# A Compromise Ratio Method with an Application to Water Resources Management: An Intuitionistic Fuzzy Set

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## Abstract

Water resources management can be regarded as an iterative process of general decision making considering the applications and modifications of waters and related lands within a geographic region. This process helps decision makers to balance their diverse requirements and applications of water as an environmental resource, and to recognize how their activities can have impacts on the long-term sustainability. This paper introduces a new compromise ratio method based on Atanassov’s intuitionistic fuzzy sets under multiple criteria in real-life situations. Atanassov’s intuitionistic fuzzy weighted averaging (AIFWA) operator is applied to aggregate individual judgments of the decision makers to rate the relative importance of the selected criteria and potential alternatives. Then a new Atanassov’s intuitionistic fuzzy ranking index is proposed to analyze the potential alternatives. Finally, the performance of the proposed fuzzy decision-making method is illustrated to a real water resources management problem from the recent literature. Computational results demonstrate that the presented method can be utilized in a large-scale multi-level assessment process to assist the decision makers the optimal solution among the potential alternatives with multiple conflicting and compromising criteria.

## Keywords

Decision analysis Water resources management Fuzzy sets Compromise ratio method## Notes

### Acknowledgements

The authors thank the editor-in-chief and anonymous referees for their constructive comments on this paper.

## References

- Abrishamchi A, Ebrahimian A, Tajrishi M, Marino MA (2005) Case study: application of multicriteria decision making to urban water supply. J Water Resour Plan Manage -ASCE 131(4):326–335CrossRefGoogle Scholar
- Afshar A, Marino MA, Saadatpour M, Afshar A (2011) Fuzzy TOPSIS multi-criteria decision analysis applied to Karun reservoirs system. Water Resour Manage 25:545–563CrossRefGoogle Scholar
- Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87–96CrossRefGoogle Scholar
- Atanassov KT (1994) New operations defined over the intuitionistic fuzzy sets. Fuzzy Sets Syst 61:137–142CrossRefGoogle Scholar
- Atanassov KT, Nikolov NG, Aladjov HT (2001) Remark on two operations over intuitionistic fuzzy sets. Int J Uncertainty Fuzziness Knowl-Based Syst 9(1):71–75Google Scholar
- Boran FE, Genc S, Kurt M, Akay D (2009) A multi-criteria intuitionistic fuzzy group decision making for supplier selection with TOPSIS method. Expert Syst Appl 36:11363–11368CrossRefGoogle Scholar
- Burillo P, Bustince H (1996) Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets. Fuzzy Sets Syst 78:305–316CrossRefGoogle Scholar
- Chen RY (2009) A problem-solving approach to product design using decision tree induction based on intuitionistic fuzzy. Eur J Oper Res 196:266–272CrossRefGoogle Scholar
- Chen TY (2007) Remarks on the subtraction and division operations over intuitionistic fuzzy sets and interval-valued fuzzy sets. INT J Fuzzy Syst 9(3):169–172Google Scholar
- Chen TY (2011) Optimistic and pessimistic decision making with dissonance reduction using interval-valued fuzzy sets. Inf Sci 181:479–502CrossRefGoogle Scholar
- Chen VYC, Lien HP, Liu CH, Liou JJH, Tzeng GH, Yang LS (2011) Fuzzy MCDM approach for selecting the best environment-watershed plan. Appl Soft Comput 11(1):265–275CrossRefGoogle Scholar
- Chung ES, Lee KS (2009) Prioritization of water management for sustainability using hydrologic simulation model and multicriteria decision making techniques. J Environ Manage 90(3):1502–1511CrossRefGoogle Scholar
- Cox E (1998) The fuzzy systems handbook—a practitioner’s guide to building, using and maintaining fuzzy systems. Academic, BostonGoogle Scholar
- De SK, Biswas R, Roy AR (2000) Some operations on intuitionistic fuzzy sets. Fuzzy Sets Syst 114:477–484CrossRefGoogle Scholar
- Deschrijver G, Kerre EE (2004) On the representation of intuitionistic fuzzy t-norms and t-conorms. IEEE T Fuzzy Syst 12:45–61CrossRefGoogle Scholar
- Hajkowicz S, Collins K (2007) A review of multiple criteria analysis for water resource planning and management. Water Resour Manage 21:1553–1566CrossRefGoogle Scholar
- Hajkowicz S, Higgins A (2008) A comparison of multiple criteria analysis techniques for water resource management. Eur J Oper Res 184:255–265CrossRefGoogle Scholar
- Hernandez EA, Uddameri V (2010) Selecting agricultural best management practices for water conservation and quality improvements using Atanassov’s intuitionistic fuzzy sets. Water Resour Manage 24:4589–4612CrossRefGoogle Scholar
- Li DF, Chen GH, Huang ZG (2010) Linear programming method for multiattribute group decision making. Inf Sci 180:1591–1609CrossRefGoogle Scholar
- Loukas A, Mylopoulos N, Vasiliades L (2007) A modeling system for the evaluation of water resources management strategies in Thessaly, Greece. Water Resour Manage 21:1673–1702CrossRefGoogle Scholar
- Lu HW, Huang GH, Zeng GM, Maqsood I, He L (2008) An inexact two-stage fuzzy-stochastic programming model for water resources management. Water Resour Manage 22:991–1016CrossRefGoogle Scholar
- Mitchell HB (2004) A correlation coefficient for intuitionistic fuzzy sets. Int J Intell Syst 19(5):483–490CrossRefGoogle Scholar
- Mousavi SM, Jolai F, Tavakkoli-Moghaddam R (2011) A Fuzzy stochastic multi-attribute group decision-making approach for selection problems. Group Decis Negot. doi: 10.1007/s10726-011-9259-1
- Mousavi SM, Torabi SA, Tavakkoli-Moghaddam R (2012) A hierarchical group decision-making approach for new product selection in a fuzzy environment. Arab J Sci Eng. doi: 10.1007/s13369-012-0430-z
- Opricovic S (2011) Fuzzy VIKOR with an application to water resources planning. Expert Syst Appl 38(10):12983–12990CrossRefGoogle Scholar
- Opricovic S, Tzeng GH (2004) Compromise solution by MCDM methods: a comparative analysis of VIKOR and TOPSIS. Eur J Oper Res 156:445–455CrossRefGoogle Scholar
- Opricovic S, Tzeng GH (2007) Extended VIKOR method in comparison with outranking methods. Eur J Oper Res 178:514–529CrossRefGoogle Scholar
- Rao RV (2013) Decision making in the manufacturing environment: using graph theory and fuzzy multiple attribute decision making methods. Springer, LondonCrossRefGoogle Scholar
- Ryu JH, Palmer RN, Jeong S, Lee JH, Kim YO (2009) Sustainable water resources management in a conflict resolution framework. J Am Water Resour Assoc 45(2):485–499CrossRefGoogle Scholar
- Sanayei A, Mousavi SF, Yazdankhah A (2010) Group decision making process for supplier selection with VIKOR under fuzzy environment. Expert Syst Appl 37:24–30CrossRefGoogle Scholar
- Shu MS, Cheng CH, Chang JR (2006) Using intuitionistic fuzzy sets for fault tree analysis on printed circuit board assembly. Microelectron Reliab 46(12):2139–2148CrossRefGoogle Scholar
- Srdjevic B, Dantas Y, Medeiros P (2008) Fuzzy AHP assessment of water management plans. Water Resour Manage 22:877–894CrossRefGoogle Scholar
- Szmidt E, Kacprzyk J (2000) Distances between intuitionistic fuzzy sets. Fuzzy Set Syst 114:505–518CrossRefGoogle Scholar
- Tavakkoli-Moghaddam R, Mousavi SM, Heydar M (2011) An integrated AHP-VIKOR methodology for plant location selection. Int J Eng Trans B 24(2):127–137Google Scholar
- UNEP (1987) Methodological guidelines for the integrated environmental evaluation of water resources development. International Hydrological Program, UNESCO, United Nations Environmental Program, ParisGoogle Scholar
- Vahdani B, Mousavi SM, Tavakkoli-Moghaddam R (2011) Group decision making based on novel fuzzy modified topsis method. Appl Math Model 35(9):4257–4269CrossRefGoogle Scholar
- Vahdani B, Mousavi SM, Hashemi H, Mousakhani M, Tavakkoli-Moghaddam R (2013) A new compromise solution method for fuzzy group decision-making problems with an application to the contractor selection. Eng Appl Artif Intell 26:779–788Google Scholar
- Weng SQ, Huang GH, Li YP (2010) An integrated scenario-based multi-criteria decision support system for water resources management and planning - A case study in the Haihe River Basin. Expert Syst Appl 37(12):8242–8254CrossRefGoogle Scholar
- Wu HY, Chen JK, Chen IS (2010) Innovation capital indicator assessment of Taiwanese Universities: a hybrid fuzzy model application. Expert Syst Appl 37(2):1635–1642CrossRefGoogle Scholar
- Xu Z (2007) Intuitionistic preference relations and their application in group decision making. Inf Sci 177(11):2363–2379CrossRefGoogle Scholar
- Xu Z (2010) A method based on distance measure for interval-valued intuitionistic fuzzy group decision making. Inf Sci 180:181–190CrossRefGoogle Scholar
- Xu Z (2011) Approaches to multiple attribute group decision making based on intuitionistic fuzzy power aggregation operators. Knowledge-Based Syst 24:749–760CrossRefGoogle Scholar
- Xu Z, Yager RR (2008) Dynamic intuitionistic fuzzy multi-attribute decision making. Int J Approx Reasoning 48:246–262CrossRefGoogle Scholar
- Ye J (2010) Fuzzy decision-making method based on the weighted correlation coefficient under intuitionistic fuzzy environment. Eur J Oper Res 205:202–204CrossRefGoogle Scholar
- Yilmaz B, Harmancioglu NB (2010) Multi-criteria decision making for water resource management: a case study of the Gediz River Basin, Turkey. Water SA 36(5):563–576CrossRefGoogle Scholar
- Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353CrossRefGoogle Scholar
- Zarghami M, Szidarovszky F (2009a) Revising the OWA operator for multi criteria decision making problems under uncertainty. Eur J Oper Res 198:259–265CrossRefGoogle Scholar
- Zarghami M, Szidarovszky F (2009b) Stochastic-fuzzy multi criteria decision making for robust water resources management. Stoch Environ Res Risk Assess 23:329–339CrossRefGoogle Scholar
- Zarghami M, Ardakanian R, Memariani A (2007) Fuzzy multiple attribute decision making on inter-basin water transfers, case study: Transfers to Zayanderud basin in Iran. Water Int 32(2):280–293CrossRefGoogle Scholar
- Zarghami M, Ardakanian R, Memariani A, Szidarovszky F (2008) Extended OWA operator for group decision making on water resources projects. J Water Resour Plan Manage -ASCE 134(3):266–275CrossRefGoogle Scholar