attributes of concern, could be very helpful to implementing the policy. However, most conventional attitude models could not approximate people's subjective evaluation process exactly by virtue of the additivity and independence assumptions. Additionally, people's decision behavior is deeply a€ected by their existing habits. Since habitual domains exist in the decision process, if the government can change or extend people's habitual thinking in favor of the public policy, the policy will receive sat-isfactory acceptance. Therefore, this study uses the habitual domain theory to analyze the public's attitude towards public policies. Furthermore, general fuzzy measures and fuzzy integrals, which require only boundary conditions and monotonicity, are also applied to develop a public attitude analysis model. An empirical study on the compress natural gas (CNG) taxi policy in Taipei City is conducted to show the applicability of the proposed model. The empirical results indicate that there are signi®cant di€erences between the public's concern and governmental publicity, and some valuable strategies are suggested to the government. Ó 2002 Elsevier Science B.V. All rights reserved.

Keywords: Attitude; Habitual domain; Fuzzy measure; Fuzzy integral; Public attitude analysis model

1. Introduction

The determination of public attitude is an es-sential issue for implementing public policies. It is dicult and troublesome for the government to promote and conduct a policy if this policy cannot be fully supported by the public. Additionally, the

*_{Corresponding author. Tel.: +886-3-328-3016 ext. 5678; fax:}

+886-3-327-1304.

E-mail address: tychen@mail.cgu.edu.tw (T.-Y. Chen).

0377-2217/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S0377-2217(01)00137-0

policy will hardly receive the expected outcome for lack of desirable communication with the public. Thus, the public attitude, that is the public ac-ceptance or rejection towards a policy, is the cru-cial key to public policies. Furthermore, specifying important attributes of public concern can be most helpful to the implementation of relevant policies. A classical and common way to capture public attitude is to use the method of a weighted mean. This method is based on the implicit assumption that attributes are independent of one another; that is, their e€ects are viewed as additive. How-ever, these attributes are interactive in most real situations. Thus, we need another method that can describe the interaction involved. If we adopt a nonadditive set function, such as a fuzzy measure (Sugeno, 1974, 1977), to characterize the impor-tance of attributes and use a fuzzy integral as a synthetic evaluator, then a reasonable and appro-priate result can be obtained.

On the other hand, from a behavioral per-spective, people's decisions are deeply a€ected by their habits. Their existing thought, thinking, judgment, and reaction will in¯uence the attitude-formation process tremendously. If the govern-ment hopes the public policy will be supported by the public, it is necessary to ®gure out their ha-bitual thinking regarding the policy. When a neg-ative attitude is found, the government should adopt a strategy that can help to change or extend people's habitual domains in favor of the policy. Since habitual thinking exists in human minds, we will apply the theory of habitual domains (Yu, 1980, 1990) to analyze the public attitude.

Summing up, based on the habitual domain theory, this study intends to apply fuzzy measures and fuzzy integrals to approximate people's sub-jective evaluation process and establish a public attitude analysis model. In order to show the ap-plicability of the proposed method, we will con-duct an empirical study about the compress natural gas (CNG) taxi policy in Taipei City. The empirical results can provide much valuable in-formation for drawing CNG taxi policies.

The rest of this paper is organized as follows: Section 2 introduces the concept of habitual do-mains. Section 3 presents the public attitude analysis model using fuzzy measures and fuzzy

integrals. Then, an empirical study of the CNG taxi policy is undertaken to implement this model. Section 4 illustrates the problem background with respect to natural gas taxies. We conducted a survey of the public and taxi drivers in Taipei City and draw some useful suggestions for the policy implementation. We end this paper with conclud-ing remarks in Section 5.

2. Habitual domain theory

Habitual domain is the central idea of this study. In brief, people's thought, thinking, judg-ment, and reaction often become stable over time and stay within a domain. This domain is called the habitual domain. Such a domain will signi®-cantly a€ect human behavior and decision pro-cesses.

The theory of habitual domains was proposed by Yu (1980). Generally, if there are no signi®cant stimuli or arrival of new information, the knowl-edge, experience, thought and skills encoded and stored in the human brain will become compara-tively stabilized after a rather long time. Then, human responses (such as cognition, understand-ing, or judgment) will tend to be habitual and form a comparatively stable pattern (Yu, 1987, 1990, 1995). Furthermore, such thought, judg-ment, and behavior are the expressions of habitual domains. In other words, habitual domains will be re¯ected in the individual's personality, character, behavior, work attitude, principle, viewpoint and so on.

The thoughts or memory encoded and stored in the human brain can be di€erentiated into ideas and operators. The former is a concept or view-point, while the latter is a procedure or method. The new ideas can be generated from previous ideas through operators. Habitual domains have four primary elements (Yu, 1985, 1991): (i) po-tential domain, which is the collection of all ideas or operators that can be potentially activated with respect to a speci®c event or problem; (ii) actual domain, which is the collection of ideas or opera-tors that are actually activated; (iii) activation propensity, which represents the possibility that ideas or operators in the potential domain have

been actually activated; and (iv) reachable domain, which is the collection of ideas or operators that can be generated from the original idea set and the original operator set.

Finally, for a decision problem, the collection of ideas or operators whose activation propensities are equivalent to or larger than a speci®c threshold value will become the core of a decision maker's habitual domains (Yu, 1990). Such a core of ha-bitual domains will control people's behaviors since the ideas or operators in the core would al-most surely be activated with respect to the deci-sion problem.

3. Establishment of public attitude analysis model Central to the public attitude analysis is the model structure. Traditional approaches are pri-marily based on the Lebesgue measure and apply linear combination models. However, the practical cases of public attitude analysis may be devoid of additivity and independence. Moreover, people's subjective evaluation process does not always ex-hibit linearity. Thus, it is more reasonable and appropriate to use a nonadditive measure to ap-proximate people's evaluation processes. Conse-quently, we will apply fuzzy measures and fuzzy integrals to analyze the public attitude towards public policies.

3.1. Preliminaries

Generally, the structure of attitudes is funda-mentally de®ned by the essential attributes and their interrelation. In such a structural analysis, a suitable model is required to decompose the atti-tude into meaningful attributes. Conventionally, the study of public attitudes used to be based on the Lebesgue measure (Onisawa et al., 1986), that is to apply a linear combination model, and its general indication is as follows (Fishbein, 1963; Fishbein and Ajzen, 1975):

Ykˆ

Xn iˆ1

bi eik; …1†

where Ykis the public attitude towards an object or

an event k (e.g., public acceptance or rejection of the policy), eikstands for the public's evaluation of

the object k in the attribute xi, bi is the degree

of belief of attribute xi about the object, and n is

the number of attributes which have prominent representation. This model has been applied in many areas, such as risk assessment and public acceptance on nuclear power (Niehaus and Swa-ton, 1981; Swaton and Renn, 1984).

The problems of the aforementioned model result from the assumptions of additivity and in-dependence. First, the linear combination form is obviously inadequate because people's subjective evaluation does not always exhibit linearity. Conventionally, Lebesgue measures assume addi-tivity of the interaction among attributes. This assumption is too strong to match human behav-iors in the real world. On the other hand, fuzzy measures only make a monotonicity assumption and thus are more general than Lebesgue mea-sures. Hence, more and more studies have applied fuzzy measures to determine grades of importance for multiple attributes. Second, the attributes considered in people's evaluation process are not always independent of each other. Additionally, it is dicult to specify their interrelation by con-ventional methods. Therefore, it would be more appropriate to use a fuzzy integral model, which is not necessary to assume additivity and indepen-dence, to approximate people's subjective evalua-tion processes. In the following, we will review the concept of general fuzzy measures.

3.2. Fuzzy measure analysis

Fuzzy measure is a measure for representing the membership degree of an object to candidate sets (Sugeno, 1974, 1977). Let X be a universal set and P…X † be the power set of X. Then a fuzzy measure, g, is de®ned by the following function:

g : P…X † ! ‰0; 1Š; …2† which assigns each crisp subset of X a number in the unit interval ‰0; 1Š. The axioms of fuzzy mea-sures include boundary conditions …g…/† ˆ 0 and

g…X † ˆ 1† and monotonicity (for every A; B 2 P…X †; if A  B, then g…A† 6 g…B††. If the universal set is in®nite, we must add an extra ax-iom of continuity (Klir and Folger, 1988). In ac-tual practice, it is enough to consider a ®nite universal set. Let X ˆ fx1; x2; . . . ; xng and i ˆ

1; 2; . . . ; n. The fuzzy measure, g…fxig†, of a single

element set, fxig, is called a fuzzy density, and we

denote giˆ g…fxig†.

In order to di€erentiate from other fuzzy mea-sure patterns (such as k-fuzzy meamea-sure, F-additive measure, classical probability measure), we use the term ``general fuzzy measure'' to designate a fuzzy measure that only requires the satisfaction of boundary conditions and monotonicity. A general fuzzy measure is the most general type of fuzzy measures because of the fewest constraints and full degrees of freedom.

Compared with other types of fuzzy measures, general fuzzy measures can provide more valuable information. Let X be a ®nite set. Consider a fuzzy measure g of …X ; P…X ††, A 2 P…X †, B 2 P…X †, A \ B ˆ /, and A; B 6ˆ /. The coupling coecient lAB is de®ned as follows (Ishii and Sugeno, 1985):

lABˆg…A [ B† ‰g…A† ‡ g…B†Š_{g…A† ^ g…B†} : …3†

Coupling coecient l_AB demonstrates the degree of additivity that the fuzzy measure holds between subsets A and B. Suppose that subsets A and B are the single element sets fxig; fxjg, respectively,

where xi; xj2 X and i 6ˆ j. L et lijˆ lfxigfxjg, then

lij ˆg…fxi; xj_gg† …gi‡ gj†

i^ gj : …4†

The degree of additivity that the fuzzy measure holds between attributes xi and xj (xi; xj2 X and

i 6ˆ j) is termed as the overlap coecient mij, where

mij2 ‰ 1; 1†. We de®ne mij as follows:

mijˆ l_lij; lij6 0; ij=…lij‡ 1†; lij> 0:



…5† Note that the normalized l_ijis mij (Onisawa et al.,

1986).

Assume that n > 1. The degree of overlap shows the average overlap between a speci®c

at-tribute and other atat-tributes. We de®ne the degree of overlap gj of attribute xjas follows:

gjˆ

P_n

iˆ1; i6ˆjm3ij

n 1 ; j ˆ 1; 2; . . . ; n: …6† Coecient gj2 ‰ 1; 1† indicates the mean degree

of overlapping between xj and other attributes.

When gjP 0, this denotes that there exists no

overlap between xj and other attributes on

aver-age. Thus, attribute xj should be withheld as it

does have some kind of in¯uence on the evaluation process. As for the situation g_j< 0, both the im-portance …gj† and overlapping …gj† should be used

to decide whether attribute xj is included in the

model or not. Then, the necessity coecient nj…2 ‰0; 1Š† of attribute xj can be used to express

the degree of necessity of xjin the model structure

(Onisawa et al., 1986): njˆ 1 ‡ gj‰1 g…fxjg†Š

ˆ 1 ‡ gj…1 gj†; 1 6 gj< 0: …7†

The above-mentioned properties of general fuzzy measures are summarized in Table 1, which includes the object that is described, theme of discussion, range of values, and the meaning of the speci®c value.

3.3. Fuzzy integrals

Consider a fuzzy measure g of …X ; P…X †† and X is a ®nite set. Let f be a measurable function from X to ‰0; 1Š, that is f : X ! ‰0; 1Š. Then, without loss of generality, assume that fxj† is monotonically

decreasing with respect to j, i.e., f …x1† P

f …x2† P


P f …xn†. If it does not hold initially,

the elements in X will be renumbered. The fuzzy integral of f with respect to g is

Z

f …x†dg ˆ_n

iˆ1

‰f …xi† ^ g…Xi†Š; …8†

where Xi:ˆ fx1; x2; . . . ; xig; i ˆ 1; 2; . . . ; n.

In practice, f can be considered the perfor-mance of an alternative on a speci®c attribute. In addition, the fuzzy measure, g, can be used to ex-press the grade of subjective importance for each

attribute (Sugeno, 1974; Ishii and Sugeno, 1985; Murofushi and Sugeno, 1989; Wang and Klir, 1992; Sugeno and Kwon, 1995). The fuzzy integral of f with respect to g gives the overall evaluation of the alternative.

Since fuzzy integrals need not assume the in-dependence of one attribute from another, they can be used in nonlinear situations. Even if two attributes are objectively independent, people may not recognize this independence subjectively. This is why fuzzy integrals with synthetic evaluations would be desirable in practice. Furthermore, peo-ple's subjective evaluations always occur according to the di€erences between the ideal and actual evaluation values of all attributes. Because each person's ideal values could be di€erent and ex-tremely dicult to be measured, it is appropriate to use subjective evaluations even if one attribute is physically independent of another. Thus, we apply fuzzy integrals to establish the analysis model of the public attitude towards public poli-cies.

We can use the same fuzzy measure, but the Choquet integral is used instead of the max±min integral (Murofushi and Sugeno, 1989; Wang and Klir, 1992; Denneberg, 1994; Pap, 1995). Even if there is complete information regarding …2n _2†

subsets, the max±min integral calculation only determines some interval at which the measure values are possibly located. On the contrary, the unique solution will be obtained if the Choquet integral is used. In addition, using the Choquet

integral can obtain more reasonable results than using the fuzzy integral in many cases (Wang and Wang, 1997). Furthermore, the usage of Choquet integrals o€ers more aid for facilitating fuzzy measure identi®cation because of the provision of extra constraints. Therefore, Choquet integrals are used in this study.

3.4. Speci®cation of public attitude analysis model For the public, there exists a set of goal func-tions to be achieved for their satisfaction level re-garding the public policy. Goal functions can be measured by a collection of elementary evaluation attributes, fx1; x2; . . . ; xng (n is the number of

at-tributes). This collection is ®nite and denoted by X. Consider the elementary attribute set, fx1; x2; . . . ; xng, to be the discussion universe for

the public acceptance or rejection problem. In the following, the assumptions for this study are ®rst elaborated, followed by the modeling of the public attitude towards the government policy.

3.4.1. Establishment of hypotheses

For applications in the management ®eld, we denote the element of power set, P…X †, on …X ; P…X †† by ``attribute aspect''. The collection of all aspects that have i elements is called the ith aspect set, where i ˆ 1; 2; . . . ; n. The degree of importance of each attribute aspect can be derived from the questionnaire investigation. The following

Table 1

Properties of general fuzzy measures

Property Object Theme Range Special meaning

Coupling coecient lAB Subsets A and B,

A; B 2 P…X † Degree of additivityof fuzzy measure between A and B

R l ˆ 0: additive; l > 0: superadditive; l < 0: subadditive; l ˆ 1: F-additive

Overlap coecient mij Attributes xiand xj,

xi; xj2 X

Degree of additivity of fuzzy measure between xiand xj

‰ 1; 1† m ˆ 0: additive Degree of overlap gj Attribute xjxj2 X Average overlap

between xjand other elements ‰ 1; 1† g > 0: relevant information; g < 0: redundant information; g ˆ 1: complete unoverlapping; g ˆ 1: complete overlapping

Necessity coecient nj Attribute xjxj2 X Degree of necessity

of xjin the structure

of the model

‰0; 1Š n ˆ 0: absolutely unnecessary; n ˆ 1: absolutely necessary

problem is encountered in practice when general fuzzy measures are used to demonstrate grades of importance for attribute aspects.

First, when excluding the boundary conditions, respondents have to make judgments on the grades of importance regarding …2n _{2† attribute aspects}

and this is highly infeasible in practice. Moreover, if we directly ask respondents the grades of im-portance for each attribute aspect, it is dicult to obtain their responses as the question is quite ab-stract. Since people's perceived grades of attribute importance are deeply a€ected by the alternatives (or object), requesting respondents to evaluate the overall performance of the concrete alternative in attribute aspects would be easier. Furthermore, if the respondents cannot indicate the performance of the alternative adequately, we can use the de-gree of belief for the evaluation value to express the uncertainty. Lastly, if more attributes are contained in the aspect, there would be a stronger possibility of con¯ict and more intertwined com-plexity.

In view of the aforementioned diculties, the following assumptions are established in this study:

1. Researchers can list all of the relevant attributes regarding the evaluation of ups and downs for the alternative or object.

2. At the point of evaluating an alternative in a speci®c attribute aspect, people have already considered the overall importance of all attri-butes contained in this aspect.

3. The accuracy of people's evaluation for an al-ternative in an attribute aspect will diminish as the number of attributes for this aspect in-creases.

For the second assumption, an alternative must be related to a set of goal functions in every evalu-ator's mind. Goal functions can be measured by ®-nite elementary attributes. When there is an unfavorable deviation in the perceived attribute value from the ideal one, this attribute will produce a corresponding level of charge (i.e., pressure). The totality of the charge by all attributes is called the charge structure. Our attention will focus on the attribute aspect that has the greatest in¯uence on the charge structure, and of course, this aspect enjoys a relatively higher grade of importance (Tzeng et al.,

1998). Thus, the evaluators' perceived grade of im-portance for each attribute aspect is, in fact, greatly a€ected by the alternative. Next, we will identify the overall importance of each attribute aspect ac-cording to fuzzy densities and the evaluation values of the alternative in each attribute aspect.

3.4.2. Public attitude analysis process

In the attitude analysis problem, the basic in-vestigation items include evaluation value eij, degree

of belief bij, and the grade of importance ^gij. We

denote eijas the evaluation of the alternative in

at-tribute xiby subject j, bijas the belief in the

evalu-ation of the alternative in attribute xi by subject j,

and ^g_ijas the perceived importance of attribute xiby

subject j. In applications, eij; bij, and ^gij can be

judged on a 7-possibility bipolar scale from )3 to 3. Evaluation values are labeled as ``extremely bad'', ``very bad'', ``bad'', ``fair'', ``good'', ``very good'', and ``extremely good'', whereas their scores are, in order, )3, )2, )1, 0, 1, 2, and 3. Likewise, the belief is labeled ``unlikely'' to ``likely'', and the grade of importance is labeled as ``unimportant'' to ``im-portant''. The score endowment is the same as that indicated in the evaluation values.

The e€ective evaluation e

ij of the ith attribute

for the alternative by subject j can be de®ned by eij

and bij; according to the de®nition by Onisawa et

al. (1986): e

ij ˆ

eij bij‡ 0:75
‡ 11:25

22:5 : …9†

The above de®nition implies the following meaning. If eijˆ 3 (extremely good) and bijˆ 3

(quite certain), then e

ijˆ 1 (best evaluation). If

eij ˆ 3 (extremely bad) and bij ˆ 3 (quite

cer-tain), then e

ij ˆ 0 (worst evaluation). If eijˆ 0

(neutral), then e

ijˆ 0:5 (neutral) in spite of bij.

From Eq. (9), we know that 0 6 e

ij6 1. Next, ^gij is normalized in ‰0; 1Š as follows: ^g ijˆ ^gij‡ 3 6 : …10†

In order to reduce the in¯uence of subjective biases caused by the individual respondents and get a more reasonable evaluation, we use an

ar-ithmetical average of the evaluation values by a number of respondents. Then, we obtain the syn-thetic evaluation of the alternative as follows:

(a) First aspect set. L et N1 denote the total

number of people interviewed for the ®rst aspect set. Let ^f …xi† and f …xi†, respectively, represent the

actual value (obtained by investigation) and the predicted value of the e€ective evaluation regard-ing attribute xi. Because the ®rst aspect set

con-tains the essential data from which one would infer the grades of importance for other aspects, let f …xi† ˆ ^f …xi†. Then f …xi† ˆ ^f …xi† ˆ_N1 1 XN1 jˆ1 e ij for i 2 ‰1; nŠ: …11†

The fuzzy density gi of each attribute can be

de-rived from the investigation data: giˆ ^giˆ_N1 1 XN1 jˆ1 ^g ij for i 2 ‰1; nŠ: …12† (b) kth aspect set, k ˆ 2; 3; . . . ; n.

Let an element of the kth aspect set be fxi1; xi2; . . . ; xikg. L et Nkdenote the total number of

people interviewed regarding the kth aspect set. If there are investigation data about ei1i2


ikj and

bi1i2


ikj; ei1i2


ikjcan be obtained in a similar way as

Eq. (9). Let E…fxi1; xi2; . . . ; xikg† denote the

pre-dicted value of the e€ective evaluation for aspect fxi1; xi2; . . . ; xikg, and let ^E…fxi1; xi2; . . . ; xikg† denote

the actual e€ective evaluation obtained from the investigation. Then, for i1; i2; . . . ; ik 2 ‰1; nŠ and

i1< i2<


< ik, ^ E…fxi1; xi2; . . . ; xikg† ˆ 1 Nk XNk jˆ1 e i1i2


ikj: …13†

The evaluation of each attribute aspect and the grade of importance of each single-attribute aspect can be used to estimate the measure values of unknown aspects. However, if the grades of im-portance of all aspects are to be solved, the eval-uation of the alternative in each aspect must be given. The data amount reaches as much as …2n _{2† and it is highly infeasible in practice.}

Therefore, the authors proposed a concept of

partial information (Chen, 1998; Chen and Tzeng, 2000). Through an experimental design approach, they designed a sampling procedure of attribute aspects to capture the most useful information and thus reduce the original data requirement in solv-ing general fuzzy measures.

To facilitate the experimental design, f must be monotonically non-decreasing in Choquet inte-grals. Consider a fuzzy measure g of …X ; P…X ††, where X is a ®nite attribute set. Let f …xi† stand for

the public's evaluation of the policy in the attrib-ute xi and f …xi† is monotonically increasing with

respect to i, that is, f …x1† 6 f …x2† 6


6 f …xn†.

Fuzzy measure gi represents the degree of

impor-tance of attribute xi. L et Xiˆ fxi; xi‡1; . . . ; xng;

i ˆ 1; 2; . . . ; n, the public attitude towards a public policy is de®ned as follows:

E…fx1; x2; . . . ; xng† ˆ …c†

Z

f …x†dg

ˆ f …x1†g…X1† ‡ f …x‰ 2† f …x1†Šg…X2† ‡

‡‰f …xn† f …xn 1†Šg…Xn†: …14†

Chen (1998) and Chen and Tzeng (2000) pro-posed the concept of ``sucient information'', which contains all information concerning grades of importance, serving as the foundation for data collection. They showed that if the evaluation values of the aspects with attribute x1 are already

known, the importance information of all aspects will be covered. The design of sucient informa-tion can contain all importance informainforma-tion and eliminate half of the data requirement for evalua-tions, but it is still dicult to collect the informa-tion with complexity O…2n 1_{†.Consequently, based}

on sucient information, the authors further proposed a method to simplify the information demand and termed such information as ``partial information''. A sampling procedure of attribute aspects was developed to reduce the data require-ment of fuzzy measure identi®cation. Under par-tial information, the complexity of data requirement is O…2n_=n†.

From the comparison among complete, su-cient, and partial information, we know that the sampling procedure under partial information can signi®cantly reduce the information demand of

evaluation values and the investigation procedure is actually feasible in practice. Therefore, partial information will be most desirable if the solution exactness is only required to reach a satisfactory level.

Based on the partial information acquired by the sampling procedure, the authors further de-veloped an identi®cation procedure to determine the values of general fuzzy measures (Chen et al., 2000). Fuzzy integrals are not di€erentiable with respect to fuzzy measures. In addition, the problem size is extremely large and the interactions among attributes are very complicated. Thus, solving general fuzzy measures is cumbersome and stren-uous. Therefore, based on partial information, Chen et al. (2000) applied genetic algorithms to develop a solution procedure as well as the detailed design for identifying general fuzzy measures.

According to the identi®cation procedure, we use the e€ective evaluation of each sample aspect and the importance of each attribute to estimate the grades of importance for other attribute as-pects. The public attitude towards a public policy can then be derived. Thus, we can realize the public attitude towards the public policy through attribute importance and fuzzy measure analysis. To show the applicability of our attitude analysis model, we applied the proposed method to the following empirical case: the promotion of the CNG taxi policy in Taipei City.

4. Empirical study

In order to realize the attitudes of the public in Taipei City towards the CNG taxi policy as well as their support for such policy, a questionnaire survey was conducted in Taipei City. The empiri-cal results can be used to review and criticize the policy implementation. Next, we will illustrate the background of the gas taxi policy.

4.1. Problem background

In Taipei City, the average daily traveling mileage for each private vehicle is about 20±30 km, while for each taxi it is about 250±300 km, and for

each bus it is about 138 km. Thus, the environment is more polluted by taxies than by other modes. If all of the 38 000 taxies in Taipei City replace gas-oline with CNG in their combustion system, the reduction of pollution emission will be nearly equal to the emission of 0.4 million private vehicles (Bureau of Transportation, 1997). This will sig-ni®cantly improve the air quality of Taipei City.

In view of this, the municipal government of Taipei City has implemented subsidies for install-ing the gas combustion system since 1996. How-ever, the explosion of a gas vehicle in Kaoshiung City brought fear to the public and seriously af-fected taxi drivers' willingness to conduct the re-placement. From the viewpoint of the government, the issues of how to change the public's habitual thoughts and how to overcome the public's intense fears are important for implementing the CNG taxi policy. Therefore, the following empirical study will investigate the acceptance or rejection of the general public and taxi drivers in Taipei City towards the gas taxi policy. The results can be employed as references for policy administration. 4.2. Questionnaire design and investigation methods

In our questionnaire survey, respondents' so-cioeconomic and demographic characteristics in-cluded gender, age, marital status, education level, occupation, and average monthly income. The major questionnaire contents are elaborated as follows:

(A) To the general public:

(i) Investigate respondents' alternative trans-portation modes and the mode-used frequency.

(ii) Conduct a survey on the respondents about their habits for taking taxies, including their fre-quency of taking taxies, their experience of taking natural gas taxies, and their attitudes towards the CNG taxi policy.

(B) To taxi drivers:

(i) Ask the drivers whether their taxies are gas vehicles or not. If the answer is positive, they are asked further about the reason they have decided to change to the gas combustion system and their overall evaluation of gas vehicles.

(ii) If the taxies are not gas vehicles, then ask the respondents their reason for not employing the gas-powered system, and try to determine whether they reject gas vehicles or not.

(C) To the general public and taxi drivers:

(i) Investigate the subjective importance of each in¯uential factor in the CNG taxi policy consid-ered by the general public. The grade of impor-tance is judged on a 7-possibility bipolar scale from )3 to 3, and the scores are labeled as unimportant to important. We determined seven in¯uential factors related to the CNG taxi policy according to the relevant studies. These attributes include:

(a) welfare …x1†, referring to the improvement of

air quality in the city;

(b) economy …x2†, referring to the

gas-recharg-ing cost of gas taxies;

(c) safety …x3†, referring to the degree of safety

of gas taxies;

(d) prevalence …x4†, referring to the perception

that the location of natural gas stations is wide-spread or not;

(e) operation …x5†, referring to the operation and

maintenance costs of gas taxies;

(f) sustenance …x6†, referring to the sustaining

distance of continuity (that is, the distance the vehicle can run between every gas-recharge) or the frequency of gas-recharging;

(g) eciency …x7†, referring to the eciency

im-provement of energy usage.

Let X be the discourse universe and X ˆ fx1; x2;

x3; x4; x5; x6; x7g. Welfare and eciency are the

at-tributes concerning the ®tness of the environment. Safety, operation, and sustenance are the attri-butes concerning the vehicle functions. Prevalence is to measure the auxiliary extent of relevant pol-icies towards gas taxi promotion. The cost-related attributes are economy and operation.

(ii) Ask respondents to evaluate the perfor-mance of gas taxies with respect to each attribute. Furthermore, since it is likely that the respondents will not understand the performance of gas taxies towards a particular attribute, the respondents are requested to mark out their degrees of belief in order to demonstrate their certainty for their own evaluation values. The evaluation and degree of belief are also judged on a 7-possibility bipolar

scale from )3 to 3, and the scores are labeled as bad to good and unlikely to likely, respectively. Then, we can derive the e€ective evaluation of each attribute aspect in the ®rst aspect set.

(iii) Conduct the sampling procedure of attrib-ute aspects under partial information. Then 17 sample aspects from the second to sixth aspect sets can be obtained, including fx1; x3g, fx2; x3g,

fx3; x4g, fx3; x5g, fx3; x6g, fx3; x7g, fx2; x3; x4g, fx1;

x3; x5g, fx3; x6; x7g, fx3; x4; x5; x7g, fx3; x4; x6; x7g,

fx2; x3; x5; x6g, fx1; x2; x3; x7g, fx1; x3; x4; x5; x6g, fx2;

x3; x4; x6; x7g, fx1; x2; x3; x5; x7g, and fx1; x2; x3;

x4; x5; x7g. The sampling procedure of attribute

aspects in detail can be found in the study of Chen and Tzeng (2000). Since we intend to use the ef-fective evaluation to derive the grade of impor-tance, we make an investigation on the evaluation of these 17 sample aspects.

(iv) Ask the respondents their opinion regard-ing the integral performance of gas taxies towards all attributes so as to appreciate their overall evaluation of gas taxies.

After collecting the required data, we can compute the following items, including the grades of importance for each attribute (^g_iˆ gi for

i 2 ‰1; 7Š), the e€ective evaluation of each single attribute aspect ( ^f …xi† ˆ f …xi† for i 2 ‰1; 7Š), the

e€ective evaluations of 17 sample aspects ( ^E…fx1; x3g†, ^E…fx2; x3g†, ^E…fx3; x4g†, ^E…fx3; x5g†, ^E

…fx3; x6g†, ^E…fx3; x7g†, ^E…fx2; x3; x4g†, ^E…fx1; x3;

x5g†, ^E…fx3; x6; x7g†, ^E…fx3; x4; x5; x7g†, ^E…fx3; x4;

x6; x7g†, ^E…fx2; x3; x5; x6g†, ^E…fx1; x2; x3; x7g†, ^E…fx1;

x3; x4; x5; x6g†, ^E…fx2; x3; x4; x6; x7g†, ^E…fx1; x2; x3;

x5; x7g†, and ^E…fx1; x2; x3; x4; x5; x7g†), and the

overall evaluation … ^E…fx1; x2; x3; x4; x5; x6; x7g††.

Next, the grades of importance for other unknown aspects can be derived according to the above-mentioned data (the identi®cation procedure of general fuzzy measures in detail can be found in Chen et al.'s study). Then, we can compute overlap coecients, degrees of overlap, and necessity co-ecients to conduct the fuzzy measure analysis.

The investigation population in this study was the general public and taxi drivers of Taipei City. We employed choice-based strati®ed sampling to the general public, and the criterion of proportion allocation was based on the proportion of each alternative mode. The alternative modes included

bus, mass rapid transit (MRT), train, taxi, private vehicle, motorcycle, and other modes. A total of 200 questionnaires were sent out and the retrieval rate was 100% since the interviews were conducted face-to-face. After removing incomplete question-naires, we obtain 189 valid copies amounting to 94.5% of the total questionnaires retrieved.

Since taxi drivers are the primary group in-¯uenced by the CNG taxi policy, we decided to take an enriched sampling in order to grasp their response towards the policy. There was no de®-nite rule in determining the sample size generally; thus, we tried to send out 200 questionnaires as well. However, it was very dicult to collect data during the pre-investigation period because of the poor cooperation by taxi drivers. Hence, we de-cided to cut down the sample size in order to reduce the diculty in practice. A total of 100 copies of questionnaires were sent out and 91 valid copies were collected after the incomplete ones were eliminated, amounting to 91.0% of the total. Thus, a total of 280 valid questionnaires were acquired.

4.3. Empirical results

As for the general public, respondents' socio-economic background statistics were as follows: male respondents amounted to 52% of the sam-ples, while females were 48% of the samples. The highest age group proportion was 41%, 30±39 year old, seconded by 20±29 year old (38%). The un-married rate is 58%. Most respondents received a college education. The occupations were mainly found to be public servants, students, or in the service and commercial industry. Their monthly incomes were NT$15,000±30,000 (35%) and NT$45,000±60,000 (27%).

In terms of taxi drivers, all samples in the in-vestigation were male. The age distributions were 40±49 year old (37%), seconded by 30±39 year old (33%). The unmarried rate is 22%. Most inter-viewed taxi drivers had obtained a secondary education. Income distribution was NT$30,000± 45,000. In addition, 91% of the drivers owned their vehicles, thus, most taxi drivers can make the

de-cision to replace the gas combustion system by themselves.

The feasibility proportion of each alternative transportation mode for the general public is shown in Table 2. Ninety percent of the respon-dents consider bus as their ordinarily available mode, and 89% of the respondents take taxies as the available mode. In addition, motorcycle (63%) and private vehicle (45%) are the other feasible modes. Since the network of the MRT in Taipei City has not been completely ®nished, most re-spondents did not place MRT as their available transportation mode.

The ranking of mode-used frequency for the general public is listed in Table 2. We ask re-spondents to rank available modes according to the frequency, and the most frequent use is regis-tered as 1, then the second one as 2, and so on. As indicated by the percentage, 43% of the respon-dents consider bus as the most frequented mode, seconded by motorcycle (36%), next private vehicle (11%), and then taxi (9%). As for the second most frequented mode reckoned by the respondents, the percentage of taxi ranks the highest (34%), fol-lowed by private vehicle (25%), bus (19%), and motorcycle (13%). With regard to the third most frequented mode, taxi tops with 31%, trailed by train (12%) and motorcycle (10%). As learned from the summarized results of the statistics, the respondents would most often take the bus and motorcycle as their modes. Furthermore, the re-spondents will most often resort to taxi as their alternative mode when their habitual mode is not available.

The proportion of respondents who have taken a ride with taxies more than six times a week amounts to 10%, while 38% for three to six times, and 52% for less than three times. It was learned that nearly half of the respondents were riding taxies with a frequency of three or more times per week. By virtue of the undistinguished external appearance between gas vehicles and gasoline ve-hicles, most respondents did not have any idea that they had taken a ride in gas vehicles. This explains why no respondents reported that they had expe-rience riding in gas vehicles. However, when asked if they are ready to take such a ride with gas taxies, 43% of them replied negatively, 46% replied with

yes, while 11% did not show any preference. This indicates that half of the people remain reluctant to ride in natural gas vehicles.

About 20% of the taxi drivers interviewed had replaced their petroleum engines with gas com-bustion systems. The primary reason for replace-ment was to reduce their operating costs since the gas-recharging cost is lower than the refueling cost. Moreover, there are also government subsi-dies to taxi owners for the replacement. These gas taxi drivers have no experience with passengers' rejection of their vehicles as passengers may not know that these taxies are natural gas-powered. Most taxi drivers are not satis®ed with the con-venience of recharging since natural gas stations have not been widely established. On the other hand, half of the remaining taxi drivers who still drive gasoline vehicles express a lack of interest in gas vehicles because of the danger of a gas explo-sion, the limited number of natural gas stations, and the intrinsic advantages of gasoline vehicles. Nevertheless, among the taxi drivers with gasoline vehicles (80% of total), about 29% of those drivers are considering replacement in the future.

The investigated data about grades of impor-tance and e€ective evaluation of the single at-tribute aspects are listed in Table 3. Here we have three sample types: the general public, taxi driv-ers, and the total sample. We observed that safety …x3† is the most important attribute for all

re-spondents from the table. of aspects in the ®rst aspect set.

In order to compare the three sample types, we further represented their di€erence graphically in Figs. 1 and 2. Fig. 1 shows the investigated im-portance of the aspects in the ®rst aspect set for the general public, taxi drivers, and the total sample. On the other hand, Fig. 2 indicates the e€ective evaluation of single attribute aspects for the dis-tinct samples.

The most important attribute is safety …x3†, and

its grade of importance reaches as high as 0.93 for the total sample (0.94 for the general public; 0.91 for taxi drivers). In general, the objectives related to survival and safety are essential for human be-ings, and these objectives are inborn drives of people's behavior. On the contrary, the objectives left outside of the survival and safety class belong

Table 3

Grades of importance and e€ective evaluations of aspects in the ®rst aspect set

Aspect Grade of importance E€ective evaluation

General public Taxi drivers Total sample General public Taxi drivers Total sample

fx1g: welfare 0.69 0.63 0.67 0.60 0.57 0.59 fx2g: economy 0.40 0.81 0.53 0.53 0.54 0.53 {x3}: safety 0.94 0.91 0.93 0.38 0.42 0.39 fx4g: prevalence 0.70 0.74 0.71 0.49 0.43 0.47 fx5g: operation 0.72 0.75 0.73 0.52 0.45 0.50 fx6g: sustenance 0.60 0.69 0.63 0.53 0.47 0.51 fx7g: eciency 0.65 0.65 0.65 0.55 0.59 0.56 Table 2

Statistics of mode-used frequency for the general public Type of transportation

mode Privatevehicle (%) Motorcycle(%) Bus(%) Mass rapidtransit (%) Taxi(%) Train(%)

Available mode 45 63 90 5 89 32 Ranking of mode-used frequency 1 11 36 43 1 9 0 2 25 13 19 0 34 9 3 8 10 6 2 31 12

to the category of self-suggestion, which is asso-ciated with post education learning, training, and experience (Yu, 1990). Unlike the objectives of self-suggestion that can tolerate large bias, the objectives of survival and safety exert severe and sensitive demands on the ideal or equilibrium condition. Thus, their acceptable bias is quite slim. Once any bias of objectives exceeds the tolerance value, people will make a rapid and obvious re-sponse. From the investigated result we know that the e€ective evaluation of gas vehicles in safety is lowest (only 0.39 for the total sample) among all attributes. Since the ideal condition of physiolog-ical objectives remains almost constant, the large di€erence of the ideal and actual values in safety creates tremendous pressure. Thus, it is clear that

safety has aroused adequate attention and its im-portance is highest correspondingly.

Economy …x2† is the least of the concerns of the

general public and its importance is only 0.40. Since it provides no extra taxi rate bene®t to the public, the incentive of lower gas-recharging cost does not encourage passengers. However, the re-duction in recharging cost is a tremendous moti-vation to taxi drivers for the replacement. Economy is the second most important attribute for taxi drivers and its importance is 0.81. For the total sample, economy is least important because the valid questionnaires of the general public amount to 67.5% of the totality of questionnaires. From Figs. 1 and 2, the ranking of importance and evaluation for di€erent attribute aspects is

Fig. 2. E€ective evaluations of aspects in the ®rst aspect set. Fig. 1. Grades of importance of aspects in the ®rst aspect set.

similar among the general public, taxi drivers, and the total sample, except in the case of the ``econ-omy'' aspect. The municipal government of Taipei City can hardly make a change to the gas-re-charging price since the fare is always restricted and determined by the city parliament. Hence, the economy aspect has little in¯uence on the formu-lation of promotional policies. In view of this sit-uation, in the following we will combine the results of the 280 valid questionnaires for simplicity.

Most respondents consider that the operation and maintenance cost of vehicles are closely re-lated to the function of the vehicle. Furthermore, vehicle function has a close relationship with safety. Consequently, operation …x5† is the second

most important attribute and its grade of impor-tance is 0.73 for the total sample (0.72 for the general public; 0.75 for taxi drivers). In addition, many respondents show concern as to whether the location of natural gas stations is widespread or not: the importance of prevalence …x4† is 0.71 for

the total sample (0.70 for the general public; 0.74 for taxi drivers).

As for the objectives of public welfare, welfare …x1† and eciency …x7† are ordinarily important

and the grades of importance are, respectively, 0.67 and 0.65. Although most people nowadays have come to realize the importance of environ-mental protection, such an issue, somehow, does not receive special attention as it is only remotely related to individual interests. In addition, people do not seem to care about the improvement of energy usage because they believe that it is pri-marily a public issue for the government. It does not exert any discernible negative impact on them directly, even in the case of bad energy eciency. Thus, welfare and eciency remain short of being widely recognized by the respondents. This further indicates that the emphatic advantages of the re-duction of air pollution and the improvement of energy usage with gas vehicles have not gathered common approval from the public. Therefore, we suggest that the notions of welfare and eciency as they pertain to gas taxies can be excluded from focus of government publicity, while more focus should be made on safety, operation, and preva-lence with which the public has indicated greater concern.

On the other hand, if the government insists that the public be educated to realize the reduction of social costs from the employment of gas vehi-cles, the government should take another ap-proach. For example, the authorities can inform the public about the danger of increased likelihood of respiratory illness or other diseases if air pol-lution worsens continuously. Moreover, ecient usage of energy resources can largely reduce reli-ance on petroleum and even indirectly bring down the price of gasoline. In other words, if the au-thorities can publicize that welfare and eciency are closely related to the objectives belonging to the categories of ``survival and safety'' and ``sen-suous grati®cation'' (Yu, 1990), the public will positively support the CNG taxi policy.

Fig. 3 shows the contrast of grades of impor-tance and e€ective evaluations for single attribute aspects. From this ®gure, it can be observed that the three most important attributes, safety, oper-ation, and prevalence, received the worst evalua-tion values. In view of the fact that these highly regarded attributes performed unsatisfactorily, it is no wonder that half of the respondents are not willing to accept gas taxies. If the authorities cannot improve people's stereotypical image of gas vehicles in these three attributes, it will be dicult to induce the public to endorse gas vehicles prev-alently. Therefore, we suggest that the government should focus its promotion on how to relieve the fear of the public rather than focus on the con-tributions of gas vehicles to welfare and eciency. Furthermore, the authorities should further in-struct taxi drivers on the proper operation and maintenance procedures for gas vehicles as well as

Fig. 3. Contrast of grades of importance and e€ective evalua-tions.

provide more locations to establish natural gas stations.

Based on the e€ective evaluations, the impor-tance and overlap coecient for each aspect in the second aspect set are derived as shown in Table 4. The overlap coecient, mij, represents the degree

of additivity of fuzzy measures between attributes xi and xj …xi; xj2 X †. It indicates the interactive

relationship between attributes.

As can be seen from Table 4, the importance of x3 and x5 only reaches as high as 0.98, indicating

that both safety and operation are absolutely im-portant in the respondents' minds. It further in-dicates that people care about the attributes directly related to their survival and safety, and these attributes form the core of human habitual domains. The public attitude and actual decision behavior are thoroughly in¯uenced by this core, and the core can be considered the actual domain at the decision time. If the government could capture the decision core of the public, it would not be dicult to induce people to accept and support the CNG taxi policy.

Furthermore, even if the other attributes are not found in the respondents' actual domains, they are still contained in the potential domains since their grades of importance are all positive. Hence, the government can turn to another approach: to transfer or extend the actual domain of the public. If the public can bring welfare and eciency into their decision core, it will help establish the

reachable domain bene®cial for gas vehicles since the public gives the highest evaluation in welfare and eciency. Under the reachable domain, it would be easy to bring down people's negative attitude towards gas taxies. However, since the degree of rigidity for habitual domains varies from person to person, it remains in controversy whe-ther the actual domains of humans can be trans-ferred or extended successfully.

Since the overlap coecient only exhibits the interaction between two attributes, we further compute the average degree of overlap for each attribute to demonstrate the average overlap be-tween an attribute and all other attributes. As shown in Table 5, the degree of overlap, g_i, of attribute xi indicates the mean degree of overlap

with regard to the information e€ect between xi

and the other six attributes. From Table 5, we know that the degrees of overlap for all attributes are smaller than zero, indicating that the e€ects provided by each attribute more or less overlap. In addition, there are higher degrees of overlap in welfare …g1ˆ 0:935† and safety …g3ˆ 0:900†.

In contrast, there are lower degrees of overlap in operation …g₅ˆ 0:730† and sustenance …g₆ˆ

0:796†.

We can use the degrees of overlap and grades of importance to identify the degree of necessity, ni,

of attribute xi, which expresses the necessity of xiin

the model structure. For example, if g_jˆ 1 (i.e., complete overlapping) and gjˆ 0 (i.e., no

impor-Table 4

Grades of importance and overlap coecients of aspects in the second aspect set

Aspect Grade of importance, g…fxi; xjg† Overlap coecient, mij Aspect Grade of importance, g…fxi; xjg† Overlap coecient, mij fx1; x2g 0.71 )0.925 fx3; x4g 0.95 )0.972 fx1; x3g 0.95 )0.970 fx3; x5g 0.98 )0.932 fx1; x4g 0.72 )0.985 fx3; x6g 0.96 )0.952 fx1; x5g 0.73 )1.000 fx3; x7g 0.94 )0.985 fx1; x6g 0.68 )0.984 fx4; x5g 0.87 )0.803 fx1; x7g 0.67 )1.000 fx4; x6g 0.72 )0.984 fx2; x3g 0.94 )0.981 fx4; x7g 0.73 )0.969 fx2; x4g 0.75 )0.925 fx5; x6g 0.85 )0.810 fx2; x5g 0.79 )0.887 fx5; x7g 0.77 )0.939 fx2; x6g 0.69 )0.887 fx6; x7g 0.70 )0.921 fx2; x7g 0.66 )0.981

tance), then njˆ 0, indicating that xj provides

re-dundant information. If njˆ 1; xjis an absolutely

necessary attribute. Thus, we can use the n value as a criterion for eliminating attributes. The maximal value of necessity coecients can be selected from the attributes whose g values are negative. If nj of

attribute xj is comparatively smaller than the

maximal value, the degree of necessity of xj is

comparatively lower than all other redundant at-tributes. Let b be a threshold value. When the proportion of nj to the maximal value is smaller

than b; xj can be eliminated. In other words,

where gj< 0, attribute xj can be dropped if nj

satis®es the following inequality: nj

max

k;gk<0nk

< b: …15†

The value of the threshold, b, is obtained by the subjective judgment of researchers and the needs of various problem patterns. A threshold value of 0.7 was proposed by Onisawa et al. (1986), and the value can be cited in this study. From Table 5, we know that the comparative necessity value of x2is

0.650 (<0.7); thus, the economy attribute can be dropped.

From Table 5, safety, operation, and preva-lence have the highest necessity coecients. Be-cause the three attributes enjoy not only the highest importance but also the greatest necessity in the model structure, the government should place more focus on them during publicity for the CNG taxi policy. For instance, the public should be informed that the natural gas vehicles have the same functions as gasoline vehicles. It also should be emphasized that quali®ed gas vehicles can be free from gas explosions, and the government will establish more natural gas stations as soon as possible.

In the seventh aspect set, the importance g…fx1; x2; x3; x4; x5; x6; x7g† ˆ 1 from the boundary

conditions. In addition, the respondents' overall evaluation regarding gas taxies is 0.54 … ^E…fx1; x2;

x3; x4; x5; x6; x7g† ˆ 0:54† in average from the

in-vestigation results.

Summing up, in order to obtain the support of the general public and taxi drivers towards the CNG taxi policy, it is necessary for the government to change or to extend their decision core. In other words, the authorities should improve people's stereotype about gas vehicles to extend their habit-ual domains in favor of the gas taxi policy. Con-cerning the attributes with higher importance, if the public and taxi drivers can appreciate the safety of gas vehicles, it would be helpful to enhance their understanding and con®dence regarding gas taxies. This can further facilitate taxi owners to adopt the gas combustion system. In addition, the authorities should educate gas taxi drivers about the operation and maintenance of gas vehicles so as to ensure safety. Moreover, the administration ought to search for more suitable locations to establish nat-ural gas stations for gas recharging. Lastly, multi-media can be used to conduct the policy marketing to the public to ensure the expected outcome of re-lated strategies. Once the public has established con®dence in gas vehicles, the government can promote gas taxies smoothly to reduce the emission of air pollution, improve air quality, and enhance the eciency of energy usage.

5. Conclusions

Public attitude is the core for implementing public policies, but so far, the conventional atti-tude models cannot clarify people's evaluation processes clearly because of the additivity and in-dependence assumptions. Additionally, human

Table 5

Degree of overlap and necessity coecient of each attribute

Attribute x1: welfare x2: economy x3: safety x4: prevalence x5: operation x6: sustenance x7: eciency

Degree of overlap, gi )0.935 )0.831 )0.900 )0.841 )0.730 )0.796 )0.903 Necessity coecient, ni(comparative value) 0.691 0.609 0.937 0.756 0.803 0.705 0.684 (0.738) (0.650) (1.000) (0.807) (0.857) (0.753) (0.730)

decision behavior is deeply a€ected by their exist-ing habits. Since habitual domains exist in human behavior, how to break (even extend) people's habitual thinking and induce the public to favor a policy becomes very important for the govern-ment. Therefore, this study used the theory of habitual domains to analyze the public's attitude towards public policies, and applied general fuzzy measures and fuzzy integrals to establish a public attitude analysis model. An empirical study for the CNG taxi policy in Taipei City was conducted to show the applicability of the proposed model.

The empirical results indicate that most re-spondents use buses and motorcycles as their ha-bitual transportation modes. When the haha-bitual modes are not available, the taxi is the major al-ternative mode for respondents. In addition, 43% of the respondents express that gas taxies are un-acceptable, indicating that most people would be reluctant to ride in natural gas vehicles. Only a small proportion of the interviewed taxi drivers have already equipped their vehicles with the gas combustion system, while half of the rest adhere to their disapproval for gas vehicles.

From the analysis results, we know that safety, operation and prevalence of charging stations are the most important attributes. However, respon-dents deliver the lowest evaluation values for those attributes, so that half of the respondents do not support the CNG taxi policy. On the other hand, welfare and eciency, though bene®cial to the en-vironment and society, do not receive as much at-tention as they deserve. Thus, the focus of the subsequent promotion activity should be placed on safety, operation, and prevalence rather than on welfare and eciency. Furthermore, the authorities should also take action to eliminate people's fear of gas vehicles, instruct gas taxi drivers with proper operation and maintenance procedures, and pro-vide more natural gas stations, so that the CNG taxi policy could be more widely accepted by the public.

Acknowledgements

The authors would like to thank the referees for providing valuable suggestions.

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