ܴཥࣽמεᏢ 103 ਠϣᚒࣴزीฝԋ݀ൔ
ीฝᜪձǺ
Һ୍ࠠीฝ ӝࠠीฝ ;ঁΓीฝ
ीฝጓဦǺMUST-103-πᆅ-7
Չය໔Ǻ 103 ԃ 1 Д 1 ВԿ 103
ԃ 9 Д 30 В
ीฝЬΓǺࢫਁബ
ӅӕЬΓǺ
ीฝୖᆶΓǺߋד◖
ጯۚࢪ
ೀБԄǺϦ໒ܭਠᆛ।
ՉൂՏǺܴཥࣽמεᏢππำᆶᆅس
ύ ҇ ୯
103 ԃ
10
Д 31
В
ኳጋηӝᑽໆӧẮନၗ౦தॶቹៜϐᔈҔ
II
Abstract
In the situations of performance measurement, decision makers (DM) usually set up their performance rating under the circumstances (1) subjective judgment (2) qualitative measurement (3) uncertainty (4) group decision making. In order to consolidate each individual performance rating into summarized results, data aggregation method should be well selected both in respects of crisp data as well as fuzzy data.
Likert Scale questionnaire is the common tool used for collection of individual judgment, and the calculated arithmetic average is assumed as the summarized results of investigated group. For crisp performance measuring data, outlier elimination methods should be applied as the filters of “bias data” to enhance the reliability of performance measurement. This research will propose Fuzzy Subsethood Measure as the “Outlier Elimination” method for fuzzy data analysis, which can reduce the impact weighting of “Outlier”Δthus adjust the calculated results escaping from the bias.
The main purpose of this research is going to survey theory of group decision making, and data aggregation methods applied in scopes of performance measurement. The measuring data for criteria rating is collected in format of either crisp data or fuzzy number (expressed in types of triangular or trapezoidal fuzzy number). Data aggregation methods surveyed in this project include, simple arithmetic mean and geometric mean used in crisp data aggregation, fuzzy weighted average and fuzzy subsethood measure processed in fuzzy number.
This research is a one-year’s survey project, the major contents will focus on group decision making, subjective and objective group consensus methods applied in criteria rating, and data aggregation for both crisp data and fuzzy number. Also an empirical performance measurement system, collected with Likert Scale questionnaires, would be just the real case study for purpose of system validation and accuracy assured..
1
ಃക ق
ࣁΑᗉխӧᕮਏຑၸำύౢғୃৡϷԋᐱᘐǴӝӭՏৎаဂᡏ،ޑБԄڗ ளӅǴࢂᕮਏຑၸำύന٫ޑᒧБਢϐǹHerrera et al.(1996)ჹဂᡏ،(Group Decision Making)ޑۓကǺ(1)ΒՏаԋୖᆶ،ǴΓ֡ԖӚԾޑᇡޕǵᄊࡋǵᐒᆶ Γ፦ǹ(2)ӸӧঁӅӕᇡޕޑୢᚒǹ(3)යఈၲԋӅӕޑ،Ƕဂᡏ،ࢂҗဂΓ ၸࢌᅿኳԄӅӕբԋ،ǴԶقဂᡏёаࢂҗہǵҺ୍λಔǵຑǵࣴزλಔ БԄԋǴԶӵՖၲԋဂᡏӅ(Group Consensus)߾ࢂဂᡏ،ୢᚒύޑख़ाፐ ᚒǹӧ،ޑၸำϐύǴሡाԵໆډ،ޑᡏ܄Ǵӕਔा༼Ӛঁ،ԋޑཀـǴሡ ाӕਔԵቾډᡏ܄کঁձཀـǶ ،ёаϩࣁۓ܄ᆶۓໆ،ٿεᜪࠠǴForman ᆶ Peniwati (1998)ᇡࣁЬाࢂၸ (1)۶Ԝ໔ޑፕᕇளӅǹ(2)߄ၲрঁΓޑୃӳ೭ٿᅿБԄǶԶ،ΞёϩዴۓރݩΠϐ ،ୢᚒ(decision under certainty)ǵ॥ᓀΠϐ،ୢᚒ(decision with risk)ǵֹӄόዴۓރݩ Πϐ،ୢᚒ(decision under strict certainty))ΟᅿǶӧ೭ᅿϐΠǴךॺჹܭঁΓޑ، ղᘐǴѸѐуаӝǴԶӸӧޑӝБݤΨԖࡐӭᅿǶӧനதـޑӝБݤύǴЬाё аεठϩࣁٿᅿǺ(1)ԋৎঁΓޑղᘐ(Aggregation of Individual Judgments)Ǵ(2)ԋ ৎঁΓޑख़ॶ(Aggregation of Individual Priorities)Ǵ೭ٿᅿБݤӚԖځҔϐጄൎǴӕ ਔΨԖ٬Ҕϐज़ڋǹ௦Ҕ AIJ ܈ࢂ AIP ޑཀـԋБݤǴࢂ٩Ᏽ،ဂᡏޑԋزഖࢂ ӝӧೀՉ،Ǵ܈ࢂϩණܭӚೀрঁΓϐ،Ƕ ୢڔፓޑၗϩࢂឦܭ AIP ޑཀـԋБݤǴޑୢڔፓதၸլԄ ໆ߄ǴаኧભຯȐ1ǵ2ǵ3ǵ4ǵ5ȑբࣁۓ܄ᑽໆಃȐٯӵǺߚதόӕཀǵӕཀǵද೯ǵ ӕཀǵߚதӕཀȑޑीϩБԄǴӆஒঁձᑽໆ่݀аද೯ѳ֡БԄуаीᆉǴ܌ளډޑѳ ֡ॶջࣁനࡕޑӅӕ่݀ǴԜᅿᑽໆᆶीᆉБԄԖځᙁൂǵБߡޑᓬᗺǶ լԄໆ߄ᆶᇟཀৡձໆ߄ीϩࣣࣁԛׇǵຯኧБԄǴԖځߡճܴዴϐᓬᗺǶ ՠࢂ༤เޣӢڙज़ܭѝૈӧኧঁӣเύϭᒧрঁเਢǴܰॐ٬༤เޣסԔԾρགڙ ԶமॐӣเǹЪόӕ༤เޣᗨᒧ࣬ӕޑᇟཀᜏǴӢᇡޕགڙޑЁࡋόӕǴځໆϯीϩ ࠅόۓ࣬ǶᔈҔլԄໆ߄ޑୢڔፓǴ༤เޣѝૈӧኧঁ٣ӃۓӳޑҞ ύϭᒧрঁเਢǴԖਔॐ٬༤เޣ۹ຎԾρޑჴགڙԶ௦ڗסԔޑӣᔈǴԶЪόӕ ༤เޣᗨᒧ࣬ӕޑᇟཀᜏǴΨӢᇡޕགڙޑЁࡋόӕǴज़ۓ௦ڗமڋ܄ൂಃޑ ᒧǴ۳۳ԋղᘐޑୃৡǶ4
ಃΒക Ў
ᕮਏຑ،ᕉნ۳۳ࢂЬᢀޑǵόёໆϯޑǵόዴۓޑǵဂᡏ،ୖᆶǴࣁΑᗉխ ӧᕮਏຑၸำύౢғୃৡϷԋᐱᘐǴӝӭՏৎаဂᡏ،ޑБԄڗளӅǴࢂᕮ ਏຑၸำύޑЬाԵໆӢનǴҁകஒଞჹᕮਏຑǵဂᡏ،ǵ լᄊࡋໆ߄ϩձу аǶ2.1
ᕮਏຑ
5
πᕮਏᆶ܌ुۓྗ࣬КၨϐΠԶϒаຑۓભǴ܌аԵਡ୷ᘵࢂ٩πޑᕮਏ߄ࣁ ЬǶ٬ҔԜБݤਔǴπ࣬ϕϐ໔ࢂόКၨޑǴதـޑ๊ჹྗԖΟᅿǺቻຑਡݤ ȐTrait-rating ScaleȑǵՉࣁۓӛຑਡݤȐBehaviorally-anchored Rating ScaleȑϷՉࣁᢀჸ ຑਡݤȐBehavior Observation ScaleȑǶ
ȐΒȑ ࣬ჹྗݤȐRelative StandardȑǺ࣬ჹྗࢂଞჹπᕮਏᆶځдπ࣬ϕКၨ ԶຑۓՖΓ߄ၨ٫ǴՖΓ߄ၨৡǴ܌аԵਡ୷ᘵࢂаπϐ໔ޑКၨࣁЬǶ
ȐΟȑ ҞᔕۓݤȐObjective-based ApproachȑǺҞԵຑ៝Ӝࡘက൩ࢂຑޣҔ ۓӳޑҞჹπՉԵຑǴ܌аԵਡ୷ᘵࢂа่݀ᏤӛޑԵຑБݤǶ
6 ဂᡏ،ёаᡣঁձ،ޣϐ໔ཀـՉҬࢬǴӧဂᡏೱុޑϕၸำύόᘐӦׯᡂᆶፓ ঁձޑཀـǴҗဂᡏ໔ޑཀـҬࢬၸำԶׯ๓،่݀ǴԶߚൂપឦܭঁΓཀـޑ ӝᡏǶ εϩޑಔᙃ،ࢂाрঁᡏԵໆޑǴόፕ،ޑၸำࢂϦ໒܈όϦ໒ޑǵ، ጄൎࢂѝज़ܭϣ܈х֖ѦޑǴךॺाӧ،ޑၸำϐύǴԵໆډ،ޑᡏ܄Ǵ ҅җܭ೭ኬঁሡाᡏԵໆޑ่݀Ǵ೯தךॺࡐᜤѐၲډဂᡏӅǴќБय़Ǵाѐ༊ ᕴӚঁ،ԋޑཀـǴΨᡂள֚ᜤӭǶ ௗΠٰϟಏΟᅿதـޑဂᡏ،ޑБݤǺ 1.တΚᐟᕏݤ(Brainstorming)
җAlex Osborn(1938)ӧځբ”How to Think u”ਜύ܌ගрǴځՅࣁတΚᐟᕏݤࣁ ᅿᐟวബཀޑဂᡏ،ኳԄǴ٠Ⴔᓰڻགྷǵ߆མߡًǴୖᆶΓኧа 5-12 Γၨ٫Ǵਔ ໔ΨόەϼߏǴЪЬΓόૈԖҺՖࡰᏤ܈ज़ڋϐقፕǴаխᓸΑ،ޣϐബཀǶ 2.ӜҞဂᡏמೌ(Nominal Group Technique,NGT)
7 ቹៜ 6. ߦᆶޣᆫขӧှ،ୢᚒǴԶ ߚΓيװᔐ 7. ׳Ԗ่״ջၲԋ،ޑག ၗٰྍǺDunham, 1991 3.ቺᅟݤ(Delphi Method)
ቺᅟݤࢂ 1950 ԃжऍ୯ើቺϦљ(Rand Corporation)җDalkey & Halmer et al.ว ीԶٰ(Dalkey & Halmer,1963)ǶၸୢڔፓޑБԄቻ၌ৎཀـǴаڗளৎϐӅӕཀ ـǴ٠аीБݤϒаևǶߐפ⢄ϐفՅǴջ౦ҽη(devil’s advocate)Ǵಔᙃࣁ ᗉխӧဂᡏ،ύǴрΑϿኧᚰᘐϷဂᡏࡘԵϐॄय़բҔǴܭࢂӧಔᙃύीΑঁග ٮόӕᢀᗺǵബཀ܄Бਢǵץղ܄ࡘԵǵࡷᏯݩޑفՅǶᓬᗺࣁёගϲဂᡏ،ϐࠔ፦Ǵ ՠࠅफ़եဂᡏ،ϐೲࡋǴӢແҹϐ۳߇ϷሡၸӭਔВǶ ،ୢᚒࢂৎᏢޣុޔӧࣴزޑፐᚒǴа۳ϐࣴزѝଞჹൂྗ߾ᄊୢᚒࣴ زǴԶӧϞᕉნזೲᡂϐᕉნΠӭǴ،ޣय़ჹޑޑ،ୢᚒࢂፄᚇӭᡂޑޣǴ۳۳ ࢂคݤၮҔൂྗ߾൩ёаှ،ǴԶࢂाஒӕঁ،ୢᚒ܌ឦӭᅿຑྗ߾યΕԵ ໆǴ٠٩Ԝрനޑ،ǴӧϞࢂǶΨӢԜǴӭྗ߾،Бݤ(Multiple Criteria Decision Making ; MCDM)ԋࣁϞத،ޣ٬ҔޑБݤǶ
2.3
լᄊࡋໆ߄
11
ಃΟക ࣴزБݤ
ৎᕮਏᑽໆӝीϩǴനத٬ҔޑБݤࣁᆉೌѳ֡ݤǴฅԶճҔᆉኧѳ֡ݤी ᆉ܌ԖৎޑӅӕᑽໆ่݀Ǵܰڙډཱུᆄॶ(Outlier)ޑቹៜǴჹܭܴዴॶᑽໆၗԶقǴ ёаᙖҗीБݤуаୀෳǴᔈҔӧকନཱུᆄॶޑதـБݤԖྗϯϩኧݤǵHampel identifier ݤǵᄒ׀ѳ֡ॶݤǵWinsorized ѳ֡ॶݤǵ౯ރკϷ Dixon Եᡍݤǹჹܭኳጋॶ ᑽໆၗԶقǴගраኳጋηӝᑽໆȐFuzzy Subsethood MeasureȑБݤǶ
12 კ 3.2! ኳጋॶϐᘜឦڄኧॶ வаΒঁკёа࣮рǴځΒᅿၗ߄ҢБԄޑ܄Ǵܴዴॶࣁ x ӧPA
x ࣁ 1 ਔϐ ॶǴаკ 3.1 ࣁٯǴ၀ॶࣁ 100ǶჹኳጋॶٰᇥǴx ӧPA
x ࣁ 1 ਔϐॶǴаკ 3.2 ࣁٯǴ ၀ॶࣁ 40Ǵՠࢂλܭ 10 کεܭ 65 ਔPA
x ࣁ 0Ǵӧ 10~40 ϐ໔ǴځPA
x ॶᒿϐϲǴ ډ 40 ਔǴPA
x ॶࣁ 1Ǵ40~60 ځPA
x ॶᒿϐΠफ़ډ 0ǹځҗܭܴዴॶࣁኳጋኧϐϯ ޑ܄፦Ƕ
3.2
ኳጋፕϟಏ
ຝЬኞӧϺႣൔਔǴ೯தѝນךॺܴϺчӦྕࢂ18ࡋډ23ࡋ໔Ǵឦܭ ਔӭอኩߘޑϺǴрߐளуҹѦϷឫߘڀǶӧВதғࢲ္Ӹӧࡐӭޑόዴۓ܄ (Uncertainty)ᆶኳጋ܄(Fuzziness)ޑၗǴฅԶךॺᜫཀௗڙኳጋޑၗǶ ኳጋፕࢂࣁΑှ،ჴШࣚύදၹӸӧޑኳጋຝԶวޑߐᏢୢǶԐӧ1920ԃ ᛥનࣁኳጋᡄᒠҥΠᡄᒠ୷ᘵǴࠅؒԖᝩុวǴޔډ1965 ԃऍ୯уԀεᏢ࢙լϩਠ(U. C. Berkeley)ޑ҄ቺ(L. A. Zadah) ௲Ǵӧၗૻᆶڋ(Information and Control)ᏢೌයтǴ ว߄ኳጋӝ(Fuzzy Sets)ޑЎകǴኳጋፕػԶғǶኳጋፕаኳጋӝࣁ୷ᘵǴЬा ϣх֖Αኳጋᡄᒠ(Fuzzy Logics)ǵኳጋ(Fuzzy Inference)ǵኳጋڋ(Fuzzy Control)… ǶኳጋፕᔈҔޑሦୱࡐቶݱǴӵৎسǵᕮਏຑໆǵቹႽձǵᇟق܈ࡰદᒤ… ǶӧKaufmann and Gupta (1988)Ϸ؋ܴғᆶ؋Ҹ౺(2003)ޑࣴزϐύΑჹኳጋፕ ޑ࣬ᜢཷۺǴаΠᘏڗᆶҁࣴزԖᜢϐҽϟಏǺ
(1) Fuzzy SetȐኳጋӝȑ
ኳጋӝځۓကࣁǺзU ࣁፕޑӄᡏჹຝǴᆀࣁፕୱ (Universe of Discourse) ǹ ፕୱύޑঁჹຝǴᆀϡનǴа u ߄ҢǹU ޑঁኳጋηAǴࢂࡰǺჹܭҺཀx ǴU
1
0
13
ࡰۓΑঁჴኧ ua
x
> @
0,1ǴᆀࣁxᗧឦܭAޑำࡋǶջuax ࣁࢀ (Mapping)Ǻ
x :U o
> @
0,1ua
ᆀࣁaޑᗧឦڄኧ (Membership Function) ǶAॶୱ={0,1}ਔǴua
x ိϯԋঁද೯η ޑቻڄኧǴaߡԋঁද೯ηǶኳጋӝޑଯࡋ (Height) ࢂࡰനεޑᗧឦำࡋ (Degree of Membership) Ǵаhgt A ߄ҢǶԿϿԖϡનϐᗧឦำࡋࣁ1 ޑኳጋӝǴᆀࣁ҅ೕϯ (Normalization) ޑኳጋӝǶӧೀჴሞୢᚒਔǴעද೯ӝޑ๊ჹᗧឦᜢ߯уаᘉкǴ ٬ϡનჹӝޑᗧឦᜢ߯ࡋҗӵڗ0܈1ȨߚԜջ۶ȩϐ܄ǴቶԿёаڗൂՏ໔(0,1) ύޑҺཀኧॶǴԶჴۓໆڅฝόዴۓ܄ୢᚒϐኳጋ܄፦Ƕ
(2) Fuzzy Number (ኳጋኧ)
ኳጋኧΏჴኧ (Real Numbers) ޑኳጋη (Fuzzy Subset) ǴԶЪѬࢂж߄ߞᒘ໔ (Confidence Interval) ᢀۺޑᅿᘉкǴ่ӝёૈ܄ϩϐD Нྗ (level D Presumption) ᆶD Нྗߞᒘ໔ϐ܄፦Ƕኳጋኧࣁόᆒዴॶ (Imprecision Number) Ǵᆶᐒፕύϐᒿ ᐒᡂኧ (Random Number) ࢂόӕޑǶኧ Ꮲڀ҅ೕϯЪࣁсӝǴаڀԖࢤ܄ೱុϐ ᗧឦڄኧϐኳጋӝǴᆀϐࣁኳጋኧǴҭջኳጋኧᅈىΠӈచҹǺ
1. с܄ޑኳጋηӝ (Convex Fuzzy Subset)
2. ҅ೕϯޑኳጋηӝ (Normality of A Fuzzy Subset) 3. ࢤೱុ (Piecewise Continvous)
ኳጋኧதҔࣁΟفኳጋኧ(Triangular Fuzzy NumbersǹT.F.N)ᆶఊኳጋኧ (Trapezoidal Fuzzy NumbersǹTr.F.N)Ƕ
16 ᙯඤԋ࣬ᜢޑኳጋኧǶӵ߄3.1܌ҢǶҭёаीБݤၸፓຒ༼ޑᗧឦڄኧ(؋ ᤞǴ1990)Ƕ ߄3.1 Ζᅿኳጋᇟཀᡂኧ߄ ᇟཀЁࡋ 1 2 3 4 5 6 7 8 ᇟཀኧ 2 3 5 5 6 7 8 11 ཱུե Ϩ ࡐե Ϩ Ϩ Ϩ Ϩ Ϩ եԿࡐե Ϩ Ϩ ե Ϩ Ϩ Ϩ Ϩ Ϩ Ϩ Ϩ ัե Ϩ Ϩ Ϩ Ϩ ٤༾ե Ϩ ύ Ϩ Ϩ Ϩ Ϩ Ϩ Ϩ Ϩ ٤༾ଯ Ϩ ัଯ Ϩ Ϩ Ϩ Ϩ ଯ Ϩ Ϩ Ϩ Ϩ Ϩ Ϩ Ϩ Ϩ ଯԿࡐଯ Ϩ Ϩ ࡐଯ Ϩ Ϩ Ϩ Ϩ Ϩ ཱུଯ Ϩ
ϨǺ߄Ңᒧڗޑᇟཀ ၗٰྍǺChen & Hwang(1992)
ҁࣴز௦ҔΟفኳጋኧ֡ϬჄϩᇟཀᡂኧጄൎޑڄኧკǴஒӚቹៜӢનख़ϐख़ा
ࡋаϖঁᇟཀЁࡋٰᑽໆǴӵ߄3.2܌ҢᇟཀЁࡋϐϩթጄൎᆶځჹᔈϐΟفኳጋኧǶ
߄3.2 ኳጋЁࡋᆶ࣬ჹᔈϐᇟཀᡂኧۓက ኳጋЁࡋ
(Intensity of fuzzy scale)
ᇟཀᡂኧϐۓက
17
πڀǶှኳጋϯ٠คൂБݤǴा٬ҔবᅿБݤǴᆄ࣮ୢᚒޑ܄ԶۓǶதҔှኳጋޑ БݤԖΠӈΎᅿǺ
ǵख़Јݤ (Center of Area
Defuzzification
)ځᢀۺ൩ࢂаኳጋӝϐȨύЈॶȩٰж߄ঁኳጋӝǴځीᆉϦԄӵΠǺ F =
¦
¦ ) ( ) ( * ) ( i a i a i x u x u x g g( xi) Ǻჹᗧឦࡋϐঁख़ा܄ෳໆኧ ua (xi) Ǻࣁኳጋӝᗧឦڄኧ F Ǻж߄ኳጋӝϐख़Ј ჹΟفኳጋኧёቪࣁӵΠϦԄ܌ҢǺ F =>
URi LRi
MRi LRi
@
LRi 3 i UR ǺΟفኳጋኧޑज़ॶΒǵЈݤ (Center of Sum
Defuzzification)
Οǵѳ֡നεᗧឦݤ (Mean of Maximal
Defuzzification)
Ѥǵ
ಃঁനεॶ
ݤ(First of Maxima Defuzzification)
ϖǵനࡕঁനεॶݤ(Last of Maxima Defuzzification)
Ϥǵനεॶϐѳ֡ॶှኳጋϯݤ(Middle of Maxima Defuzzification)
ΎǵʳύЈѳ֡ॶှኳጋϯݤ(Center Average Defuzzification)
18 լԄໆ߄ ᇟཀຒ ߚதόᅈཀ όᅈཀ ั༾ᅈཀ ᅈཀ ߚதᅈཀ ჹᔈीϩॶ 1 2 3 4 5 ᇟཀৡձໆ߄ ᇟཀຒ ߚதόᅈཀ ߚதᅈཀ ჹᔈीϩॶ 1 2 3 4 5 6 7 8 9 10 լԄໆ߄ᆶᇟཀৡձໆ߄ीϩࣣࣁԛׇǵຯኧБԄǴԖځߡճܴዴϐᓬᗺǶ ՠࢂ༤เޣӢڙज़ܭѝૈӧኧঁӣเύϭᒧрঁเਢǴܰॐ٬༤เޣסԔԾρགڙ ԶமॐӣเǹЪόӕ༤เޣᗨᒧ࣬ӕޑᇟཀᜏǴӢᇡޕགڙޑЁࡋόӕǴځໆϯीϩ ࠅόۓ࣬ǶӢԜǴ࣬ᜢЎࡰрໆ߄ޑीϩۘӸԖऩυલᗺ (ֆ࢙݅Ǵ҇83)Ǻ () ΓᜪޑࡘԵᆶՉࣁҁٰкᅈኳጋၸำǴୢڔதၸࡋޑှញǶ (Β) ࣁ߆ӝኧӷޑᆒዴाǴჴᡍၗதԖၸࡋ٬Ҕϐ༮Ƕ (Ο) ࣁᙁϯ܈फ़եኧᏢኳԄޑፄᚇ܄Ǵࠅஒჴሞރݩ໔ϐ࣬ᜢᆶᄊ፦۹ౣΖ ᔈҔլԄໆ߄ޑୢڔፓǴ༤เޣѝૈӧኧঁ٣ӃۓӳޑҞύϭᒧр ঁเਢǴԖਔॐ٬༤เޣ۹ຎԾρޑჴགڙԶ௦ڗסԔޑӣᔈǴԶЪόӕ༤เޣᗨᒧ ࣬ӕޑᇟཀᜏǴΨӢᇡޕགڙޑЁࡋόӕǴज़ۓ௦ڗமڋ܄ൂಃޑᒧǴ۳۳ ԋղᘐޑୃৡǶ
ࣁှ،ୢڔፓໆ߄ޑલᗺǴճҔΟفኳጋኧȐT.F.N.: Triangular Fuzzy Numberȑ ܈ఊኳጋኧȐTr.F.N.: Trapezoidal Fuzzy Numberȑа߄ҢᑽໆᇟཀຒϐᗧឦำࡋǴа
19
3.4
ኳጋηӝᑽໆБݤ
FormanᆶPeniwati (1998) ᇡࣁǴӧՉဂᡏ،ਔǴЬाࢂၸ(1)۶Ԝ໔ޑፕᕇ ளӅǹ(2)߄ၲрঁΓޑୃӳ೭ٿᅿБԄǶӧ೭ᅿϐΠǴჹܭঁΓޑ،ղᘐǴѸ ѐуа༼ǴԶӸӧޑ༼БݤΨԖࡐӭᅿǶӧനதـޑ༼БݤύǴЬाёаεठϩ ࣁٿᅿǺ(1)ԋৎঁΓޑղᘐ (Aggregation of individual judgments, AIJ)Ǻឦܭۓ܄،
(2)ԋৎঁΓޑख़ॶ (Aggregation of individual priorities, AIP)Ǻឦܭۓໆ،
3.4.1 ኳጋηӝ ޑӝፕ(Set Theory)ύǴऩӝAύޑঁϡનឦܭӝBǴ߾ᆀAࢂB ޑηǴҭё᠐բAх֖ܭBǴ٠аA BϐǶ ኳጋηӝӧኳጋӝࢂࡐख़ाޑཷۺǶZadehჹኳጋӝޑȨх֖ȩۓကǴ
x mA ǴmB
x ϩձࣁAǴ BޑᗧឦڄኧЪAǴBࣁۓကܭX ޑኳጋӝǴჹ܌Ԗឦܭ X ޑx ԶقѝԖӧmA
x dmB
x ਔǴ߾ᆀኳጋӝAх֖ܭኳጋӝBύ(A B)ǴЪำ ࡋϟܭ0ډ1ϐ໔Ƕ Kosko߾ЬmA
x dmB
x όԄѝӧࢌ٤xόᅈىਔךॺϝёаԵቾኳጋӝA ࢂኳጋӝBޑηӝޑำࡋǴаS (A,B)߄ҢǴᆀϐࣁኳጋηӝᑽໆǶKoskoۓကӵΠǺ
° ¯ ° ® z
¦
¦
0 0 1 deg , A A M B A M x m x m x m A B A ree B A S X x A X x A B20
Young ଞჹZadehჹηӝޑᑽໆޑۓကǵKosko ჹηӝޑᑽໆᆶ⪖ϐ໔ᜢᖄޑ ǴаϷኳጋӝύх֖ਔޑ࣬ჹᔈᜢ߯բࣁηӝޑᑽໆޑచҹǴගрΟঁηӝӝޑ ᑽໆޑϦǶ٠ೱ่ኳጋ⪖ǵᐒکኳጋᡄᒠǶ
FanǴXie کPei ჹηӝޑᑽໆගрཥޑۓကǴаޜӝᆶӹӝޑᜢ߯Ϸኳጋӝ х֖ਔޑᜢ߯ǴुۓηӝޑᑽໆޑϦǶ٠ЪӧԜϦΠޑηࡋޑ٤ၮᆉࢂց ڀԖ࠾ഈ܄ǶനࡕӆၮҔܭᆫᜪБݤޑຑሽǶ ηӝޑᑽໆޑԄ٠คྗኬԄǴଞჹٿӝх֖ޑᜢ߯Ǵ٩ᏵόӕޑሡाǴёа ۓрόӕޑԄрٰǶࣁΑዴۓ܌ۓޑԄࢂӝޑǴ಄ӝϦࢂ୷ҁाǶԶ܌ளрޑ ኧॶёаຎࣁࢂᅿၗԄޑᙯඤǴஒٿঁӝϐ໔ޑх֖ᜢ߯ᙯᡂԋϟܭȘ0,1șޑໆ ϯኧॶǶ
3.4.2 ኳጋηӝᑽໆ༼ݤ(Subsethood Aggregation Method, SbAM)
ҁࣴزଞჹKosko(1986)ගрٿኳጋӝϐҬޑᢀᗺ܌ۓကޑηӝᑽໆࣁᔈҔޑ ჹຝǶவKoskoޑ(1986)ۓကёޕǴٿՏৎཀـҬ࣬ӕਔǴৎޑཀـጄൎຫεޣǴ ܌ளޑளηӝޑำࡋ൩ຫλǴϸϐৎޑཀـጄൎຫλޣǴ܌ளޑளηӝޑำࡋ ൩ຫεǴόӕܭZwick et al(1987)ගр࣬՟ำࡋໆෳǴόፕৎޑཀـጄൎε܈λǴࠅԖ ࣬ӕޑ࣬՟܄ीॶǶЪёճҔኳጋηӝᑽໆޑᢀۺǴஒৎཀـ༼่݀ᆶϖಃ(ࡐ όӕཀǴόӕཀǴۘёӕཀǴӕཀǴߚதӕཀ)ำࡋϰଛ(Match Degree)Ǵёளډӄᡏ ৎϐᇟཀղۓǶ
ҁࣴزගрኳጋηӝᑽໆ༼ݤ(Subsethood Aggregation Method, SbAM)ޑᏹբำ ׇΠǺ 1. ीᆉҺٿՏৎ໔ϐኳጋηӝ࣬՟ำࡋ Ǻ ஒৎঁձϐኳጋຑॶՉٿٿଛჹǴЪр،ޣ۶Ԝ໔ϐኳጋηӝ࣬՟ำࡋी ॶǶٿኳጋຑॶϐኳጋηӝ࣬՟ำࡋीᆉϦԄӵΠǺ ኳጋηӝ࣬՟ำࡋीॶޑཀကӧܭǴٿՏৎϐ໔ޑཀـख़᠄ϩ࣬ӕਔǴ ৎཀـጄൎຫεǴ߾ኳጋηӝ࣬՟ำࡋीॶຫλǴϸϐǴৎཀـጄൎຫλǴ߾ኳጋ ηӝ࣬՟ำࡋीॶຫεǶ
2. ࡌᄬᇡӕંତ(Agreement Matrix, AM)Ǻ
21
3. ीᆉՏৎޑѳ֡ᇡӕำࡋ( A E i) Ǻ ճҔᡯΒᇡӕંତǴीᆉՏৎE i n i , Γ1,2,..., Ǵᆶځдৎޑѳ֡ᇡӕำࡋ(Average Agreement of Expert)ǴीᆉϦԄӵΠǺ
4. ीᆉՏৎޑ࣬ჹᇡӕำࡋ(Relative Agreement Degree, RAD)Ǻ
ीᆉрৎi E ޑ࣬ჹᇡӕำࡋǴջᆀࣁ҅ೕϯǴаi RAD ߄ҢǴीᆉϦԄӵΠǺ
5. ीᆉՏৎޑӅำࡋ߯ኧ(Consensus Degree Coefficient, CDC)Ǻ
22
ಃѤക ਢٯᔈҔ
Linguistic variables can be used as the expression to match with natural language, term and its related modifier (hedge) formed completed terms for full descriptions on the real case scenario (Yen and Langari1999). Fuzzy numbers, especially Triangular Fuzzy Number (T.F.N.), are adopted for imprecise or vague judgments, and their arithmetic calculation were provided by Kaufmann & Gupta (1991) as well as by Zimmermann (1991). Likert’s type questionnaire is the common tool used for collection of individual judgment, and the calculated arithmetic average is assumed as the summarized results of investigated group generally. We will demonstrate an empirical example in details as followings.
Table 4-1 shows the linguistic terms and their corresponding T.F.N. for five criteria rating, they are (1, 1, 2) for Very Low(VL), (1, 2, 3) for Low(L), (2, 3, 4) for Medium(M), (3, 4, 5) for High(H), and (4, 5, 5) for Very High(VH) in respective. Figure 4-1 lists T.F.N. membership diagrams for these five criteria rating.
Table 4-1: Linguistic terms and their T.F.N. for five criteria rating Linguistic termsCorresponding
fuzzy number Very Low (VL) ( 1, 1 , 2 ) Low (L) ( 1, 2 , 3 ) Medium (M) ( 2, 3 , 4 ) High (H) ( 3, 4 , 5 ) Very High (VH) ( 4, 5 , 5 )
Figure 4-1: Membership diagram for five criteria rating
23
paired fuzzy subsethood measure are calculated, where Sii = 1, S12 = 0.5, S21 = 0.25 (
50 . 0 ~ ~ ~ ~ , ~ 1 2 1 2 1 R R R R R S
~ 0.25 ~ ~ ~ , ~ 2 2 1 1 2 R R R R R
S ) and etc.. A 5x5 agreement matrix (AM) is
constructed and listed in Table 4-2.
Table 4-2: Agreement matrix for five criteria rating Criteria Rating VL L M H VH VL 1 .5 0 0 0 L .25 1 .25 0 0 M 0 .25 1 .25 0 H 0 0 .25 1 .25 VH 0 0 0 .5 1
The general formula for each summarized degree of subsethood measure Sij is listed in Table 4-3. For example, every questionnaire in group of Very Low(VL), would get s11 = (n1 - 1 ) and s12 = (.5 * n2) , then the summarized degree of subsethood measure (multiply n1) S11 = n1 * (n1 - 1 ) and S12 = n1 * (.5 * n2). If the number of questionnaire corrected is 50, and the number of questionnaire corresponding to each criteria rating are n1=2 for Very Low(VL), n2=5 for Low(L), n3=14 for Medium(M), n4=25 for High(H), and n5=4 for Very High(VH) in respective. Table 4-4 list the calculation results while setting n1=2, n2=5, n3=14, n4=25 and n5=4 to corresponding contents of table 4-3. Then sum of each row, listed in column “Sum”, can be got easily, and the criteria weighting derived from SbAM method, listed in column “SbAM Wt.”, can be calculated via. individual row-sum divided by total row-sum.
Table 4-3: Agreement matrix for five criteria rating with corresponding frequency Term (Fre.) VL (n1) L (n2) M (n3) H (n4) VH (n5) VL (n1) n1 * (n1 - 1 ) n1 * (.5 * n2) 0 0 0 L (n2) n2 * (.25 * n1) n2 * (n2 - 1 ) n2 * (.25 * n3) 0 0 M (n3) 0 n3 * (.25 * n2) n3 * (n3 - 1 ) n3 * (.25 * n4) 0 H (n4) 0 0 n4 * (.25 * n3) n4 * (n4 - 1 ) n4 * (.25 * n5) VH (n5) 0 0 0 n5 * (.5 * n4) n5 * (n5 - 1 )
Table 4-4 : Example for criteria weighting calculation (SbAM vs. Equal Wt.) Term (Fre.) VL (2) L (5) M (14) H (25) VH (4) Sum SbAM Wt. Equal Wt.
VL (2) 2 5 0 0 0 7 .006 .040
L (5) 2.5 20 17.5 0 0 40 .036 .100 M (14) 0 17.5 182 87.5 0 297 .266 .280 H (25) 0 0 87.5 600 25 712.5 .637 .500
24
25
ಃϖക ่ፕ
Methodologies for weights setting of DM under group decision making have been discussed in previous sections. We provide three sets of test data, each one contains three measurements in forms of T.F.N. arranged by three experts in respective. Table 5-1 lists these test data, weights setting via various approaches, and aggregated fuzzy measurement. R~1~R~3 represents individual
fuzzy measurement, S~ represents aggregated fuzzy measurement, data in the same row
corresponding to R~1~ 3 ~
R represent Weighs Setting via assigned approach. Each decision maker’s
weighting is set equally and all measurements are aggregated via arithmetic average in traditional performance evaluation model. Approach of arithmetic average neglects mutual interactions among DM, but the others include SAM, SbAM, LSDM, DLSM and OAM are all approaches of mutual interactions.
Both SAM and SbAM are based on degree of “superposition” for each paired measurements. If “span” of all measurements are equal, then same conclusions will be got for both SAM and SbAM. Test data set 1 listed in table 5-1 demonstrates the conclusion. According to test data set 2, if “span” of a certain measurements is varied, e.g. DM 2 revised its measurement from (2, 3, 4) to (1, 3, 5), and assumed the others were left unchanged. Based on test data set 2, we observed that results referred to SAM kept unchanged, while referred to SbAM, weighting of DM 2 has been reduced from 0.5 to 0.333 due to its measurement with wide “span” (less precise). It’s just fit to the practical conclusion “the wider the decision range is, the smaller the decision effect should be”.
26
Continue to review on test data set 3, measurement of DM 3 has no interaction to both DM1 and DM2. Based on degree of “superposition”, there is no doubt about the fact that weighting of DM3 is set to zero. If weighting of a DM is set to zero, there is no effect on final conclusion, which can be looked as the filter to outliers. Both SAM and SbAM support functionality to sift normal data from outliers. Let’s review test data set 3 in deep, the measurement range of DM1 is less than that of DM2, in other words, the judgment from DM1 is more precise than that of DM2. It is obvious that weighting of DM1 would be larger than that of DM2. SbAM made it sense, but SAM seemed to have a bias. The bias existed in the instance that the one with more precise judgment has same effect to that with loose.
The decision weighting of each DM is set equally in traditional performance evaluation model, and arithmetic average is applied as the method for group data aggregation. Actually it is not fair and not reasonable, especially in case of outliers are existed. Once bias has been caused by outliers, it is far apart from the actual group consensus. Even then the calculation results will be varied from the various methods applied, but all methods discussed are all dependent on group interaction. One word to say, decision weighting of each DM is impacted by total decision group.
27
ୖԵЎ
1. ЦЎߪǴᇡFuzzyǴӄࣽמკਜϦљǴ2001Ƕ 2. ؋ܴғǵ؋Ҹ౺Ǵ”ኳጋቫભϩݤᔈҔܭIC ౢࡹᒧڗϐࣴز”Ǵ୯ҥύξεᏢϦ Ӆ٣୍ᆅࣴز܌ᅺγፕЎǴ2003Ƕ 3. ࢫਁബǴЦ୯ܴǵ៝דᇻǴ”ဂᡏ،ΠኳጋᕮਏຑኳԄϐࡌᄬᆶᔈҔ”ǴϡඵπᏢ ଣππำࣴز܌റγፕЎǴ1996Ƕ 4. ࢫਁബǵጰίǴȹڀӣ㎸фૈϐኳጋᕮਏຑၗԏسɡӧᆛሞᆛၡϐी ᆶᔈҔȹǴՉࡹଣ୯ࣽ(NSC -87-2213-E-159-008)Ǵ1997Ƕ 5. ༡ӂ፵ǵࢫਁബǴ”ဂᡏ،ᕮਏᑽໆኳԄӧނࢬύЈբϐᔈҔ-ܴዴॶǵ໔ ॶᆶኳጋॶϐၗԏᆶϩ”ǴܴཥࣽמεᏢπำᆅࣴز܌ᅺγፕЎǴ2006Ƕ 6. ୯ԽǵҺǴᇳ۸፣ǵֻדǵྕڷᘶጓঅǴኳጋፕ୷ᘵᆶᔈҔǴཥЎ٧໒ วрހިҽԖज़ϦљǴ2007Ƕ 7. ླྀےϘǴኳጋਡߥۓය䘔ᓀϐǴεᏢኧࣽᏢࣴز܌ᅺγፕЎǴ2002Ƕ 8. ᖙᑯ߭ǵࢫਁബǴᔈҔৎဂᡏ،БݤࡌᄬނࢬύЈঊᓯϐᕮਏຑࢎᄬǴܴ ཥࣽמεᏢπำᆅࣴز܌ᅺγᏢՏፕЎǴ2005Ƕ 9. ዐྤڻǵࢫਁബǴၗԋၮᆉБݤϐϷځӧᕮਏຑسϐᔈҔа௲ৣԾך ຑໆࣁٯǴܴཥࣽמεᏢπำᆅࣴز܌ᅺγᏢՏፕЎǴ2007Ƕ 10. ֆދᐝǵࢫਁബǴኳጋηӝᑽໆӧᡏ،Πྗ߾ख़ۓᆶᕮਏᑽໆϐᔈҔ аᏢғჹԴৣϐ௲ᏢຑໆࣁٯǴܴཥࣽמεᏢπำᆅࣴز܌ᅺγᏢՏፕЎǴ2009Ƕ 11. ᐽ۸ǵէഩԋǵ৪ԓǵᒲӇᗶǵণϘਏुǴಔᙃՉࣁᏢɡፕᆶჴ୍Ǵϖࠄკ ਜрހϦљǴ2000Ƕ12. Bart KoskoǴ݅୷ᑫǴኳጋࡘԵ (Fuzzy Thinking)ǴӄࣽמკਜϦљǴ1994Ƕ
13. Chua-Chin Wang, Hon-Son Don, A modified measure for fuzzy subsethood, Information Sciences, Volume 79, Issues 3-4, July 1994, Pages 223-232
14. Dennis, A. R., Nunamaker, J.R. and Vogel, D.R., “A Comparison of Laboratory and Field Research in the Study of Electronic Meeting System.” Journal of Management Information System, Vol. 7, No.3, pp.107-135, 1991.
15. Delbecq, A. L., Van de Ven, A. H. and Gustafson, D. H. “Group Technique for Program Planning, a Guide to Norminal Group Technique and Delphi Process.” Scott Foreman, USA, 1975
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