Received July 7 2012, Revised August 29 2012, Accepted April 4 2013
Copyright ⵑ 2013 by the Korean Society of Civil Engineers
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0)
ǣǣȀȀǤǤȀͳͲǤͳʹͷʹȀ ǤʹͲͳ͵Ǥ͵͵Ǥ͵Ǥͻͳ Ǥ ǤǤ
Ḛ≂⡢㡶#Ɱ⛞⟚Ⳃ#ቮⷓⴂ#Ⳃ㬚#Ix}}|#ᢢᏮ⺾#ⴖ♪ቮⷓᏮ≓ⴖ#Ⱨ
ࣲ֜ ȵ୨ଠন
Bong Gu Han*, Eun Sung Chung**
Application of Fuzzy Multi-criteria Decision Making Techniques for Robust Prioritization
ABSTRACT
This study presents the feasibility of fuzzy multi-criteria decision making (MCDM) techniques for the robust prioritization of projects.
It is applied to water resources planning problem. Results from weighted sum method (WSM), analytic hierarchy process (AHP), revised analytic hierarchy process (R-AHP), and TOPSIS are compared with those from Fuzzy WSM, Fuzzy, AHP, Fuzzy R-AHP, and Fuzzy TOPSIS. For the calculation, all weights on criteria and the normalized data were obtained from the same investigation.
As a result, the rankings from four MCDM techniques are slightly different while those from fuzzy MCDM show the comparatively consistent ranking. Therefore, it is desirable to use fuzzy MCDM technique when MCDM is used for the prioritization problem, since fuzzy MCDM can include the uncertain variability of input data and weighting values on criteria.
Key words : Fuzzy multi-criteria decision making (MCDM) technique, Triangular fuzzy number, Robust prioritization, Water resource planning
Ⅹಾ
ᅙᩑǍ۵ಽქᜅ✙ᬑᖁᙽ᭥đᱶᮥ᭥⦽⟝ḡ݅ʑᵡ᮹ᔍđᱶʑჶ᮹┡ݚᖒᮥᙹᯱᬱĥ⫮ᙹพྙᱽᨱᱢᬊ⦹ᩍᱽ⦹ᩡ݅. ᷪᯝၹᱢᯙ݅
ʑᵡ᮹ᔍđᱶʑჶᯙaᵲ⧊ĥჶ, ĥ⊖⪵ᇥᕾŝᱶ, ᙹᱶĥ⊖⪵ᇥᕾŝᱶ, TOPSIS ႊჶŝ⟝ḡaᵲ⧊ĥჶ, ⟝ḡĥ⊖⪵ᇥᕾŝᱶ, ⟝ḡᙹᱶĥ
⊖⪵ᇥᕾŝᱶ, ⟝ḡTOPSIS ႊჶᮥᔍᬊ⦹ᩍđŝෝእƱ⦹ᩡ݅. ᯕভᔍᬊࡽb⠪aʑᵡᄥᯱഭ۵࠺ᯝ⦹í⢽ᵡ⪵ࡹᨩᮝ໑baᵲ⊹ࠥ࠺
ᯝ⦽ႊჶᮝಽđᱶࡹᨩ݅. ᇥᕾđŝ݅ʑᵡ᮹ᔍđᱶႊჶᨱ᳑ɩᦊ݅ෙᙽ᭥aࠥ⇽ࡹᨩᮝӹ, ⟝ḡ݅ʑᵡ᮹ᔍđᱶʑჶᮥᔍᬊ⧁Ğᬑ
ᔍᨦॅ᮹ᙽ᭥ᄡ࠺ᖒᯕ⟝ḡෝᔍᬊ⦹ḡᦫᮥভᅕ݅Ⓧḡᦫᦥᅕ݅ᯝšࡽᙽ᭥ෝᮁࠥ⦹ᩡ݅. ᕽᔍᨦ᮹ᬑᖁᙽ᭥ෝđᱶ⦹۵ྙᱽᨱᕽ
ᯱഭ᪡aᵲ⊹᮹ᇩ⪶ᝅᖒᮥŁಅ⧁ᙹᯩ۵⟝ḡ݅ʑᵡ᮹ᔍđᱶʑჶᮥ⪽ᬊ⧕ᕽႊჶ᮹ᄡ⪵ಽᯙ⦽ᙽ᭥᮹ᄡ࠺ᖒᮥ↽ᗭ⪵⧕ᕽಽქᜅ✙
ᙽ᭥ෝđᱶ⦹۵äᯕᅕ݅⬉ŝᱢᯕ݅.
áᔪᨕ ⟝ḡ݅ʑᵡ᮹ᔍđᱶʑჶ, ᔝb⩶⟝ḡᚌᯱ, ಽქᜅ✙ᬑᖁᙽ᭥đᱶ, ᙹᯱᬱĥ⫮
1. ᕽು
1.1 ֜ଭࢼլࢫࡧୡ
݅ʑᵡ᮹ᔍđᱶ(Multi-Criteria Decision Making, MCDM) ᇥ۵ ↽ɝ40֥e ḡᗮᱢᮝಽၽᱥࡹᨕ᪵ᮝ໑ ᙹᯱᬱᇥᩎ
սėॡ
1990֥ݡ ᯕ⬥ MCDM᮹ ᱢᬊᨱ ݡ⧕ Йᵡ⯩ ᩑǍࡹᨕ ᪵݅.
݅ʑᵡ ᮹ᔍđᱶʑჶᮡ ݅༊ᱢ ᮹ᔍđᱶ༉⩶(multi-objective decision making, MODM)ŝ݅ᗮᖒ᮹ᔍđᱶ༉⩶(Multi-Attribute Decision Making, MADM)ᮝಽǍᇥࢁᙹᯩ݅(Hwang and Yoon, 1981). MODMᮡᙹ⦺ᱢ༉⩶ᮥ☁ݡಽᩑᗮᱢᯙ(continuous)
⧕᮹Ŗeᮥᦥԕ۵ࠥǍಽᕽ↽ᱢ⧕(optimal solution)ෝᦥ ԕ۵ߑᮁᬊ⦹݅. ၹ໕ᨱᯕᔑ(discrete) ᮹ᔍđᱶྙᱽᨱᔍᬊࡹ۵
MADMᮡ ᮁ⦽}᮹ ݡᦩᯕ ᳕ᰍ⦹ʑ ভྙᨱ ↽ᱢ⧕ෝ ḡ۵
ᦫḡอฯᮡݡᦩॅ᮹ᬑᖁᙽ᭥ෝđᱶ⦹۵ߑᔍᬊࡽ݅. ᷪ, Łಅ
⦽ݡᦩŝ❱݉ʑᵡᨱݡ⧕aᰆᬑᖁᙽ᭥a׳ᮡݡᦩॅᮥᱽ⦹
ʑভྙᨱ⩥ᝅᨱᕽฯᮡྙᱽෝ⧕đ⧁ᙹᯩ݅. MCDMᮡ
MADMŝᨥĊ⦽₉ᯕaᯩᮭᨱࠥᇩǍ⦹Łݡᇡᇥ᮹MCDM
ྙᱽॅᯕMADMᮝಽ⧕đࡹʑভྙᨱMCDM ᬊᨕ۵MADM
ྙᱽᨱࠥ⮵⯩ᔍᬊࡹŁᯩ݅. ᕽᅙᩑǍᨱᕽ۵MADM ݡ ᝁ ᅕ݅ ᯝၹᱢᯙ ᬊᨕᯙ MCDMᮥ ᔍᬊ⦹ʑಽ ⦽݅.
ǎԕ᮹ĞᬑMCDM ʑჶᮥᙹᯱᬱĥ⫮ᇥᨱᔍᬊ⦽ᩑǍ ۵Ko ॒(1992)ᯕݱᬕᩢᨱCompromise Programming(CP)
ᮥ ᱢᬊ⦹ʑ ᯲⦽ ᯕ⬥ ḡᗮᱢᮝಽ ᱢᬊࡹᨕ ᪵݅. Lee ॒ (2005)ᮡ⊹ᙹᔍᨦ᮹ĥ⫮MCDM ʑჶᵲ⦹ӹᯙĥ⊖⪵ᇥᕾŝ ᱶ(Analytic Hierarchy Process, AHP)ŝ݅ᗮᖒ⬉ᬊᯕು(multi- attribute utility theory, MAUT)ᮥᯕᬊ⦹ᩍ⊹ᙹݡᦩॅ᮹ᬑᖁᙽ
᭥ෝ ᱽ⦹ᩡŁ, Kim ॒(2006)ᮡ ݱ ᔍᨦ᮹ ⚍ᯱᬑᖁᙽ᭥ෝ
đᱶ⦹ʑ᭥⧕ELECTRE I, II᪡Compromise Programmingᮥ
ᔍᬊ⦹ᩡ݅. Lim and Lee (2009)۵Compromise Programmingŝ GIS ʑᚁᮥ đ⧊⦹ᩍ ⊹ᙹ ᱡq ᖅᨱ ݡ⦽ ᬑᖁᙽ᭥ෝ ᇥᕾ
⦽ၵᯩᮝ໑Chung ॒(2011)ᮡᮁᩎ⪹Ğ}ᖁᔍᨦॅ᮹ᬑᖁᙽ
᭥ෝᱽ⦹ʑ᭥⧕ᩑᗮᮁ⇽༉᮹༉⩶ᯙSWMM ༉⩶ᮥᯕᬊ⦹
ᩍᔍᨦ᮹⬉ŝᇥᕾᮥᝅ⧪⦹Łᔍ⫭ᱢ, Ğᱽᱢ, Ŗ⦺ᱢʑᵡॅᮥ
Łಅ⦹ᩍ ݅᧲⦽ ݅ʑᵡ ᮹ᔍđᱶʑჶᮥ ᔍᬊ⦹ᩡ݅.
ǎ᮹ĞᬑRaju ॒(2000)ᮡྜྷšญӹญ᪅ᨱݡ⦽MCDM
⠪aෝᙹ⧪⦹ʑ᭥⧕PROMETHEE II, ELECTRE III, ELECTRE IV, Compromise Programming ॒ᮥᔍᬊ⦽ၵᯩŁ, Ganoulis (2003)۵ELECTRE III, ELECTRE IVෝᔍᬊ⦹ᩍ⦹ᙹญᙹ
ᰍᯕᬊᨱݡ⦽ᱥఖᮥ⠪a⦹ᩡŁSrdjevic ॒(2004)ᮡTOPSIS
ႊჶᮥᔍᬊ⦹ᩍྜྷšญӹญ᪅ॅᮥ⠪a⦽ၵᯩ݅. Elshorbagy (2006)۵ELECTRE II᪡Additive Value ⧉ᙹෝᯕᬊ⧕ᕽᮁᩎ
šญ⥥ಽəఉ᮹⬉ŝෝᇥᕾ⦹ᩡŁLevy ॒(2007)ᮡAHPෝ
ᯕᬊ⦹ᩍ⪮ᙹ᭥⨹ࠥᱡqᮥ᭥⦽᮹ᔍđᱶḡᬱᜅ▽ᮥǍ⇶⦹
ᩡŁZardari ॒(2010)ᮡELECTRE ႊჶᮥᯕᬊ⦹ᩍᨦᬊᙹ
⧁ݚᮥ᭥⦽᮹ᔍđᱶᮥᙹ⧪⦹ᩡ݅. ᯕ౨ॐǎԕᐱᦥܩǎᨱ ᕽࠥ↽ɝMCDM ʑჶᮥᱢᬊ⦹ᩍ݅᧲⦽ᇥᨱᕽŲჵ᭥⦹í
ᔍᬊࡹŁ ᯩ݅.
MCDM ʑჶᨱᕽᔍᬊࡹŁᯩ۵aᵲ⊹ӹ⠪a⊹ᨱݡ⦽ᇩ⪶
ᝅᖒᯕԕᰍࡹŁᯩʑভྙᨱ↽ɝᨱ۵⟝ḡᯕುᵲFuzzy ᚌᯱ᪡
MCDMʑჶॅᮥđ⧊⦹ᩍᔍᬊ⦽ᔍಡaኩჩ⧕ḡŁᯩ݅. Raj and Kumar(1998)۵⟝ḡᚌᯱ}ֱᮥᯕᬊ⦹ᩍᮁᩎĥ⫮ᙹพᨱ
MCDM ʑჶᮥ ᔍᬊ⦹ᩍ ᔍᨦ᮹ ᬑᖁᙽ᭥ෝ ᱽ⦽ ၵ ᯩŁ, Gupta ॒(2000)ᮡšĥᬊᙹŖɪĥ⫮ᙹพᮥ᭥⧕᯲ྜྷ᮹᳦ඹ
ෝᖁ┾⦹۵MCDM ྙᱽᨱ⟝ḡᖁ⩶ĥ⫮ჶᮥᔍᬊ⦽ၵᯩ݅.
Hajkowicz and Collins(2007)۵ྜྷšญᩑǍᨱᱢᬊࡽฯᮡ᮹ᔍ đᱶʑჶॅᮥ᳑ᔍ⦹ᩡŁəđŝbḡ⢽ॅ᮹᯦ಆᯱഭ᪡aᵲ⊹
᮹ᇩ⪶ᝅᖒᮥ⧕ᗭ⦹ʑ᭥⧕MCDMᨱ⟝ḡ}ֱᮥđ⧊⦹ᩡᮝ໑
✚⯩TOPSIS ʑჶᯕaᰆฯᯕᔍᬊࡹᨩ݅ŁᅕŁ⦽ၵᯩ݅.
Ashtian ॒(2009)ᮡḡ⢽᮹aᵲ⊹ෝđᱶ⧁ভၽᔾ⦹۵ᇩ⪶ᝅᖒ
ᮥ⧕ᗭ⦹ʑ᭥⧕Ǎesᮥᯕᬊ⦽Fuzzy TOPSIS ༉⩶ᮥᱽᦩ⦽
ၵᯩ݅. Alipour ॒(2010)ᮡ≉ᙹḡᱱᮥᖁ┾⦹ʑ᭥⧕݅ᖐ}
᮹⬥ᅕḡෝݡᔢᮝಽ8}᮹ᖁ┾ʑᵡᨱݡ⧕Fuzzy MCDM ʑ ჶᮥᱢᬊ⦽ၵᯩŁ, Afshar ॒(2011)ŝKrohling and Campanharo (2011)۵Fuzzy TOPSIS ႊჶᮥᯕᬊ⦹ᩍ↽ᱢ᭥⊹ᖁᱶྙᱽ᪡
ݱᬕᩢႊᦩᙹพྙᱽෝᱲɝ⦹ᩡŁKaya and Kahraman(2011)
ᮡᚓšญෝ᭥⦽᮹ᔍđᱶᮥ᭥⧕VIKOR ႊჶŝAHP ႊჶᮥ
đ⧊⦽Fuzzy ʑჶᮥᯕᬊ⦹ᩡ݅. SoltanPanah ॒(2011)ᮡʑ᳕
᮹MCDMᮡᇩ⪶ᝅᖒྙᱽෝ⧕đ⧁ᙹᨧᮝ໑MCDMᨱ⟝ḡ
ᯕುᮥđ⧊⧉ᮝಽ៉᳡ᱶ⪶⦽đŝෝᮥᙹᯩ݅Ł⦹ᩡ
Ł ݡ⩶Ʊపॅ᮹ ≉᧞ᖒ ḡᙹෝ ᔑᱶ⦹ʑ᭥⧕ Fuzzy TOPSIS
ෝᱢᬊ⦽ၵᯩ݅. Farajzadeh ॒(2011)ᮡḡḥᨱݡ⦽≉᧞ᖒ
ḡᙹෝᔑᱶ⦹۵ߑᖁᱶࡽḡ⢽ॅ᮹ᇩ⪶ᝅᖒ ভྙᨱ⟝ḡᙹෝ
đ⧊⦽Fuzzy TOPSIS ༉ߙᮥ}ၽ⦽ၵᯩ݅. Yazdani ॒(2012)
ᮡᵲ⦽ᔍ⫭ʑၹᖅ᮹≉᧞ᖒḡᙹෝᔑᱶ⦹۵ߑྙᱽᯱℕ aᅖᰂ⦹ŁŁᮁ᮹ᇩ⪶ᝅᖒভྙᨱbʑᵡ᮹aᵲ⊹ෝᱶ⦹۵ߑ
ᯩᨕ Fuzzy TOPSISෝ ᔍᬊ⦽ ၵ ᯩ݅.
ǎԕݡᇡᇥ᮹ᩑǍᨱᕽ۵ᗭᙹ᮹ᯝၹᱢᯙMCDM ʑჶॅᮥ
ᱢᬊ⧕ᕽࠥ⇽⦽đŝෝᱽ⦽ᩑǍaݡᇡᇥᯕḡอᯕౕĞᬑ
đŝᨱݡ⦽ᇩ⪶ᝅᖒᯕๅᬑ׳݅. ✚⯩ᱢᬊࡽʑჶॅᄥಽ݅ෙ
đŝaᮁࠥࢁᙹᯩᮝအಽᱢᱩ⦽MCDM ʑჶ᮹đᱶᮡᛞḡ
ᦫᮡྙᱽᯕ݅. ᕽᅙᩑǍᨱᕽ۵ǎԕᨱᕽᱢᬊ⦽ၵᯩ۵
4}᮹MCDM ႊჶŝ↽ɝฯᯕᱢᬊࡹŁᯩ۵⟝ḡaᵲ⧊ĥჶ,
⟝ḡ ĥ⊖⪵ᇥᕾʑჶ, ⟝ḡ ᙹᱶĥ⊖⪵ᇥᕾʑჶ, ⟝ḡ TOPSIS ʑჶᮥᱢᬊ⧕ᕽᙽ᭥đŝෝእƱ⦹ᩡ݅. ᅙᩑǍ۵ᯕෝ☖⧕
⟝ḡ MCDM ʑჶॅ᮹ ⪽ᬊ a܆ᖒᮥ ⪶ᯙ⦹Łᯱ ⦽݅.
2. ᩑǍႊჶ
2.1 ֜ୣఙ
MCDMŝFuzzy MCDM ႊჶᮡFig. 1ŝzᯕ༉ࢱ6݉ĥ
ŝᱶᮥÑ⊽݅. 1݉ĥݡᦩ᮹}ၽ, 2݉ĥ⠪aʑᵡ᮹ᖁ┾, 3݉
Fig. 1. Flowchart of This Study
ĥ⠪aʑᵡᄥaᵲ⊹ੱ۵Fuzzy aᵲ⊹᮹đᱶ, 4݉ĥ᮹ᔍđᱶ
ᮥ᭥⦽ݡᦩᄥ⠪a⢽(payoff matrix) ੱ۵⟝ḡ⠪a⢽᮹ࠥ⇽, 5݉ĥMCDM ੱ۵Fuzzy MCDM ʑჶᮥᯕᬊ⦽ᙽ᭥᮹đᱶ ᮝಽǍᖒࡹᨕᯩ݅. ᅙᩑǍᨱᕽ۵ࢱᩑǍđŝ᮹እƱෝ᭥⧕
6݉ĥࢱđŝ᮹እƱᱩ₉ෝ⇵a⦹ᩡ݅. ᅙᩑǍ۵Fuzzy MCDM ʑჶ᮹ᱢᬊđŝ᮹ࠥ⇽ᯕᵝ༊⢽ᯕအಽ1, 2݉ĥ᮹ŝᱶŝ
3݉ĥaᵲ⊹ੱ۵⟝ḡaᵲ⊹۵ᯝၹᱢᮝಽŁಅࢁᙹᯩ۵s
ᮥaᱶ⦹ᩡŁ4݉ĥMCDM ႊჶ᮹ᔍᬊᮥ᭥⦽ݡᦩᄥ⠪a⢽
۵Chung ॒(2008a)ᨱᕽࠥ⇽⦽sᮥəݡಽᔍᬊ⦹ᩡ݅. ᕽ
ᅙᩑǍ۵Fuzzy MCDMᮥ᭥⦽4݉ĥ, 5݉ĥ᪡6݉ĥෝᙹ⧪⦹
ᩡ݅.
2.2 ൵ۗ׆ஜଭॷէ୨׆࣑
⟝ḡᯕುᮡᇩ⪶ᝅᖒᯕᔑᰍ⧕ᯩŁᧁๅ༉⪙⦽ྙᱽෝ݅ʑ ᨱᱢ⧊⦽ᇥಽZadeh(1965)ᨱ᮹⧕ᮭᗭ}ࡹᨩŁMamdani (1975)a⟝ḡŁญ᷹ŝᅖᰂ⦽ᜅ▽᮹ᨙᨕ༉ߙยᮥᯕᬊ⦹ᩍ
ᱽᨕᨱ᮲ᬊ⦹໕ᕽ⟝ḡᯕುᯕᅙĊᱢᮝಽᯕᬊࡹʑ᯲⦹ᩡ݅.
ᯝၹᱢᮝಽŖ⦺ᇥᨱᕽ݅۵ᚌᯱ۵⪶⦽(crisp) ᚌᯱᯕ
݅. aಚ10ᯕ໕ᱶ⪶⯩10ᮥ᮹ၙ⦽݅. əߑᬑญॅᯝᔢᔾ
⪽ᨱᕽᥑ۵ᚌᯱ۵ᯕ᪡ݍญᱶ⪶⦹íਉᨕḡḡᦫ۵ݡఖ10 ᱶࠥ᮹᮹ၙෝw۵ᚌᯱࠥᯩ݅. ᙹᯱᬱŖ⦺ᇥᨱᕽᔍᬊࡹ۵
ݡᇡᇥ᮹ᚌᯱ۵ᇩ⪶ᝅᖒ᮹ᱶࠥ₉ᯕaᯩḡอᯕ᪡zᮡ᮹ၙ
ෝwŁᯩ݅. ༉᮹⦹ᩍᩩ⊂ࡽđŝॅᮡݡᇡᇥᯕᨱ⧕ݚࡽ݅Ł
ᅝ ᙹ ᯩ݅.
⟝ḡᚌᯱ10ᮡ᧞10ᮥ᮹ၙ⦹ḡอ10ᯝa܆ᖒᯕaᰆ׳Ł
10ŝມᨕḩᙹಾᔢݡᱢᮝಽa܆ᖒᯕԏᦥḥ݅. ᯕ్⦽⟝ḡᚌ
ᯱ᮹⩶┽۵ᩍ్aḡaᯩḡอəᵲᔝb⟝ḡᚌᯱ(triangular
fuzzy number, TFN)᮹ᔍᬊኩࠥaaᰆ׳݅. TFNᮡᖙ}᮹
ᱱᮝಽ⢽⩥⧁ᙹᯩʑভྙᨱaᰆe⠙⦹໑, TFN,, á ÞƊìƋìƓß
᪡zᯕ⢽⩥ࢁᙹᯩŁᗭᗮ⧉ᙹ(membership function)᮹sᮡ
݅ᮭŝ zᯕ ᱶ᮹ࢁ ᙹ ᯩ݅.
łƋÞƖß á Ē ē Ĕ
ĕ ĕ
ćƋ à ƊÎ Ɩà ćƋ à ƊƊ ì ƖãƊìƋä ćƋ à ƓÎ
Ɩ à ćƋ à ƓƓ
×
ƖãƋìƓ ä
Ɩã×ìƊ ä ãƋìÎä (1)
TFN ᯕᨱᔍ݅ญΕ, ᔍb⩶⟝ḡᚌᯱ॒ᯕᯩ݅. ⟝ḡᗭᗮ
⧉ᙹ᪡ݡᇡᇥ᮹݅ʑᵡ᮹ᔍđᱶʑჶॅᮡđ⧊⦹ᩍᔍᬊa܆⦹
ʑভྙᨱ⩥ᰍʭḡWSM, AHP, TOPSIS ॒ŝđ⧊ࡹᨕᔍᬊࡽ
ᔍಡ۵ๅᬑฯ݅. ↽ɝᨱ۵MCDM ʑჶॅᯕaḡŁᯩ۵ᇩ⪶ᝅ ᖒᮥ ᱲɝ⦹ʑ ᭥⧕ ݅᧲⦽ Fuzzy ᯕುॅŝ đ⧊⦹ᩍ ᔩಽᬕ
ʑᚁᯕ}ၽࡹŁᯩ݅. bbᨱݡ⦽ᔢᖙ⦽ԕᬊᮡMakropoulos and Butler(2006)ŝ Alipour ॒(2010)ᨱ ᱽࡹᨕ ᯩ݅.
bݡᦩᨱᯩᨕTFNᨱݡ⦽ᙽ᭥ෝᖁᱶ⦹ʑ᭥⧕ᕽ۵ᱶపᱢᯙ
እƱa⦥⦹݅. ᙽ᭥ෝእƱ⦹ʑ᭥⧕ᕽTFNᮥᯕᬊ⧕እ⟝ḡ⪵
(defuzzication)ෝᙹ⧪⧕⦽݅. እ⟝ḡ⪵۵TFN᮹⪶⦽ᙹᯙ
Best Nonfuzzy Performance (BNP) sᮝಽӹ┡ԙ݅. እ⟝ḡ⪵᮹
aᰆᅕ⠙ᱢᯙႊჶᮝಽ۵↽ݡ⠪Ɂჶ, ᵲᦺ໕ᱢჶ, alpha-cutᯕ
ᯩ݅(Zhao and Govind, 1991). ᅙᩑǍᨱᕽ۵e݉⦹Ł}ᯙ᮹
❱݉ᮥ Ǎ⦹ḡ ᦫ۵ ᵲᦺ໕ᱢჶᮥ ᔍᬊ⦹ᩡ݅. ᵲᦺ໕ᱢჶᮡ
݅ᮭ Eq. 2ಽ ӹ┡ԝ ᙹ ᯩ݅.
§©Ƈƈá ãÞƓƇƈà ƊƇƈß âÞƋƇƈà ƊƇƈßäîÐ âƊƇƈ (2)
2.3 ۗ׆ஜଭॷէ୨׆࣑ଭஂࠑ
ᯝၹᱢᮝಽฯᯕᔍᬊ⦹Łᯩ۵ʑჶᵲᅙᩑǍᨱᕽᱽ⦹ḡ
ᦫᮡႊჶᮝಽ۵ᅖ⧊ĥ⫮ჶ(Composite Programming; Bardossy and Bogadi, 1983)ŝPromethee ႊჶ॒ᯕᯩ݅. ᅖ⧊ĥ⫮ჶ᮹
Ğᬑ᮹ᔍđᱶᮥ᭥⦽ʑᵡᯕᅖᰂ⧕ḩĞᬑCompromise Pro- grammingᮥĥ⊖ᱢᮝಽ⪶ᰆ⧕ᕽᔍᬊ⦽ʑჶᯕအಽᅙᩑǍ᮹
ྙᱽ᪡۵ᱢ⧊⦹ḡᦫʑভྙᨱᱽ⦹ᩡŁPromethee ႊჶᮡᯕ
ುŝᱢᬊᯕᅖᰂ⦹ᩍ⦹ӹ᮹ᵝᱽಽᱲɝ⧕⦹အಽᅙᩑǍ᮹
✚ᖒŝ ᯝ⊹⦹ḡ ᦫᦥ ᱽ⦹ᩡ݅.
2.3.1 ԧணծ࣑(Weighted Sum Method, WSM) aᵲ⧊ĥჶᮡᯝၹᱢᮝಽaᰆᛞíᔍᬊࡹ۵ႊჶᮝಽƋ} ᮹ݡᦩŝƌ}᮹⠪aʑᵡᨱݡ⧕݅ᮭŝzᮡᙹᮥᯕᬊ⧕ᕽ
sᮥ Ǎ⦽ ⬥ ↽Łsᮥ ↽Ł(best) ݡᦩᮝಽ ᖁᱶ⦽݅.
©ÞƇß áƈ á Îāƌ ſƇƈƕƈ, (݉, Ƈ á Îì Ïì Ðì íííì Ƌ) (3-1)
ᩍʑᕽ©ÞƇß۵MCDMᮝಽᔑᱶ⦽ݡᦩƇ᮹⠪asᯕ໑ſƇƈ ۵ݡᦩƇ᮹ʑᵡƈᨱݡ⦽⢽ᵡ⪵ࡽ(normalized) sᯕ໑ƕƈ۵
ʑᵡƈᨱ ݡ⦽ aᵲ⊹ᯕ݅.
⟝ḡaᵲ⧊ĥჶᮡ݅ᮭŝEq. 3-2᪡zᯕᔝb⟝ḡᙹ(ýſƇƈ,ýƕƈ)
ෝ ᯕᬊ⦹ᩍ ĥᔑ⧁ ᙹ ᯩ݅.
ý©ÞƇß áƈ á Îāƌ ýſƇƈýƕƈ, (݉, Ƈ á Îì Ïì Ðì íííì Ƌ) (3-2)
2.3.2 ծ౾ฃंজր୨(Analytic Hierarchy Process, AHP) ĥ⊖⪵ᇥᕾŝᱶ(Saaty, 1980)ᮡ ᔍᬊᔢ ⠙ญ⧉ᮝಽ ᯙ⧕ ↽ ɝaᰆ⡎մí⪽ᬊࡹŁᯩ۵ႊჶᯕ݅. ᯝၹᱢᮝಽaᵲ⊹ᔑᱶᮥ
᭥⧕ ኩჩ⦹í ᔍᬊࡹḡอ zᮡ ᬱญಽ ᬑᖁᙽ᭥ đᱶᮥ ᭥⦽
݅ʑᵡ᮹ᔍđᱶʑჶᮝಽࠥ⪽ᬊࢁᙹᯩ݅. WSMŝ݅ෙᱱᮡ
bᯱഭ᮹⢽ᵡ⪵ෝ᭥⧕݅ᮭEq. 4-1ŝzᯕ⠪aʑᵡᄥݡᦩॅ᮹
⠪as᮹⧊ᮝಽӹ٥ᨕᕽᔍᬊ⦽݅۵ᱱᯕ݅. ᷪbʑᵡᨱݡ⧕
༉ु ݡᦩॅ᮹ sᮥ ⦹໕ 1ᯕ ࡽ݅.
©ÞƇß áƈ á Îāƌ Ė
Ę ćƉ á ÎāƋſƉƈ
ſƇƈ ę
ě
ƕƈ (4-1)
⟝ḡĥ⊖⪵ᇥᕾŝᱶᮡ݅ᮭEq. 4-2᪡zᯕᔝb⟝ḡᙹ(ýſƇƈ, ýƕƈ)ෝ ᯕᬊ⦹ᩍ ĥᔑ⧁ ᙹ ᯩ݅.
ý©ÞƇß áƈ á Îāƌ Ė
Ę ćƉ á ÎāƋýſƉƈ
ýſƇƈ ę
ě
ýƕƈ (4-2)
2.3.3 ୨ծ౾ฃंজր୨(Revised AHP, R-AHP) Belton and Gear(1983)ᨱ ᮹⧕ }ၽࡽ ᙹᱶ AHP ႊჶ(R- AHP)ᮡ݅ᮭEq. 5-1ŝzᯕʑ᳕᮹AHP ႊჶᨱ᳕ᰍ⦹۵ᙽ᭥
ᇩᯝ⊹ᖒ(inconsistency)ᨱݡ⧕ᯝᇡ}ᖁ⦹ࠥಾᱽࡹᨩ݅. ᷪ
⢽ᵡ⪵ෝ ᭥⧕ ʑ᳕ AHP۵ ⠪aʑᵡᄥ ݡᦩॅ᮹ s᮹ ⧊ᮝಽ
ӹ٩ߑၹ⧕ᙹᱶAHP۵⠪aʑᵡᄥݡᦩॅ᮹sॅᵲ↽Łsᮝಽ
ӹ٥۵ႊჶᮥᔍᬊ⦹ᩡ݅. ᕽbʑᵡᨱݡ⧕ᱢᨕࠥ⦹ӹ᮹
ݡᦩᮡ ⧎ᔢ 1ᯕ ᳕ᰍ⦽݅.
©ÞƇß áāƈ á Îƌ Ė
Ę
ć ſƉƈ Ɖ
ſƇƈ ę ě
ƕƈ (5-1)
⟝ḡᙹᱶĥ⊖⪵ᇥᕾŝᱶᮡ݅ᮭEq. 5-2᪡zᯕᔝb⟝ḡᙹ (ýſƇƈ, ýƕƈ)ෝ ᯕᬊ⦹ᩍ ĥᔑ⧁ ᙹ ᯩ݅.
ý©ÞƇß áāƈ á Îƌ Ė
Ę
ć ýſƉƈ Ɖ
ýſƇƈ ę
ě
ýƕƈ (5-2)
2.3.4 TOPSIS (Technique for Order Preference by Similarity to Ideal Solution)
TOPSIS۵᧲᮹ᯕᔢᱢᯙ⧕(Positive Ideal Solution, PIS)ಽ
ᇡ░aᰆaʭᬕÑญᨱᯩŁᮭ᮹ᯕᔢᱢᯙ⧕(Negative Ideal Solution, NIS)ಽᇡ░۵aᰆຝÑญᨱᯩ۵ݡᦩᮥᖁᱶ⦹۵
}ֱᮝಽ↽ᖁ᮹ݡᦩŝ↽ᦦ᮹ݡᦩᮥ࠺ᨱŁಅ⦹ᩍᯙe᮹
⧊ญᱢᖁ┾ᯕa܆⦹ࠥಾᮁࠥ⦹۵ʑჶᯕ݅. ੱ⦽݅ᗮᖒšᱱᨱ ᕽ༉ुݡᦩॅᨱݡ⦽⠪ađŝෝ᳦⧊⦹ᩍᱶప⪵⧁ᙹᯩ݅.
TOPSIS۵ᯕ్⦽ᯕᮁಽฯᮡᙹᯱᬱ᮹ᔍđᱶྙᱽᨱᔍᬊࡹŁ
ᯩ݅ (Kim et al., 2012).
Hwang and Yoon(1981)ᨱ ᮹⧕ ᱽࡽ TOPSIS ႊჶᮡ
ELECTRE ႊჶ᮹ݡᦩᮝಽ}ၽࡹᨩᮝ໑↽ɝᨱᔍᬊኩࠥa᷾
a⦹Łᯩ۵ႊჶᯕ݅. TOPSIS ႊჶᮡᖁ┾ࡽݡᦩᯕᯕᔢ⧕(ideal solution)ᨱᕽaᰆaʾŁᮭ᮹ᯕᔢ⧕(negative ideal solution)ᨱ ᕽaᰆມญਉᨕᲙ⦽݅۵ᱱᨱᕽ᯲ࡽ݅. TOPSIS ႊჶᮡ
⬉ᬊᯕ݉᳑í(monotonically) ᷾a⦹Łqᗭ⦹۵äᮝಽaᱶ
⦹໑ᯕᔢ⧕᪡ᮭ᮹ᯕᔢ⧕ෝᱶ᮹⧕⦹ŁEuclidean Ñญᱲɝ ჶᮥ ☖⧕ ᯕᔢᱱŝ᮹ ᔢݡᱢ ɝᱲᖒᮥ ⠪a⦹ࠥಾ ࡹᨕ ᯩ݅.
TOPSIS ႊჶᮡ݅ᮭŝzᯕⅾ6}݉ĥಽǍᖒࡹᨕᯩ݅. 1݉ĥᨱ ۵ ᯱഭෝ Eq. 6ෝ ᯕᬊ⦹ᩍ ⢽ᵡ⪵⦽݅.
ƐƇƈá ć
ö
ćāƉ á ÎƋƖƇƈƖƉƈÏ (6)2݉ĥᨱ۵aᵲ⢽ᵡ⪵s(weighted normalized value)ᮥǍ⦽
݅. ᷪ⢽ᵡ⪵⦽sᨱaᵲ⊹ෝŒ⧕ᕽEq. 7ᮥᯕᬊ⧕ᕽᱶญ⦽݅.
¯ áƙ
ƜƚƕƕíííÎƐÎÎ ƕÏíííƐÎÏ ííí ƕƌƐÎƌƛƝƞ
ÎƐƋÎƕÏƐƋÎ ííí ƕƌƐƋƌ (7)
3݉ĥ۵ᯕᔢ⧕᪡ᮭ᮹ᯕᔢ⧕ෝǍ⦽݅. ᅕ☖↽ݡsŝ↽ᗭ sᮥᯕᬊ⦽݅. 4݉ĥᨱᕽ۵ᯕᔢ⧕ಽᇡ░᮹Euclidean Ñญ᪡ᮭ
᮹ᯕᔢ⧕ಽᇡ░᮹Euclidean ÑญෝEq. 8ᮥᯕᬊ⧕ᕽᔑᱶ⦽݅.
¬ƇÝá
ö
ćāƈ á Îƌ ÞƔƇƈà ƔƈÝßϬƇ àá
ö
ćāƈ á Îƌ ÞƔƇƈà ƔƈàßÏ(8)
5݉ĥᨱᕽ۵݅ᮭᙹᮥᯕᬊ⦹ᩍᯕᔢᱱᮝಽᇡ░ᔢݡᱢᯙ
ᱲɝᱶࠥ(closeness)ෝ ĥᔑ⦽݅.
ƇÝá ć¬ƇÝâ¬Ƈ à
¬Ƈ à
(9)
6݉ĥ۵ᯕᔢᱱᮝಽᇡ░aᰆaʭᬕŔᨱᯩ۵ᙽᕽಽᬑᖁᙽ
᭥ෝ ᖁᱶ⦽݅.
2.3.5 Fuzzy TOPSIS
TFNᮥ TOPSISᨱ ᱢᬊ⦹ʑ᭥⧕ TFN᮹ ᕽಽ ݅ෙ ⇶ᮥ
TFN᮹ᖒḩᮥᮁḡ⦹໕ᕽእƱa܆⦽⇶ᮝಽ⢽ᵡ⪵⧕⦽݅.
⢽ᵡ⪵ࡽ ⟝ḡ ⧪Ā«ᮡ Eq. 10ŝ zᯕ ӹ┡ԝ ᙹ ᯩ݅.
Ā«á ãĀƐƇƈä, ÞƇ á ÎìÏìíííì Ƌß
Þƈ á ÎìÏìíííì ƌß (10)
ᩍʑᕽ, ĀƐᮡ ⢽ᵡ⪵ࡽ TFNᮥ ᮹ၙ⦹໑Ƈ۵ b ḡᯱℕ, ƈ۵
b ᗮᖒ᮹ ᙹෝ ᮹ၙ⦽݅. ੱ⦽ Eqs. 11ⴇ14᮹ ᪡ ۵
b⠙ᯖʑᵡ(⊂ᱶ⊹aⓕᙹಾᖁ⪙ࡹ۵ʑᵡ)ŝእᬊʑᵡ(⊂ᱶ
⊹a ᯲ᮥᙹಾ ᖁ⪙ࡹ۵ ʑᵡ)᮹ Ḳ⧊ᯕ݅.
ƁƈÝá ƁƇƈì ƈ
Ƈ
(11)
ĀƐƇƈá ÞćƁƈÝ ſƇƈ
ì ćƁƈÝ ƀƇƈ
ì ćƁƈÝ
ƁƇƈßì ƈ (12)
ſƈÝá ſƇƈì ƈ
Ƈ
(13)
ĀƐƇƈá ÞćƁƇƈ
ſƈÝ
ì ćƀƇƈ
ſƈÝ
ì ćſƇƈ
ſƈÝ
ßì ƈ (14)
ᩍʑᕽ,ĀƐƇƈá ÞķƇƈì ĸƇƈì ĹƇƈß⧁ভ⢽ᵡ⪵ࡽ⟝ḡ⧪Ā«ಽᇡ░
⟝ḡ᧲᮹ᯕᔢᱢᯙ⧕(Fuzzy Positive Ideal Solution, FPIS)᪡
⟝ḡᮭ᮹ᯕᔢᱢᯙ⧕(Fuzzy Negative Ideal Solution, FNIS)۵
Eq. 15᪡ zᯕ ᱶ᮹ࡽ݅.
âáĀƔÎâìĀƔÏâìíííĀƔƌâ ੱ۵ àáĀƔÎàìĀƔÏàìíííĀƔƌà (15)
ᩍʑᕽ,ĀƔƈâá ÞƔƈâì Ɣƈâì Ɣƈâß,ĀƔƈàá ÞƔƈàì Ɣƈàì ƔƈàßᯕŁ, Ɣƈâá ĹƇƈ
Ƈ
,
Ɣƈàá ķƇƈ
Ƈ ᯕ݅. â(FPIS), à(FNIS)᪡bݡᦩÞƇßŝ᮹Ñ ญ۵Eq. 16ŝzᯕTFN ĀƋá ÞƋÎìƋÏìƋÐßŝTFN Āƌá ÞƌÎìƌÏìƌÐß ᮹ÑญෝǍ⦹۵ႊჶᮝಽĥᔑ⧁ᙹᯩ݅. ੱ⦽ â(FPIS)᪡
à(FNIS)ಽ ᇡ░ b ݡᦩÞƇßŝ᮹ eĊƂƇâ᪡ƂƇàᮡ Eqs. 17, 18ᮥ ᯕᬊ⧕ ᮁࠥ⧁ ᙹ ᯩᮝ໑ b ݡᦩ᮹ ᔢݡᱢ ɝᱲࠥ ĥᙹ (similarity), C+۵ Eq. 19ෝ ᯕᬊ⧕ᕽ ࠥ⇽⧁ ᙹ ᯩ݅.
ƂÞĀƋìĀƌß áöćÐÎ ãÞƋÎà ƌÎßÏâÞƋÏà ƌÏßÏâÞƋÐà ƌÐßÏä
(16)
ƂƇâáāƈ á Îƌ ƂÞĀƐƇƈìĀƔƈâß (17)
ƂƇàáāƈ á Îƌ ƂÞĀƐƇƈìĀƔƈàß (18)
«Ƈá ćÞƂƇââƂƇàß ƂƇà
(19)
2.4 ୡુ୪
ᅙᩑǍ᮹ݡᔢᮁᩎᮡᦩ᧲ᮁᩎ(Fig. 2)ᮝಽḡӽ40ᩍ֥e
ɪĊ⦽ࠥ⪵ಽᯙ⧕ḡᮡÕ⪵ࡹŁᙹḩᮡᦦ⪵ࡽᔢ┽ᯕ݅
(Chung ॒, 2008a). ᯕෝ᭥⧕݅᧲⦽ᔍᨦॅᯕḡᗮᱢᮝಽ⇵ḥࡹ
Łᯩ۵ߑݡᇡᇥᙹప}ᖁੱ۵ᙹḩ⨆ᔢ॒݉ᯝ༊ᱢᔍᨦॅᯕ
ᵝෝᯕŁᯩᨕᔍᨦeᔢ⪙ᬑᖁᙽ᭥đᱶᯕᇩa܆⦽ᔢ⫊ᯕ݅.
Chung ॒(2008a)ᨱᕽ۵ᦩ᧲ᮁᩎᨱ19}ᔍᨦᮥᱽᦩ⦹ᩡŁ
ᯕᨱݡ⦽ᙹྙ⦺ᱢᇥᕾŝ݅ʑᵡ᮹ᔍđᱶʑჶᮥᯕᬊ⦹ᩍᔍᨦ ᮹ᬑᖁᙽ᭥ෝᱽ⦽ၵᯩ݅. ⦹ḡอᙹྙ⦺ᱢᇥᕾđŝ᮹ᇩ⪶ᝅ ᖒŝ⠪aʑᵡᨱݡ⦽aᵲ⊹᮹ᇩ⪶ᝅᖒᮡᱥ⩡Łಅࡹḡᦫᦹᮝ အಽᅙᩑǍᨱᕽ۵ᯕෝݡᔢᮝಽFuzzy ݅ʑᵡ᮹ᔍđᱶʑჶᮥ
ᱢᬊ⦹ᩡ݅.
ᅙᩑǍ۵Fuzzy MCDM᮹┡ݚᖒᮥá᷾⦹ʑ᭥⦽ᩑǍᯕအಽ
19}ᔍᨦݡᝁʑ᳕ᩑǍᨱᕽᔢ᭥ᙽ᭥ෝʑಾ⦽5}ݡᦩᮥ
ᖁ┾⦹ᩡ݅. ᷪ, ʑ᳕ᨱᬑᙹ⦹݅Ł⠪aࡽ5}᮹ݡᦩॅᔍᯕ᮹
ᔢݡᱢᯙ⠪aෝᙹ⧪⦹ᩍၙᖙ⦽₉ᯕಽᯙ⦽ᬑᖁᙽ᭥᮹ᄡ⪵
ෝ⪶ᯙ⦹ʑ᭥⧉ᯕ݅. 5}ݡᦩᨱݡ⦽ᖅᮡTable 1ŝzŁ
᭥⊹۵Fig. 1ᨱᔍb⩶ၶᜅಽ⢽ࡹᨕᯩ݅. ᅙᩑǍᨱᕽŁಅ⦽
ݡᦩॅᮡᱡᙹḡᰍ}ၽ(Alt 1), ᅖ}⦹ᅖᬱ(Alt 2, 3, 4), ᗭȽ༉
Fig. 2. Feasible Alternatives for This Study
Table 1. Specific Descriptions of Feasible Alternatives
Category of Alternatives Name of sub-watershed Description Name
Reservoir
redevelop-ment GS - Proper operation
(release: 0.05 cms from Oct. to May) Alt 1
Restoration of covered stream
DJ
- To remove roads and restore the stream - Construction of sewers
- Covered length: 1.59 km Alt 2
SB - Covered length: 2.74 km Alt 3
SA - Covered length: 0.645 km Alt 4
Construction of small
wastewater treatment DR - Capacity: 19,000 m3/day Alt 5
⦹ᙹญᰆ Õᖅ(Alt 5)ᯕ݅.
ݡᦩॅᮥ⠪a⦹۵⠪aḡᵡᮡDPSIR(driving force-pressure- state-impact-response; European Environmental Agency, 1999) ℕĥෝᯕᬊ⧕ᕽChung ॒(2008a)ᨱᕽᱽᦩ⦽đŝෝᯕᬊ⦹ᩡ
݅. DPSIR ༉⩶ᮡEEA(1999)aʑ᳕᮹OECD(1993)᮹Pressure- State-Response(PSR) ༉⩶ᮥ}ᖁ⦹ᩍḡᗮa܆ᖒ(sustainability)
ᮥḡ⢽⪵⦹ʑ᭥⧕}ၽ⦹ᩡ݅. ʑ᳕᮹PSR ༉⩶ᮡᅖᰂ⦽ᔾ┽
⦺ᱢŝᱶŝᯙe⪹Ğ᮹ᯙŝšĥෝᖅ⦹ḡ༜⦽݅. ✚⯩ᔢ┽
᮹ᄡ⪵ಽᇡ░ᔾʑ۵ᩢ⨆(impact)ᮥᱥ⩡ᖅ⦹ḡ༜⦹۵݉ᱱ
ᮥaḡŁᯩᮥᐱอᦥܩၹ᮲ᯕᜅ▽ᨱᩢ⨆ᮥၙ⊹۵ᔢ⫊ᮥ
ၹᩢ⦹ḡ༜⦽݅. ᷪPSR ༉⩶ᮡᯙe᮹⪽࠺(pressure)ᯕ⪹Ğ (state)ᨱᩢ⨆ᮥၙ⊹Ł⪹Ğᮡ݅ᯙeᮝಽ⦹ᩍɩᦶಆᮥᵥᯕ
ʑ᭥⦽⪽࠺(response)ᮥⅪḥ⦹í⦽݅. ə్ӹDPSIR ༉⩶ᮡ
ᩍʑᨱࢱaḡ}ֱᯕ⇵aࡹᨩ݅. ᯙe᮹⧪ᅖᮡ⪹Ğ᮹ḩŝ
šĥaᯩŁᔍ⫭᮹⪽࠺ŝĞᱽᱢᦶಆᮡ⪹Ğŝᯙe᮹⧪ᅖᨱ
ᩢ⨆ᮥၙ⊽݅۵äᯕ݅. ᯕ్⦽}ֱᮡᔍ⫭ᱢᯙ(driving force or drivers)ŝᩢ⨆(impact)ᨱၹᩢࡹᨕPSR ༉⩶ᨱ⇵aࡹᨩ݅.
ᕽDPSIR ༉⩶ᮡᔍ⫭᮹ᔍ⫭ᱢᯙᯕᯙeᔍ⫭ᨱᦶಆᮥ
ၽᔾ┅Ł ᦶಆᯕ ᔢ┽ᨱ ᩢ⨆ᮥ ၙ⋉ᨱ ᔢ┽a ၹ᮲ᮥ
ʑ⦹۵ᩢ⨆ᮥ ᮁၽ⦹໑ ݅ၹ᮲ᮡ ᯕᔢ᮹ օaḡ ᗭᨱ
bb ݅ ᩢ⨆ᮥ ၙ⊽݅۵ šĥᨱ ₊ᦩ⦽݅. ᩍʑᕽ ᬱ࠺ಆᮡ
⪹Ğᨱᩢ⨆ᮥၙ⊹۵ᔍ⫭-ĞᱽᱢᗭಽᯝၹᱢᮝಽᯙǍ, ᯱᬱ᮹
ᔍᬊప, Ʊᮂᙹᵡ, Ñᵝᯱᙹ, ᨱթḡ ᗭእప ॒ᯕ ᯩ݅. ᦶಆᮡ
⪹Ğ᮹ᔢ┽ᨱḢᱲᱢᮝಽᩢ⨆ᮥၙ⊹۵ᯱᩑᱢᯙᗭಽ᪅ᩝᇡ
⦹ప, CO2 ႑⇽ప ॒ᯕ ᯩ݅. ᔢ┽۵ ⪹Ğ᮹ ḩŝ ᯱᩑᯱᬱ᮹
᧲ᮥ ᱶపᱢᮝಽ ⊂ᱶ⦹۵ äᮝಽ ⦹ᙹḩ ࠥ, ᪅᳕᮹ ࠥ
॒ᯕ ᯩ݅. ᩢ⨆ᮡ ⪹Ğ᮹ ᔢ┽a ᯙe, ࠺ྜྷ, ᔾ⪵⦺ᱢ ŝᱶᨱ
ၙ⊹۵ᩢ⨆ᮝಽḩᄲ᮹ᱶࠥ, ᔾ┽ĥᨱ⪹Ğ᪅ᩝྜྷḩ႑⇽ప॒ᯕ
ᯩ݅. ၹ᮲ᮡ ⪹Ğ᮹ ᄡ⪵ᨱ ݡ⦽ ᔍ⫭᮹ ၹ᮲ᮝಽ ⪹Ğ}ᖁᮥ
᭥⦽ ݅᧲⦽ ⪽࠺ ॒ᯕ ᯕᨱ ⧕ݚࡽ݅.
ᅙ ᩑǍᨱᕽ۵ ྜྷᙽ⪹ᨱ aᰆ ฯᮡ ᩢ⨆ᮥ ၙ⊹۵ ɝᅙᱢᯙ
ᔍ⫭ᱢ ᯙ(D)ᮥ ᯙǍ᪡ ᯙǍၡࠥಽ aᱶ⦹ᩡŁ ᯙe᮹ ⪽࠺
ᵲྜྷᙽ⪹ᨱᇡᱶᱢᯙᦶಆ(P)ᮥၙ⊹۵ᗭಽᯕᙹ⊂໕ᨱᕽ۵
ࠥḡᩎእᮉŝ⦹ᙹ٥ᙹᩍᇡ, ᮁᩎĞᔍ, ḡ⦹ᙹ≉ᙹపᮥ
ᔍᬊ⦹ᩡᮝ໑ ᙹḩšญ ⊂໕ᨱᕽ۵ BOD, COD, SS, TN, TP ᇡ⦹ప, ၙญ⦹ᙹᮁ᯦ᩍᇡ, ᅖ}Ǎeእᮉ, ᯙǍၡࠥෝaᱶ⦹
ᩡ݅. ᯕ్⦽ᦶಆᮝಽᯙ⧕ᩢ⨆ᮥၼ۵ᯱᩑᔢ┽ᗭ۵ᯕᙹ
⊂໕ᨱᕽᮁ⫊łᖁᨱᕽ⠪Ɂiᙹపŝ⠪Ɂᱡᙹప᮹༊⢽ᙹྙ
⦺ᱢiᙹపᨱݡ⦽እᮉಽaᱶ⦹ᩡŁ, ᙹḩšญ⊂໕ᨱᕽ۵༊
⢽ᙹḩݡእBOD ⠪Ɂࠥ, ᯝ↽ݡ⨩ᬊᇡ⦹ప(total maximum daily load, TMDL) ݡእBOD ⠪Ɂᯝⅾᇡ⦹పᮝಽaᱶ⦹ᩡ݅.
ྜྷᙽ⪹᮹ᦦ⪵ಽᯙ⧕ᯙeᨱíӹ┡ӹ۵Ḣᱲᱢᯙᩢ⨆ᮡᯕᙹ⊂
໕ᨱᕽᩑᵲᮁḡᮁపᇡ᳒ᯝᙹ, ᙹḩ⊂໕ᨱᕽ۵ᩑᵲTMDLᮥ
อ᳒⦹ḡ༜⦹۵ᯝᙹಽaᱶ⦹ᩡ݅. ᯕ్⦽ᩢ⨆ᮥ⫭ᅖ⦹ʑ᭥⧕
ǎa, ᔍ⫭, šญᇡ॒ᨱᕽࠥ⦹۵ᩍ్ݡᦩॅᮥၹ᮲ᯕŁ
Table 2. Original Calculated Data from Chung et al. (2008a) and Normalized Data for This Study Original calculated data
Name of Alternative D P S I R Cost
Alt 1 0.063 0.323 0.682 0.488 0.674 0.989
Alt 2 0.394 0.4385 1 1 0.312 0.100
Alt 3 0.086 0.1315 0.42 0.326 0.3525 0.956
Alt 4 0.226 0.211 0.0365 0.064 0.385 0.978
Alt 5 0.761 0.6325 0.501 0.1435 0.557 0.357
Normalized Data
Name of Alternative D P S I R Cost
Weights 0.1 0.1 0.15 0.15 0.2 0.3
Alt 1 0.083 0.511 0.682 0.488 1.000 0.989
Alt 2 0.518 0.693 1.000 1.000 0.463 0.100
Alt 3 0.113 0.208 0.420 0.326 0.523 0.956
Alt 4 0.297 0.334 0.037 0.064 0.571 0.978
Alt 5 1.000 1.000 0.501 0.144 0.826 0.357
⦹໑ၹ᮲ᮝಽᯙ⦽⬉ŝෝᱶప⪵⦹ʑ᭥⧕ᖁ┾ࡽbb᮹ʑᵡॅ
ᮡᱶపᱢᇥᕾᯕa܆⦽ᔢ┽᪡ᩢ⨆᮹ᯙᯱॅ᮹ᄡ⪵sᮥᔍᬊ⦹
ᩡ݅. ᩍʑᕽၹ᮲᮹⬉ŝෝᱶప⪵⦹ʑ᭥⦽⠪aʑᵡᮝಽD᪡
Pෝᔍᬊ⦹ḡᦫ۵ᯕᮁ۵D᪡P ᯱℕෝᄡ⪵┅ಅ۵ݡᦩᮥ
ᖅᱶ⦹ḡᦫ۵⦽Ḣᱲᱢᮝಽᯕॅŝ᮹ᩑšᖒᮥȽ⦹ʑᨕಖʑ
ভྙᯕ݅.
ੱ⦽ ᅙ ᩑǍ۵ Chung ॒(2008b)ŝ۵ ݅í እᬊ(C)⧎༊
ᮥ⇵a⦹ᩍᕽ⠪aʑᵡᮥ6}ಽ⦹ᩡ݅. እᬊᯱഭ۵Chung ॒ (2008b)ᨱᱽࡽsᮥᯕᬊ⦹ᩡ݅. ݡᇡᇥ☁༊ᔍᨦ᮹ᬑᖁᙽ᭥
đᱶᮡB/C እᮉ᮹ⓍʑಽđᱶࡹŁᯩᮝӹChung ॒(2008b)ᨱᕽ
ᯕၙB/C۵ࠥ⇽⦹ᩡᮝအಽᅙᩑǍᨱᕽ۵⟝ḡ݅ʑᵡ᮹ᔍđᱶ ʑჶ᮹ᱢᬊ┡ݚᖒᨱݡ⦽á᷾ᮥ᭥⧕እᬊ⧎༊ᮥ⠪aʑᵡᮝಽ
⇵a⧕ᕽ ᔢݡᱢ ᬑᖁᙽ᭥อ ᱽ⦹ᩡ݅.
݅ʑᵡ ᮹ᔍđᱶ ʑჶᮥ ᱢᬊ⦹ʑ ᭥⦽ ⢽ᵡ⪵ ᱥ⬥᮹ ᯱഭ ۵Table 2ᨱᱽࡹᨕᯩ݅. ⠪aᯙᯱᄥaᵲ⊹۵ʑ᳕ᩑǍ᮹
sŝ ᔩಽ ⇵aࡽ እᬊ⧎༊ᮥ Łಅ⦹ᩍ ݅ᮭŝ zᯕ eఖ⦹í
aᱶ⦹ᩡ݅.
D(ᔍ⫭ᱢᯙ) = P(ᦶಆ) = 0.1, S(ᔢ┽) = I(ᩢ⨆) = 0.15, R(ၹ᮲) = 0.2, እᬊ(C) = 0.3
ੱ⦽⟝ḡ݅ʑᵡ᮹ᔍđᱶʑჶᮥᱢᬊ⦹ʑ᭥⧕⢽ᵡ⪵⦽ᯱ
ഭෝᔝb⟝ḡᙹෝᯕᬊ⦹ᩍTable 3ŝzᯕaᱶ⦹ᩡ݅. bᯱഭ᮹
ᔢ᭥, ⦹᭥Ğĥ۵↽ኩs(modal value)᮹120% sŝ80% sᮥ
ᔍᬊ⧩݅. ᯕভ0 ᯕ⦹ੱ۵1 ᯕᔢᯝĞᬑ0ŝ1ᯕŁaᱶ⦹ᩡ݅.
3. ᩑǍđŝ
3.1 ۗ׆ஜଭॷէ୨׆࣑ଭୡ
WSM᮹ĞᬑEq. 1ᮥᔍᬊ⦹ᩍĥᔑࢁᙹᯩᮝ໑đŝTable 4ᨱᱽࡽၵ᪡z݅. Alt 1ŝAlt 4ෝᱽ⦹Łӹນḡݡᦩॅᮡ
እƱᱢ᳢ᮡჵ᭥ᨱ༑ಅᯩᮝအಽaᵲ⊹᮹đᱶŝ݅ʑᵡ᮹ᔍđ ᱶʑჶ᮹᳦ඹᨱᔢݚ⦽ᄡ⪵aᯩᮥäᮝಽᩩᔢࡽ݅. WSM ᮹ĞᬑMCDM᮹ʑᅙႊჶᯕ໕ᕽᔍᬊኩࠥaᱩݡᱢᮝಽ׳݅.
ᕽ݅ෙMCDM ႊჶॅ᮹ᇥᕾđŝ᪡⧎ᔢእƱࡹအಽaᰆ
ᵲ⦹݅Ł ᅝ ᙹ ᯩ݅.
WSM, AHP, ᙹᱶ AHP, TOPSIS ႊჶᮥ ᯕᬊ⧕ᕽ ࠥ⇽⦽
ݡᦩॅ᮹ᙽ᭥ෝᱶญ⦹໕Table 6ŝz݅. AHP ႊჶᮥᔍᬊ⧁
ĞᬑWSMᨱᕽእ⦽sᮥᅕᯙAlt 2, 3, 5᮹ᙽᕽa݅í
ӹ┡ӹ۵äᮥᙹᯩ݅. ၹ໕ᙹᱶAHP᮹ĞᬑWSMŝzᮡ
đŝෝ ᅕᯕ۵ äᮝಽ ӹ┡ԍ݅.
TOPSIS ႊჶ᮹ Ğᬑ Alt 1ᯕ 1॒ᮝಽ ࠥ⇽ࡽ đŝ۵ ݅ෙ
ႊჶŝ࠺ᯝ⧩ᮝӹAlt 4a5॒ᮝಽࠥ⇽ࡽ݅ෙႊჶॅ᮹đŝ᪡
۵݅í4॒ᮝಽӹ┡ԍᮝ໑Alt 5a5॒ᮝಽӹ┡ԍ݅. ᯕᔢ᮹
đŝಽᇡ░Alt 1ᯕ1॒ᯙᱱᨱݡ⧕ᕽ۵ݡᇡᇥ࠺ᯝ⦽đŝa
ࠥ⇽ࡹᨩ݅. อ᧞1॒ᮥđᱶ⧕⦹۵᮹ᔍđᱶྙᱽ໕᮹ᔍđᱶ
ᯱॅe᮹čᯝ⊹aa܆⧁ᙹᯩ݅. ⦹ḡอ2-5॒᮹ᙽ᭥۵ๅᬑ
⪝ᰂ⦽ ᔢ⫊ᮝಽ ᅝ ᙹ ᯩ݅. ݡℕಽ Alt 4a ⠪Ɂ 4.8॒, Alt 3ᮡ⠪Ɂ3.5॒ᯕအಽ݅ෙݡᦩᨱእ⧕ᔢݡᱢᮝಽᩕ॒⦹݅Ł
ᅝᙹᯩ݅. ⦹ḡอAlt 2᪡Alt 5۵ๅᬑእ⦽ᙹᵡᮝಽ2॒ɪᮝಽ
⠪a⧁ᙹᯩ݅. ੱ⦽ᙽ᭥ᨱݡ⦽⢽ᵡ⠙₉ෝǍ⦹ᩍbݡᦩᨱ
Table 3. Data for Fuzzy MCDM
Name of Alternative Driving Force Pressure
Lower modal Upper Lower modal Upper
Weights 0 0.1 0.25 0 0.1 0.25
Alt 1 0.066 0.083 0.099 0.409 0.511 0.613
Alt 2 0.414 0.518 0.621 0.555 0.693 0.832
Alt 3 0.090 0.113 0.136 0.166 0.208 0.249
Alt 4 0.238 0.297 0.356 0.267 0.334 0.400
Alt 5 0.800 1.000 1.000 0.800 1.000 1.000
Name of Alternative State Impact
Weights 0 0.15 0.3 0 0.15 0.3
Alt 1 0.546 0.682 0.818 0.390 0.488 0.586
Alt 2 0.800 1.000 1.000 0.800 1.000 1.000
Alt 3 0.336 0.420 0.504 0.261 0.326 0.391
Alt 4 0.029 0.037 0.044 0.051 0.064 0.077
Alt 5 0.401 0.501 0.601 0.115 0.144 0.172
Name of Alternative Response Cost
Weights 0.05 0.2 0.35 0.15 0.3 0.45
Alt 1 0.800 1.000 1.000 0.791 0.989 1.000
Alt 2 0.370 0.463 0.555 0.080 0.100 0.120
Alt 3 0.418 0.523 0.628 0.765 0.956 1.000
Alt 4 0.457 0.571 0.685 0.783 0.978 1.000
Alt 5 0.661 0.826 0.992 0.286 0.357 0.429
Table 4. Preferences from WSM Name of
Alternative Alt 1 Alt 2 Alt 3 Alt 4 Alt 5 Preference 0.732 0.544 0.535 0.486 0.569
Table 5. Summary of Alternative Rankings and Standard Deviation from Various MCDM Techniques
Name of
Alternative WSM AHP R-AHP TOPSIS Ave. STDEV
Alt 1 1 1 1 1 1 0
Alt 2 3 2 3 3 2.8 0.43
Alt 3 4 4 4 2 3.5 0.87
Alt 4 5 5 5 4 4.8 0.43
Alt 5 2 3 2 5 3 1.22
ݡ⦽ ⢽ᵡ᪅₉ෝ Ǎ⦽ đŝ Alt 5᮹ Ğᬑ 1.22ಽ ݅ෙ ݡᦩᨱ
እ⧕ᕽ׳íӹ᪡᪅₉᮹Ⓧʑaaᰆⓑäᮝಽӹ┡ԍᮝ໑Alt 1ᮡ᪅₉a0ᮝಽ1᭥ᖁᱶᨱ۵༉ुMCDM ʑჶ᮹ᙽ᭥ᨱᕽ
zᮡ sᯕ ӹ᪅۵ äᮝಽ ӹ┡ԍ݅.
3.2 ൵ۗ׆ஜଭॷէ୨׆࣑ଭୡ
⟝ḡ ᯕು᮹ ᱢᬊᮥ ᭥⧕ᕽ۵ ݡᦩᄥ ⬉ŝḡᙹᨱ ݡ⦽ s᮹
༉⪙⧉ŝaᵲ⊹᮹༉⪙⧉ᮥ༉ࢱŁಅ⧕⦽݅. ᕽTable 3ᨱᕽaᱶ⦽⟝ḡsᮥᯕᬊ⦹ᩡ݅. Fuzzy MCDM ႊჶᮥᱢᬊ⦹
ʑ᭥⧕Fuzzy WSM, Fuzzy AHP, Fuzzy ᙹᱶAHP, Fuzzy TOPSISᨱݡ⧕ᇥᕾ⦹ᩡᮝ໑đŝ۵Table 6ŝz݅. Fuzzy WSMŝFuzzy ᙹᱶAHP, Fuzzy TOPSIS۵zᮡđŝෝᅕᩡ۵ ߑʑ᳕᮹WSM, ᙹᱶAHP ॒ŝ࠺ᯝ⦹ᩡᮝ໑Fuzzy AHP۵
ʑ᳕᮹AHP᪡݅ෙᙽ᭥ෝᅕᩡ݅. ᯕᔢ᮹đŝಽᇡ░Alt 1ᯕ
1॒ᯕŁAlt 3a4॒, Alt 4a5॒ᮝಽ༉ࢱa࠺ᯝ⦹íᱽࡹᨩᮝ ӹAlt 2᪡Alt 5۵݅ෙMCDM ႊჶॅŝzᯕᙽ᭥᮹ᄡ࠺ᯕ
ᝍ⧩݅. ੱ⦽MCDM ʑჶŝ ษ₍aḡಽ ⢽ᵡ⠙₉ෝ Ǎ⦹ᩍᅙ
đŝAlt 3ŝ4۵⢽ᵡ⠙₉a0ᮝಽᔑ⇽ࡹᨕ༉ुFuzzy MCDM ʑჶᨱᕽݡᦩ᮹ᙽ᭥۵bb4॒ŝ5॒ᮥӹ┡ԥᮥᙹᯩᨩ
݅. ੱ⦽ʑ᳕᮹MCDM ʑჶŝ۵݅íAlt 1ᨱᕽᙽ᭥᮹ᄡ࠺
ᯕᔾĉ1᭥ᖁᱶᨱ݅ෙFuzzy MCDMᮥŁಅ⦹۵äᯕၵ௭ Ḣ⦹݅.
Table 6. Summary of Alternative Rankings and Standard Deviation from Various Fuzzy MCDM Techniques
Name of Alternative Fuzzy-WSM Fuzzy AHP Fuzzy-R-AHP Fuzzy TOPSIS Ave. * STDEV
Alt 1 1 2 1 1 1.25 0.43
Alt 2 2 1 2 3 2 0.71
Alt 3 4 4 4 4 4.0 0
Alt 4 5 5 5 5 5.0 0
Alt 5 3 3 3 2 2.75 0.43
* Fuzzy WSM, AHP, ս܁AHP, TOPSIS ѓѪχथŒॠٕڼ
4. đು
ᅙᩑǍ۵ಽქᜅ✙ᬑᖁᙽ᭥đᱶᮥ᭥⦽⟝ḡ݅ʑᵡ᮹ᔍđᱶ ʑჶ ᱢᬊ᮹ ┡ݚᖒᮥ ᱽ⦹ʑ ᭥⧕ ᙹᯱᬱ ĥ⫮ᙹพ ྙᱽᨱ
ᱢᬊ⦹ᩡ݅. ݡᔢݡᦩॅ᮹⠪aʑᵡᨱݡ⦽ᯱഭ᮹⢽ᵡ⪵, aᵲ⊹
᮹đᱶᯕ࠺ᯝ⦹íᙹ⧪ࡹᨩࠥᖁ┾⦽݅ʑᵡ᮹ᔍđᱶʑჶ ᮹₉ᯕಽᯙ⧕đŝa⪶ᩑ⦹íݍḩᙹᯩᮭᯕ⪶ᯙ⦹ᩡ݅.
⦹ḡอ⟝ḡ݅ʑᵡ᮹ᔍđᱶʑჶᮥᯕᬊ⧁Ğᬑ᮹ᔍđᱶᨱᔍᬊ
ࡽᯱഭ᮹ᇩ⪶ᝅᖒŝ⠪aʑᵡᨱݡ⦽aᵲ⊹᮹ᇩ⪶ᝅᖒᮥ༉ࢱ
Łಅ⦹ᩍݡᦩॅ᮹ᬑᖁᙽ᭥ෝᱽ⧁ᙹᯩᮝအಽእƱᱢᦩᱶᱢ ᯙᔍᨦ᮹ᙽ᭥ෝࠥ⇽⧁ᙹᯩ݅. ᕽᔍᨦ᮹ᬑᖁᙽ᭥ෝđᱶ⦹
۵ ྙᱽᨱᕽᯱഭ᪡ aᵲ⊹᮹ ᇩ⪶ᝅᖒᮥŁಅ⧁ ᙹ ᯩ۵⟝ḡ
݅ʑᵡ᮹ᔍđᱶʑჶᮥ⪽ᬊ⧁Ğᬑႊჶ᮹ᄡ⪵ಽᯙ⦽ᙽ᭥᮹
ᄡ࠺ᖒᮥ↽ᗭ⪵⦹ᩍᯝšࡽᙽ᭥ෝᱽ⦹۵äᯕᅕ݅⬉ŝᱢᯝ
ᙹ ᯩ݅. ⨆⬥ ݅᧲⦽ ᱢᬊ ᔍಡa Ǎࡽ݅.
qᔍ᮹ɡ
ᅙᩑǍ۵ᕽᬙŝ⦺ʑᚁݡ⦺ƱƱԕ⦺ᚁᩑǍእḡᬱᮝಽᙹ⧪
ࡹᨩܩ݅.
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