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Applied Soft Computing
j o u r n a l h o m e p a g e :w w w . e l s e v i e r . c o m / l o c a t e / a s o c
Fuzzy MCDM approach for selecting the best environment-watershed plan
Vivien Y.C. Chen
a, Hui-Pang Lien
b, Chui-Hua Liu
c, James J.H. Liou
d,
Gwo-Hshiung Tzeng
e,f,∗,1, Lung-Shih Yang
g aDepartment of Leisure Management, Taiwan Hospitality & Tourism College, Taiwan bDepartment of Water Resources Engineering and Conservation, Feng Chia University, Taiwan cDepartment of Tourism & Hospitality, Kainan University, TaiwandDepartment of Air Transportation, Kainan University, Taiwan
eInstitute of Project Management, Department of Business and Entrepreneurial Management, Kainan University, Taiwan fInstitute of Management of Technology, National Chiao Tung University, Taiwan
gOffice of the Vice President, Feng Chia University, Taiwan
a r t i c l e i n f o
Article history:Received 29 November 2008
Received in revised form 14 October 2009 Accepted 16 November 2009
Available online 3 December 2009 Keywords:
Environment-watershed plan Watershed management Fuzzy theory
Fuzzy analytic hierarchy process (FAHP) Fuzzy multiple-criteria decision-making (FMCDM)
Tourism
a b s t r a c t
In the real word, the decision-making problems are very vague and uncertain in a number of ways. Most of the criteria have interdependent and interactive features, so they cannot be evaluated by conventional measure method. Such as the feasibility, thus, to approximate the human subjective eval-uation process, it would be more suitable to apply a fuzzy method in the environment-watershed plan topic. This paper describes the design of a fuzzy decision support system in multi-criteria analysis approach for selecting the best plan alternatives or strategies in environment watershed. The fuzzy analytic hierarchy process (FAHP) method is used to determine the preference weightings of criteria for decision makers by subjective perception (natural language). A questionnaire was used to find out from three related groups comprising 15 experts, including 5 from the university of expert scholars (include Water Resources Engineering and Conservation, Landscape and Recreation, Urban Planning, Environment Engineering, Architectural Engineering, etc.), 5 from the government departments, and 5 from industry. Subjectivity and vagueness analysis is dealt with the criteria and alternatives for selec-tion process and simulaselec-tion results by using fuzzy numbers with linguistic terms. It incorporated the decision-makers’ attitude towards the preference; overall performance value of each alternative can be obtained based on the concept of fuzzy multiple-criteria decision-making (FMCDM). This research also gives an example of evaluation consisting of five alternatives, solicited from an environment-watershed plan work in Taiwan, is illustrated to demonstrate the effectiveness and usefulness of the proposed approach. The result is useful for destination planning and the sustainability of watershed tourism resources as well.
© 2010 Published by Elsevier B.V.
1. Introduction
Ordinary selection and evaluation of the environment-watershed plan considering various criteria is a multiple-criteria decision-making (MCDM) process and then it is a popular approach to decision analysis in the watershed management, use and plan [1–4]. However, in the past, many precision-based methods of MCDM for evaluating/selecting alternatives have been developed.
∗ Corresponding author at: Department of Leisure Management, Taiwan Hospi-tality & Tourism College, No. 268, Chung-Hsing ST., Feng-Shan Village, Shou-Feng County, Hualien 974, Taiwan.
E-mail addresses:[email protected](V.Y.C. Chen), [email protected],[email protected](G.-H. Tzeng).
1Distinguished Chair Professor.
These methods have been widely used in various fields such as location selection, information project selection, material selection, management decisions, strategy selection, and problems relating to be decision-making[5–7]. In the last few years, numerous attempts to handle this uncertainty, imprecision and subjectiveness have been carried out basically by fuzzy set theory, and the applications of fuzzy set theory to multi-criteria evaluation methods under the framework of utility theory have proven to be an effective approach [8,7,9].
When in initiating the best environment-watershed plan project, most government departments must consider life, produce ecologic environment engineering services in order to develop the preliminary plans and the associated details. In a project life cycle, this best plan phase is most critical to project success. Yet, when a best plan alternative is selected, most environment-watershed plan of government department owners is to lack the ability of effec-1568-4946/$ – see front matter © 2010 Published by Elsevier B.V.
tively evaluating the candidates. Substandard the best plan work is often a direct result of inadequate tender selection.
For the best plan or government authorities, plan engineering not only acquires nice planning and design but also good plan to achieve the three goals for planning management with high effi-ciency and high quality: Firstly, the evaluation criteria are generally multiple and often structured in multilevel hierarchies; secondly, the evaluation process usually involves subjective assessments by perception, resulting in the use of qualitative and fallacious data; thirdly, other related interest groups’ input for the best plan alter-native selection process should be considered.
The analytic hierarchy process (AHP) method is widely used for multiple-criteria decision-making (MCDM) and has successfully been applied to many practical decision-making problems[10]. In spite of its popularity, the method is often criticized for its inabil-ity to adequately handle the inherent uncertainty and imprecision associated with the mapping of a decision-maker’s perception to crisp numbers. The empirical effectiveness and theoretical valid-ity of the AHP have also been discussed by many authors[11,12], and this discussion has focused on four main areas: the axiomatic foundation, the correct meaning of priorities, the 1–9 measurement scale and the rank reversal problem. However, most of the problems in these areas have been partially resolved, at least for three-level hierarchic structures[13]. It is not our intention to contribute fur-ther to that discussion. Rafur-ther, the main objective of this paper is to propose a new approach to tackle uncertainty and imprecision within the prioritization process in the AHP, in particular, when the decision-maker’s judgments are represented as fuzzy numbers or fuzzy sets. In the AHP, the decision problem is structured hierar-chically at different levels, each level consisting of a finite number of elements.
However, in many cases the preference model of the human decision maker is uncertain and fuzzy and it is relatively difficult crisp numerical values of the comparison ratios to be provided by subjective perception. The decision maker may be subjective and uncertain about his level of preference due to incomplete information or knowledge, inherent complexity and uncertainty within the decision environment, lack of an appropriate measure or scale.
An effective evaluation procedure is essential in promoting deci-sion quality for problem solving and a governmental agency must be able to respond to these problems and incorporate/solve them into the overall process. This study examines this group decision-making process and proposes a multi-criteria framework for the best plan alternative selection in the environment-watershed.
Fuzzy analytic hierarchy process (FAHP) and fuzzy multiple-criteria decision-making (FMCDM) analysis have been widely used to deal with decision-making problems involving multiple-criteria evaluation/selection of alternatives[14,15,12,16–23], have shown advantages in handling unquantifiable/qualitative criteria and obtained quite reliable results. Thus, this research applied fuzzy set theory to the managerial decision-making problems of alterna-tive selection, with the intention of establishing a framework of incorporating FAHP and FMCDM, in order to help a government entity select the most appropriate plan candidate for environment-watershed improvement/investment.
This research uses the FAHP to determine the criteria weights from subjective judgments of decision-making domain experts. Since the evaluation criteria of the best plan have the diverse con-notations and meanings, there is no logical reason to treat them, as if they are each of equal importance. Furthermore, the FMCDM was used to evaluate the synthetic performance for the best plan alter-natives, in order to handle qualitative (such as natural language) criteria that are difficult to describe in crisp values, thus strengthen the comprehensiveness and reasonableness of the decision-making process.
The rest of this paper is organized as follows. Section2provides discussion on the establishment of a hierarchical structure for the best plan evaluation, and a brief introduction to FAHP and FMCDM methods. In Section3, in order to demonstrate the applicability of the framework, we then examine an empirical case as an illus-tration to demonstrate the synthesis decision using integration of FAHP and FMCDM approach for environment-watershed plan. In Section4discussions are conducted. Finally concluding remarks are presented in Section5.
2. The best plan environment-watershed measurements
The purpose of this section is to establish a hierarchical structure for tackling the evaluation problem of the best environment-watershed plan alternative. Multiple-criteria decision-making (MCDM) is an analytic method to evaluate the advantages and disadvantages of alternatives based on multiple criteria. MCDM problems can be broadly classified into two categories: multi-ple objective programming (MOP) and multimulti-ple-criteria evaluation (MCE) [24]. Since this study focuses mainly on the evaluation problem, the second category is emphasized. The typical multiple-criteria evaluation problem examines a set of feasible alternatives and considers more than one criterion to determine a priority rank-ing and improvement for alternative implementation. The contents include three subsections: building hierarchical structure of eval-uation criteria, determining the evaleval-uation criteria weights, and getting the performance value.
2.1. Building hierarchical structure of environment-watershed evaluation criteria
What is watershed? Component landform that commonly occurs in a watershed include steam channels, flood plains, stream terraces, alluvial valley bottoms, alluvial fans, mountain slopes, and ridge tops[17]. Environment-watershed plan measurements involve a number of complex factors, however, including engi-neering of management, ecological restoration, environmental construction, and environmental conservation issues. Once upon a time a plan dimension index could be based, simply, on the aggre-gate environment engineering of catastrophe rate for a period of time or landing cycles but this may be incomplete. Yeh and Lin [4]suggested that the merge of ecological engineering measures into the framework of watershed management becomes one of the most crucial research topics for our local authority institu-tions. At the moment, we need to consider many factors/criteria the environment-watershed plan index focused on catastrophe, human safety, comfortable, interest, ecological system and sustain-able environment. Chen et al.[1]suggested the four dimensions and 26 criteria. While many studies provide useful methodology and models based on problem-solving procedures have been mainly applied to the field of environment-watershed plan management in Taiwan and the rest of the world for decades. A watershed plan, restoration and management have a specific hydrologic func-tion and ecological potential. To inventory, evaluafunc-tion and plan watershed restoration are based on geomorphic, hydrologic and ecological principles. That is nature approach to watershed plan that works with nature to restore degraded watershed[17]. The operation procedures of several key model components, partici-pation of local community, utilization of geographical information systems, investigation and analysis of the ecosystem, habitat, and landscape, and allocation of ecological engineering measures, are illustrated in detail for better understanding on their values in the model [25,4]. In Austrian Danube case study, there are 12 alternatives and 33 criteria. The criteria include mainly three con-flicting types of interest: economy, ecology and sociology. Apart
Fig. 1. The hierarchical structure for the best plan alternatives assessment.
from calamity, which still accounts for environment-watershed plan in nature catastrophe, engineering design error and incident data, maintenance, and operational deficiencies are typically cited as causes of plan failed. It has been suggested that “proactive” plan measures are instituted, especially during monitoring human-error-related engineering design error.
Environment-watershed problems in the world statistics describe from natural disasters and artificially jamming two lev-els, in the first the typhoon, torrential rain and earthquake cause the flood to overflow, violent perturbation of landslide, potential debris flow torrent and so on[2,3]. In addition the reason why space and water environmental demand increase in artificial dis-turbance because of population expansion, so that the changes of land pattern utilizing and terrain features, moreover carry out the transition of developing and also leading to the fact road water and soil conservation is destroyed, the environment falls in the destruction, biological habitat in destroyed, rivers and creeks of the quality had polluted, threatened fish species, loss of forest cover, erosion and urban growth, among other things. How can we do for solving environment-watershed problems? Firstly from the environment-watershed survey data found characteristic value to improve stabilize the river canal shape, increase the activities of biological community, habitat mold and regeneration, structure integrality of ecological corridor, and to create peripheral landscape and natural environment features, develop from tour facilities and resources of humane industry, repeat structure nature of beautiful
Fig. 2. The membership function of the triangular fuzzy number.
material, and in the environment-watershed of precipitous slope where the soil-stone flow outpost area and environment preserve against district are, it needs to minimize artificial disturbance or forbid development absolutely. In summarization, we need to con-sider intact factors/criteria, which have to enclose four dimensions and ten factors/criteria, i.e. including: (1) watershed management and erosion control, (2) ecological restoration, (3) environmental construction, and (4) environmental conservation. Based on these, 10 evaluation criteria for the hierarchical structure were to be used in our study.
The hierarchical structure adopted in this study to deal with the problems of plan assessment for environment-watershed as shown inFig. 1.
2.2. Determining the evaluation criteria weights
Since the criteria of the best plan evaluation have diverse sig-nificance and meanings, we cannot assume that each evaluation criteria is of equal importance. There are many methods that can be employed to determine weights [24]such as the eigen-vector method, weighted least square method, entropy method, AHP (analytic hierarchy process), and LINMAP (linear program-ming techniques for Multidimensional of Analysis Preference). The selection of method depends on the nature of problems. To evalu-ate the best plan is a complex and wide-ranging problem, so this problem requires the most inclusive and flexible method. Since the AHP was developed by Saaty[26,27], it is a very useful decision analysis tool in dealing with multiple-criteria decision problem, and has successfully been applied to many construction indus-try decision areas[11,28–30,12]. However, in operation process of applying AHP method, it is more easy and humanistic for evalua-tors to assess “criterion A is much more important than criterion B” than to consider “the importance of principle A and principle B is seven to one”. Hence, Buckley[31]extended Saaty’s AHP to the case where the evaluators are allowed to employ fuzzy ratios in place of exact ratios to handle the difficulty for people to assign exact ratios when comparing two criteria and derive the fuzzy weights
Fig. 3. Membership functions of linguistic variables for comparing two criteria (example).
of criteria by geometric mean method. Therefore, in this study, we employ Buckley’s method, FAHP, to fuzzify hierarchical analysis by allowing fuzzy numbers for the pairwise comparisons and find the fuzzy weights. In this section, we briefly review concepts for fuzzy hierarchical evaluation.
2.2.1. Fuzzy number
Fuzzy numbers are a fuzzy subset of real numbers, representing the expansion of the idea of the confidence interval. According to the definition of Laarhoven and Pedrycz[32], a triangular fuzzy number (TFN) (Fig. 2) should possess the following basic features.
A fuzzy number ˜A on R to be a TFN if it is membership function x ∈ ˜A, A˜(x) : R → [0, 1] is equal to A˜(x) =
(x − l)/(m − l), l ≤ x ≤ m (u − x)/(u − m), m ≤ x ≤ u 0, otherwise (1)where l and u stand for the lower and upper bounds of the fuzzy number ˜A, respectively, and m for the modal value (see Fig. 2). The TFN can be denoted by ˜A = (l, m, u) and the following is the operational laws of two TFNs ˜A1= (l1, m1, u1) and ˜A2= (l2, m2, u2).
• Addition of a fuzzy number ⊕: ˜
A1⊕ ˜A2= (l1, m1, u1)⊕ (l2, m2, u2)= (l1+ l2, m1+ m2, u1+ u2)
(2) • Multiplication of a fuzzy number ⊗:
˜
A1⊗ ˜A2= (l1, m1, u1)⊗ (l2, m2, u2)= (l1l2, m1m2, u1u2),
forl1, l2> 0; m1, m2> 0; u1, u2> 0 (3)
• Subtraction of a fuzzy number : ˜
A1˜A2= (l1, m1, u1)(l2, m2, u2)= (l1− u2, m1− m2, u1− l2)
(4) • Division of a fuzzy number ∅:
˜ A1∅˜A2= (l1, m1, u1)∅(l2, m2, u2)=
l 1 u2, m1 m2, u1 l2 , forl1, l2> 0; m1, m2> 0; u1, u2> 0 (5) Table 1Membership function of linguistic scales (example).
Fuzzy number Linguistic scales Scale of fuzzy number ˜
1 Equally important (Eq) (1,1,2) ˜
3 Weakly important (Wq) (2,3,4) ˜
5 Essentially important (Es) (4,5,6) ˜
7 Very strongly important (Vs) (6,7,8) ˜
9 Absolutely important (Ab) (8,9,9)
Note: This table is synthesized by the linguistic scales defined by Chiou and Tzeng
[34]and fuzzy number scale used in Mon et al.[35].
• Reciprocal of a fuzzy number: ˜ A−1= (l 1, m1, u1)−1=
1 u1, 1 m1, 1 l1 , forl1, l2> 0; m1, m2> 0; u1, u2> 0 (6) 2.2.2. Linguistic variablesAccording to Zadeh[33], it is very difficult for conventional quantification to express reasonably those situations that are overtly complex or hard to define; so the notion of a linguistic variable is necessary in such situation. A linguistic variable is a variable whose values are words or sentences in a natural or arti-ficial language. Here, we use this kind of expression to compare to build the best plan evaluation criteria by five basic linguis-tic terms, as “absolutely important,” “very strongly important,” “essentially important,” “weakly important” and “equally impor-tant” with respect to a fuzzy five level scale (seeFig. 3)[34]. In this paper, the computational technique is based on the follow-ing fuzzy numbers defined by Mon et al. [35] in Table 1. Here each membership function (scale of fuzzy number) is defined by three parameters of the symmetric triangular fuzzy number, the left point, middle point, and right point of the range over which the function is defined. The use of linguistic variables is currently widespread and the linguistic effect values of the best plan alterna-tives found in this study are primarily used to assess the linguistic ratings given by the evaluators. Furthermore, linguistic variables are used as a way to measure the performance value of the best plan alternative for each criterion as “very good,” “good,” “fair,” “poor” and “very poor”. Triangular fuzzy numbers (TFN), as shown inFig. 4for an example, can indicate the membership functions of the expression values.
2.2.3. Fuzzy analytic hierarchy process
The procedure for determining the evaluation criteria weights by FAHP can be summarized as follows:
• Step 1: Construct pairwise comparison matrices among all the elements/criteria in the dimensions of the hierarchy system. Assign linguistic terms to the pairwise comparisons by asking
Fig. 4. Membership functions of linguistic variables for measuring the performance
which is more important in each of the two elements/criteria, such as: ˜ A =
⎡
⎢
⎢
⎣
˜1 a˜12 · · · ˜a1n ˜ a21 1˜ · · · ˜a2n . . . ... . .. ... ˜ an1 a˜n2 · · · 1˜⎤
⎥
⎥
⎦
=⎡
⎢
⎢
⎣
˜1 a˜12 · · · ˜a1n 1/˜a21 1˜ · · · ˜a2n . . . ... . .. ... 1/˜an1 1/˜an2 · · · 1˜⎤
⎥
⎥
⎦
(7)where ˜aij measure denotes, let ˜1 be (1,1,1), when i equal
j (i.e. i = j); if 1˜, ˜2, ˜3, ˜4, ˜5, ˜6, ˜7, ˜8, ˜9 measure that crite-rion i is relatively important to critecrite-rion j and then ˜
1−1, ˜2−1, ˜3−1, ˜4−1, ˜5−1, ˜6−1, ˜7−1, ˜8−1, ˜9−1measure that criterion
j is relatively important to criterion i.
• Step 2: To use geometric mean technique to define the fuzzy geo-metric mean and fuzzy weights of each criterion by Buckley[31] as follows:
˜
ri= (˜ai1⊗ ˜ai2⊗ · · · ⊗ ˜ain)1/n,
and then w˜i= ˜ri⊗ (˜r1⊗ · · · ⊗ ˜rn)−1 (8) where ˜ainis fuzzy comparison value of criterion i to criterion n,
thus, ˜riis geometric mean of fuzzy comparison value of criterion i to each criterion, ˜wiis the fuzzy weight of the ith criterion, can
be indicated by a TFN, ˜wi= (lwi, mwi, uwi). Herelwi,mwianduwi
stand for the lower, middle and upper values of the fuzzy weight of the ith criterion, respectively.
2.3. Fuzzy multiple-criteria decision-making
Bellman and Zadeh[36]were the first to probe into the decision-making problem under a fuzzy environment-watershed and they heralded the initiation of FMCDM. This analysis method has been widely used to deal with decision-making problems involving multiple-criteria evaluation/selection of alternatives. The practical applications reported in the literatures: weapon system evaluat-ing[35], technology transfer strategy selection in biotechnology [37], optimization the design process of truck components[14], energy supply mix decisions [18], urban transportation invest-ment alternatives selection [20], tourist risk evaluation [22], electronic marketing strategies evaluation in the information ser-vice industry[21], restaurant location selection[19], performance evaluation of distribution centers in logistics and bank prediction [8,38]. These studies show advantages in handling unquantifi-able/qualitative criteria, and obtained quite reliable results. This study uses this method to evaluate the best plan alternatives performance and rank the priority for them accordingly. The following will be the method and procedures of the FMCDM theory.
2.3.1. Alternatives measurement
Using the measurement of linguistic variables to demonstrate the criteria performance/evaluation (effect-values) by expressions such as “very good,” “good,” “fair,” “poor,” “very poor,” the evalu-ators are asked for conduct their subjective judgments by natural language, and each linguistic variable can be indicated by a TFN within the scale range 0–100, as shown inFig. 4. In addition, the evaluators can subjectively assign their personal range of the lin-guistic variable that can indicate the membership functions of the expression values of each evaluator. Take ˜ek
ijto indicate the fuzzy
performance/evaluation value of evaluator p towards alternative k under criterion i, and all of the evaluation criteria will be indicated by ˜epki= (lepki, mepki, uepki). Since the perception of each evaluator varies according to the evaluator’s experience and knowledge, and the definitions of the linguistic variables vary as well, this study uses the notion of average value to integrate the fuzzy judgment
values of q evaluators, that is, ˜ eki=
1 q ⊗ (˜e1 ki⊕ · · · ⊕ ˜epki⊕ · · · ⊕ ˜eqki), p = 1, 2, . . . , q. (9)The sign⊗ denotes fuzzy multiplication, the sign ⊕ denotes fuzzy addition, ˜ekishows the average fuzzy number of the judgment
of the decision makers, which can be displayed by a triangular fuzzy number as ˜eki= (leki, meki, ueki). The end-point values leki, mekiand
uekican be solved by the method put forward by Buckley[31], that
is, leki=
q p=1lepki q ; meki=
q p=1mepki q ; ueki=
q p=1uepki q (10) 2.3.2. Fuzzy synthetic decision
The weights of the each criterion of building P&D evaluation as well as the fuzzy performance values must be integrated by the calculation of fuzzy numbers, so as to be located at the fuzzy performance value (effect-value) of the integral evaluation. Accord-ing to the each criterion weight ˜widerived by FAHP, the criteria
weight vector ˜w = ( ˜w1, . . . , ˜wi, . . . , ˜wn)tcan be obtained, whereas
the fuzzy performance/evaluation matrix ˜E of each of the
alterna-tives can also be obtained from the fuzzy performance value of each alternative under n criteria, that is, ˜E = (eki)m×n. From the criteria
weight vector ˜w and fuzzy performance matrix ˜E, the final fuzzy
synthetic decision can be conducted, and the derived result will be the fuzzy synthetic decision vector ˜e = (e1, . . . , ek, . . . , em), that is,
˜
e = ˜E ⊗ ˜w = ˜w⊗ ˜E. (11) The sign “⊗” indicates the calculation of the fuzzy numbers, including fuzzy addition and fuzzy multiplication. Since the calcula-tion of fuzzy multiplicacalcula-tion is rather complex, it is usually denoted by the approximate multiplied result of the fuzzy multiplication and the approximate fuzzy number ˜si, of the fuzzy synthetic deci-sion of each alternative can be shown as ˜ek= (lek, mek, uek), where
lsk, mskand uskare the lower, middle and upper synthetic
perfor-mance values of the alternative k respectively, that is: lek=
n i=1leki× lwi, mek=
n i=1meki× mwi, uek=
n i=1ueki× uwi. (12)
2.3.3. Ranking the fuzzy number
The result of the fuzzy synthetic decision reached by each alter-native is a fuzzy number. Therefore, it is necessary that a non-fuzzy ranking method for fuzzy numbers be employed for comparison of each of the best plan alternative. In other words, the procedure of defuzzification is to locate the Best Non-fuzzy Performance value (BNP)[16]. Methods of such defuzzified fuzzy ranking generally include mean of maximal (MOM), center of area (COA), and␣-cut. To utilize the COA method to find out the BNP is a simple and prac-tical method, and there is no need to bring in the preferences of any evaluators, so it is used in this study. The BNP value of the fuzzy number ˜ek= (lek, mek, uek) can be found by the following
equation:
BNPk= lek+(uek− lek)+ (me3 k− lek),
∀
k. (13)According to the value of the derived BNP for each of the alter-natives, the ranking of the best plan of each of the alternatives can then proceed.
Fig. 5. Regional map of the Pei-Keng brook of catchments area.
3. An empirical case for selecting the best environment-watershed plan
When a government entity would like to construct a new envi-ronment watershed in Taiwan, it must follow sub-paragraph 9 of first paragraph, article 10 of the Government Procurement Law, to publicly and objectively select the best plan consultant company to provide professional services for follow-up to build environment watershed. Thus, this study used the previous case of the Pei-Keng Brook Environment-Watershed plan to exercise the process of engi-neering service tender selection.
Fig. 6. High Cheng’s distribution map of the Pei-Keng brook of catchment’s area.
The Pei-Keng brook catchments geography position is sit-uated in the Guoxing town part of Nantou County, Taiwan (23◦5315N–23◦5836N, 120◦4915E–120◦5301E). With aids from geographical information system (GIS) and cover about 3810.21 ha, accounting for 46% of the total land area of the towns (Fig. 5). Within the boundaries mountain winds, presents the north and south long and narrow tendency, the brook flows from south to north, in the area the highest sierra is about approximately 1200 m, the lowest river valley elevation is about approximately 300 m, the average elevation is 686.96 m (Fig. 6). The entire district third-level slope reaches 56.83%, above the third-third-level slope accounts for
Fig. 8. The slope is to the distribution map of the Pei-Keng brook of catchment’s
area.
77.95% (Fig. 7). The slope accounts are many of the easts for 22.14% (Fig. 8). Gather and fall and is located in gorges in the main coun-tryside, surrounded by mountains on four sides. Collect the average width in water district about 4.5 km, length is about 9 km on aver-age, and plan the major length in the area of about 11.2 km, it is about 1/11 that the average slope is lowered. With ‘Kuizhulin for-mation’ and ‘Zhanghukeng shale’ take heavy proportion most as 35.52% and 31.67%, respectively, stratum (Fig. 9). Geological struc-ture Israel ‘the Sandstone and Shale correlation, coal formation, include the coal seam’ 57.49% (Fig. 10) in order to mainly take, have ‘large cogon-grass Pu – a winter, fault of the hole in water’ with the main fault. The soil makes up and relies mainly on the fact that ‘Colluvial soils’ accounts for 39.95% (Fig. 11).
In this case, five consultant companies submitted proposals for the new environment-watershed plan to the region authorities. 3.1. The weights calculation of the evaluation criteria
According to the formulated structure of the best plan alter-natives evaluation, the weights of the dimension hierarchy and criterion hierarchy can be analyzed. The simulation process was followed by a series of interviews with three decision-making groups: domain experts (evaluators), including five from the uni-versity of expert scholars (include Water Resources Engineering and Conservation, Landscape and Recreation, Urban Planning, Envi-ronment Engineering, Architectural Engineering), five from the government departments, and five from industry. Weights were obtained by using the FAHP method; then the weights of each decision-making group and average weights were derived by geo-metric mean method suggested by Buckley[31]. The following example demonstrates the computational procedure of the weights of dimensions for domain experts:
Fig. 9. Stratum distribution map of the Pei-Keng brook of catchment’s area.
Fig. 11. Soil distribution map of the Pei-Keng brook of catchment’s area.
(1) According to the interviews with domain experts about the importance of evaluation dimensions, then the pairwise com-parison matrices of dimensions and computing the elements of synthetic pairwise comparison matrix by using the geo-metric mean method suggested by Buckley[31]that is: ˜aij=
(˜a1
ij⊗ ˜a2ij⊗ ˜a3ij⊗ ˜a4ij) 1/4
. It can be obtained the other matrix ele-ments by the same computational procedure, therefore, the synthetic pairwise comparison matrices will be constructed and to use Eq. (8)the fuzzy weights of dimensions domain experts can be obtained as shown inTable 2.
(2) To employ the COA method to compute the BNP value of the fuzzy weights of each dimension: To take the BNP value of the weight of environment-watershed for domain experts.
Similarly, the weights for the remaining dimensions and cri-teria for domain experts can be found as shown inTable 3. However, we listed the final BNP value of them inTable 3.
Table 2
Weights of dimensions.
Dimensions l m u
D1: Watershed management of erosion control 0.144 0.352 0.559
D2: Ecological restoration 0.190 0.454 0.718
D3: Environment construction 0.059 0.103 0.147
D4: Environment conservation 0.055 0.091 0.127
From the FAHP results, for the domain experts, we find the first two most important aspects are ecological restoration (0.454) and watershed management of erosion control (0.352); whereas the least important is environment conservation (0.091). These results indicate that the domain experts are worried about the ecological restoration in the environment-watershed, in addition, they also care about the watershed management of erosion control which will be considering the environment conservation.
3.2. Estimating the performance matrix
The evaluators can define their own individual range for the linguistic variables employed in this study according to their sub-jective judgments within a scale of 0–100 (Table 4) reveals a degree of variation in their definitions of the linguistic variables. It can be seen in the divergent understandings of the 3rd and 4th evalua-tor with respect to the same linguistic variable. For each evaluaevalua-tor with the same importance, this study employed the method of average value to integrate the fuzzy/vague judgment values of dif-ferent evaluators regarding the same evaluation criteria. In other words, fuzzy addition and fuzzy multiplication are used to solve for the average fuzzy numbers of the performance values under each evaluation criterion shared by the evaluators for the five best plan alternatives.
For alternative A-1 as an example, the average fuzzy perfor-mance values of criterion-C01 (balance of site layout) from experts’ judgment can be obtained as follows:
(1) The experts assigned their subjective judgments for A-1 under C01 by expressions “very good (VG),” “good (G),” “fair (F),” “poor (P),” “very poor (VP)” and corresponding to the linguistic vari-able ofTable 4, it can obtain the fuzzy performance matrix ˜ek
ij, exampleek 11, k = 1, 2, 3, 4, 5:
e1 11 (10, 30, 50) e2 11 (60, 70, 80) e3 11 (23, 36, 65) e4 11 (80, 100, 100) e5 11 (75, 80, 90) Table 3
Weights of dimensions and criteria for domain experts.
Dimensions and criteria Local weights Global weight BNP (Normal)
l m u Local Global
Watershed management of erosion control 0.144 0.352 0.559 0.352
Potential debris flow torrent 0.292 0.527 0.848 0.042 0.183 0.474 0.556 0.195 River of erosion and deposition 0.106 0.260 0.365 0.015 0.090 0.204 0.243 0.086 Soil and water conservation of roads 0.082 0.214 0.308 0.012 0.074 0.172 0.201 0.071
Ecological restoration 0.190 0.454 0.718 0.454
Activities of biological community 0.197 0.405 0.751 0.037 0.182 0.540 0.451 0.205 Integrality of ecological corridor 0.197 0.481 0.583 0.037 0.216 0.419 0.420 0.191 Ecological monitoring and management 0.060 0.114 0.211 0.011 0.051 0.152 0.128 0.058
Environment construction 0.059 0.103 0.147 0.103
Landscape tour and natural features 0.551 0.691 0.812 0.033 0.070 0.119 0.685 0.071 Human industry and resource of land 0.258 0.309 0.379 0.015 0.032 0.056 0.315 0.033
Environment conservation 0.055 0.091 0.127 0.091
Artificial disturbance minimizing 0.401 0.634 0.798 0.024 0.065 0.101 0.611 0.055 Forbid developing 0.268 0.366 0.533 0.016 0.037 0.068 0.389 0.035
Table 4
Subjective cognition results of evaluators towards the five levels of linguistic variables.
Evaluator Linguistic variable
Very poor Poor Fair Good Very good 1 (0,0,25) (10,30,50) (30,50,70) (65,75,85) (80,100,100) 2 (0,0,40) (15,30,60) (60,70,80) (80,85,90) (90,100,100) 3 (0,0,19) (23,36,57) (38,58,66) (54,77,88) (87,100,100) 4 (0,0,25) (10,30,50) (30,50,70) (65,75,85) (80,100,100) 5 (0,0,15) (15,30,45) (45,60,75) (75,80,90) (90,100,100)
(2) To employ Eqs.(9) and (10)to obtain the fuzzy performance value of A-1 under C01, that is:
e11=
5 p=1lep11 15 ,
5 p=1mep11 15 ,
5 p=1ukp11 15 = (49.6, 63.2, 75.4)
The remainder elements of fuzzy performance values of each criterion of experts for each alternative can be obtained by the same procedure, and it is shown inTable 5.
3.3. Ranking the alternatives
From the criteria weights of three decision-making groups of the obtained by FAHP (Table 3) and the average fuzzy performance values of each criterion of experts for each alternative (Table 5), the final fuzzy synthetic decision (ek) can then be processed. After
the fuzzy synthetic decision is processed, the non-fuzzy rank-ing method is then employed, and finally the fuzzy numbers are changed into non-fuzzy values. Though there are methods to rank these fuzzy numbers, this study has employed COA to determine the BNP value, which is used to rank the evaluation results of each of the best plan alternative. We use Eq.(11)to find out its A-1 alternative value, details of the results are presented inTable 6.
Table 7
Performance value and ranking by various criteria weightings.
Alternatives Performance BNPk Ranking
˜ e = ˜E ⊗ ˜w = ˜w⊗ ˜E ˜ e = ˜E ⊗ ˜w = ˜w⊗ ˜E A-1 (09.36,48.85,152.54) (09.36,48.85,100.0) 52.74 5 A-2 (12.02,65.62,175.86) (12.02,65.62,100.0) 59.72 1 A-3 (09.83,53.14,155.02) (09.83,53.14,100.0) 54.32 4 A-4 (09.98,55.23,158.92) (09.98,55.23,100.0) 55.07 3 A-5 (10.85,58.57,163.10) (10.85,58.57,100.0) 56.48 2 Note: Compromised refer to the weights of average of three groups, which are com-puted by geometric mean.
To take the fuzzy synthetic decision value of alternative A-1 under weights of domain experts as an example, we can use Eq. (12)to obtain this value. Next, we use Eq.(13)to find out its BNP value, details of the results are presented inTable 7.
As we can be seen fromTable 7that when using traditional plan rate as a plan index, the plan levels of environment watershed are identical. Table 7can be seen from the alternative evalua-tion results, alternative A-2 is the best alternative considering the weights. The results inTable 7reflect the perception that changes in criteria weights may affect the evaluation outcome to a certain degree. It is clear that most alternatives maintain similar relative rankings under different criteria weights. In addition, obviously, the Alternative A-1 has poorest performance rating relative to other alternatives, which is the most common consensus among the decision-making domain experts.
4. Discussions
This research presented the selection plan in the environment-watershed of a fuzzy decision support system for the assessment of alternative strategies proposed. It is highly affected by environment conservation and environment construction. In terms of the results, the priority order of weights of criteria for decision-making domain
Table 5
Average fuzzy performance matrix ( ˜E) of each criterion of domain experts for alternatives.
Criteria A-1 A-2 A-3 A-4 A-5
Potential debris flow torrent (49.6,63.2,75.4) (61.8,77.4,85.6) (55.6,69.2,79.4) (44.6,58.2,74.4) (61.8,77.4,85.6) River of erosion and deposition (48.6,55.2,69.4) (30.6,47.6,62.2) (36.6,45.2,60.4) (51.6,63.2,77.4) (57.8,68.4,78.6) Soil and water conservation of roads (38.6,48.2,65.4) (71.4,84.0,90.0) (45.6,56.2,69.4) (53.6,66.2,77.4) (42.8,53.4,66.6) Activities of biological community (34.6,50.6,67.2) (52.6,64.6,74.2) (41.6,55.6,67.2) (46.6,60.6,73.2) (41.6,55.6,67.2) Integrality of ecological corridor (48.6,35.2,57.4) (41.6,56.6,69.2) (25.6,37.2,55.4) (28.6,41.6,53.2) (28.6,41.6,57.2) Ecological monitoring and management (22.6,35.6,55.2) (40.6,57.6,69.2) (34.6,47.6,63.2) (30.6,47.6,62.2) (34.6,47.6,63.2) Landscape tour and natural features (21.6,49.2,69.4) (47.8,64.4,78.6) (41.6,56.2,72.4) (40.6,54.2,69.4) (47.8,64.4,78.6) Human industry and resource of land (34.6,58.6,72.2) (57.4,71.0,82.0) (43.6,58.6,71.2) (52.6,67.6,77.2) (53.4,67.0,78.0) Artificial disturbance minimizing (43.6,41.2,61.4) (43.8,61.4,76.6) (33.6,49.2,66.4) (34.6,48.2,63.4) (29.8,47.4,62.6) Forbid developing (43.6,41.2,61.4) (50.8,66.4,79.6) (40.6,54.2,69.4) (34.6,48.2,63.4) (46.8,62.4,75.6)
Table 6
A-1 alternative various synthetic performance value.
A-1 alternative (example) e˜1i w˜i e˜1i⊗ ˜wi
Potential debris flow torrent (49.6,63.2,75.4) (0.042,0.185,0.474) (2.089,11.710,35.774) River of erosion and deposition (48.6,55.2,69.4) (0.015,0.091,0.204) (0.742,5.045,14.150) Soil and water conservation of roads (38.6,48.2,65.4) (0.012,0.075,0.172) (0.457,3.621,11.247) Activities of biological community (34.6,50.6,67.2) (0.037,0.184,0.540) (1.296,9.316,36.269) Integrality of ecological corridor (48.6,35.2,57.4) (0.037,0.218,0.491) (1.821,7.684,24.030) Ecological monitoring and management (22.6,35.6,55.2) (0.011,0.052,0.152) (0.259,1.843,8.376) Landscape tour and natural features (21.6,49.2,69.4) (0.033,0.071,0.119) (0.707,3.509,8.284) Human industry and resource of land (34.6,58.6,72.2) (0.015,0.032,0.056) (0.529,1.869,4.026) Artificial disturbance minimizing (43.6,41.2,61.4) (0.024,0.065,0.101) (1.037,2.696,6.225) Forbid developing (43.6,41.2,61.4) (0.016,0.038,0.068) (0.423,1.556,4.163)
10
i=1˜e1i⊗ ˜wi – – (9.36,48.85,152.54)
experts in the complete evaluation criteria hierarchy, we can see the decision-making domain experts in the decision-making pro-cess.
In this study of the best environment-watershed plan alterna-tive evaluation, the domain experts from the FAHP results, for the domain experts, by the compromise ranking method, the compro-mise solution is determined, which would be most acceptable to the decision makers. Via the priority decision-making we find the first most important dimensions are ecological restoration (0.454) and watershed management of erosion control (0.352); whereas the least important is environment conservation (0.091). On the other hand, the domain expert is more concerned about the plan-ning of landscape tour and natural features, because they think that these criteria may identify the design ability of a designer (the first three important criteria are: Activities of biological commu-nity 0.205, Potential debris flow torrent 0.195 and Integrality of ecological corridor 0.191).
The results inTable 7 reflect the perception that changes in criteria weights may affect the evaluation outcome in a sense. It is clear that most alternatives maintain similar relative rank-ings under different criteria weights. In addition, obviously, the Alternative A-1 got the domain expert 52.74 that has the poor-est performance rating relative to other alternatives. Alternative A-2 has got 59.72 it has the best alternative, which is the most common consensus among the decision-making domain experts. Thus, an effective evaluation procedure is essential to promote the decision quality. This work examines this group decision-making process and proposes a multi-criteria framework for the best plan selection. To deal with the qualitative attributes in subjective judg-ment, this work employs fuzzy analytic hierarchy process (FAHP) to determine the weights of decision criteria for domain experts, including five from the university of expert scholars (include Water Resources Engineering and Conservation, Landscape and Recre-ation, Urban Planning, Environment Engineering, Architectural Engineering), five from the government departments, and five from industry.
An empirical case study of nine proposed plan alternatives for a new plan project of the Pei-Keng Brook Environment Watershed is used to exemplify the approach. The underlying concepts applied were intelligible to the decision-making groups, and the compu-tation required is straightforward and simple. It will also assist the government agencies in making critical decisions during the selection of the best environment-watershed plan alternatives.
5. Concluding remarks
Using the FMCDM can decide the relative weights of criteria. The FMCDM to construct a new plan model for environment-watershed effects, which may be worth doing further researches. This is an important finding in the study. The proposed model well suitable deal with any decision problem which constructs complicated and confused and whose criteria are dependent, so it can be applied to many fields, such as environment plan, psychology, consumer behavior, human resources management and so on. The study sets up causal model of the best environment-watershed plan effect and the relational structure model is verified through satisfactory statistical technique in order to confirm the model efficiency. In cur-rent methods of the best plan selection, government agencies rely only on a panel of experts to perform the evaluation, neglecting the fuzziness of subjective judgment and other relative perception in this process. Then the fuzzy multiple-criteria decision-making (FMCDM) approach is used to synthesize the group decision. This process enables decision makers to formalize and effectively solve the complicated, multi-criteria and fuzzy/vague perception prob-lem of most appropriate and the best plan alternative selection. Over the past its poor watershed plan record has led to Taiwan’s
Soil and Water Conservation Bureau, Council of Agriculture, con-ducting annual plan evaluations of Pei-Keng brook of watershed. Traditionally, the plan is assessed on the number of storm water of catastrophes, and possibly “land and monitored” during audits. These statistics are not always helpful when catastrophes incident or land and monitored rates are very low and give little indi-cation of possible future trends. Based on several aspects of the best environment-watershed plan systems we have used FAHP and FMCDM methods and approach that considers independent between a range of criteria and their weighting. An empirical test-ing of the approach ustest-ing a Taiwanese case study illustrates its usefulness.
References
[1] Y.C. Chen, H.P. Lien, G.H. Tzeng, L.S. Yang, Watershed of environment to inte-grate conservation plan measurement, in: The 17th Hydraulic Engineering Conference, August 5–6, 2008.
[2] I.C. Goulter, H.G. Wenzel Jr., L.D. Hopkins, Watershed land-use planning under certainty, Environment and Planning A 15 (7) (1983) 987–992.
[3] X. Wang, C. White-Hull, S. Dyer, Y. Yang, GIS-ROUT: a river model for water-shed planning, Environment and Planning B: Planning and Design 27 (2) (2000) 231–246.
[4] C. Yeh, B. Lin, Integrated planning and design model of ecological engineering measures for watershed management, in: EWRI Watershed Management 2005 Conference, Williamsburg, Virginia, USA, July 19–22, 2005.
[5] C. Carlsson, Tackling an MCDM-problem with the help of some results from fuzzy set theory, European Journal of Operational Research 10 (3) (1982) 270–278.
[6] C.T. Chen, Extensions of the TOPSIS for group decision-making under fuzzy environment, Fuzzy Sets and Systems 114 (1) (2000) 1–9.
[7] H.K. Chiou, G.H. Tzeng, D.C. Cheng, Evaluating sustainable fishing development strategies using fuzzy MCDM approach, Omega 33 (3) (2005) 223–234. [8] Y.C. Chen, An application of fuzzy set theory to external performance evaluation
of distribution centers in logistics, Soft Computing 6 (1) (2002) 64–70. [9] M.-F. Chen, G.-H. Tzeng, C.G. Ding, Combining fuzzy AHP with MDS in
iden-tifying the preference similarity of alternatives, Applied Soft Computing 8 (1) (2008) 110–117.
[10] S. Lai, A preference-based interpretation of AHP, Omega 23 (4) (1995) 453–462. [11] F.K.T. Cheung, J.L.F. Kuen, M. Skitmore, Multi-criteria evaluation model for the selection of architecture consultants, Construction Management and Eco-nomics 20 (7) (2002) 569–580.
[12] C. Mcintyre, M.K. Parfitt, Decision support system for residential land develop-ment site selection process, Journal of Architecture Engineering 4 (4) (1998) 125–131.
[13] T.Y. Hsieh, S.-T. Lu, G.H. Tzeng, Fuzzy MCDM approach for planning and design tenders selection in public office buildings, International Journal of Project Management 22 (7) (2004) 573–584.
[14] C.V. Altrock, B. Krause, Multi-criteria decision-making in German automo-tive industry using fuzzy logic, Fuzzy Sets and Systems 63 (3) (1994) 375– 380.
[15] S.-P. Li, B.F. Will, A fuzzy logic system for visual evaluation, Environment and Planning B: Planning and Design 32 (2) (2005) 293–304.
[16] S. Opricovic, G.H. Tzeng, Defuzzification within a fuzzy multicriteria decision model, International Journal of Uncertainty, Fuzziness and Knowledge-based Systems 11 (2003) 635–652.
[17] M.M. Petersen, A natural approach to watershed planning, restoration and management, Water Science and Technology 39 (12) (1999) 347–352. [18] G.H Tzeng, T.A. Shiah, J.Y. Teng, A multiobjective decision making approach
to energy supply mix decisions in Taiwan, Energy Sources 16 (3) (1994) 301– 316.
[19] G.H. Tzeng, M.H. Tzen, J.J. Chen, C. Opricovic, Multicriteria selection for a restau-rant location in Taipei, International Journal of Hospitality Management 21 (2) (2002) 175–192.
[20] J.Y. Teng, G.H. Tzeng, Fuzzy multicriteria ranking of urban transportation investment alternative, Transportation Planning and Technology 20 (1) (1996) 15–31.
[21] M.T. Tang, G.H. Tzeng, S.W. Wang, A hierarchy fuzzy MCDM method for studying electronic marketing strategies in the information service industry, Journal of International Information Management 8 (1) (1999) 1–22.
[22] S.H. Tsaur, G.H. Tzeng, G.C. Wang, Evaluating tourist risks from fuzzy perspec-tives, Annals of Tourism Research 24 (4) (1997) 796–812.
[23] H.B. Willey, Fuzzy theory and environmental control in buildings, Environment and Planning B 6 (3) (1979) 279–291.
[24] C.L. Hwang, K. Yoon, Multiple attribute decision making: methods and appli-cations, Lecture Notes in Economics and Mathematical Systems 186 (1981) (Springer).
[25] E.C. Ozelkan, L. Duckstein, Analyzing water resources alternatives and han-dling criteria by multi-criterion decision techniques, Journal of Environmental Management 48 (1) (2002) 69–96.
[26] T.L. Saaty, A scaling method for priorities in hierarchical structures, Journal of Mathematical Psychology 15 (2) (1997) 234–281.
[27] T.L. Saaty, The Analytic Hierarchy Process, McGraw-Hill, New York, 1980. [28] S.O. Cheung, T.I. Lam, M.Y. Leung, Y.W. Wan, An analytical hierarchy process
based procurement selection method, Construction Management Economics 19 (1) (2001) 427–437.
[29] S.W. Fong, S.K.Y. Choi, Final contractor selection using the analytical hierarchy process, Construction Management Economics 18 (5) (2000) 547–557. [30] M. Hastak, Advanced automation or conventional construction process,
Automation Construction 7 (4) (1998) 299–314.
[31] J.J. Buckley, Fuzzy hierarchical analysis, Fuzzy Sets and Systems 17 (1) (1985) 233–247.
[32] P.J.M. Laarhoven, W. Pedrycz, A fuzzy extension of Saaty’s priority theory, Fuzzy Sets and Systems 11 (3) (1983) 229–241.
[33] L.A. Zadeh, The concept of a linguistic variable and its application to approxi-mate reasoning, Information Sciences 8 (2) (1975) 199–249.
[34] H.K. Chiou, G.H. Tzeng, Fuzzy hierarchical evaluation with grey relation model of green engineering for industry, International Journal of Fuzzy System 3 (3) (2001) 466–475.
[35] D.L. Mon, C.H. Cheng, J.C. Lin, Evaluating weapon system using fuzzy analytic hierarchy process based on entropy weight, Fuzzy Sets and Systems 62 (2) (1994) 127–134.
[36] R.E. Bellman, L.A. Zadeh, Decision-making in a fuzzy environment management, Science 17 (4) (1970) 141–164.
[37] P.L. Chang, Y.C. Chen, A fuzzy multi-criteria decision making method for tech-nology transfer strategy selection in biotechtech-nology, Fuzzy Sets and Systems 63 (1) (1994) 131–139.
[38] V. Ravi, H. Kurniawan, P.N.K. Thai, P. Ravi Kumar, Soft computing system for bank performance prediction, Applied Soft Computing 8 (1) (2008) 305– 315.
