A Novel Trapezoidal Bipolar Fuzzy TOPSIS Method for Group Decision-Making
In this research article, the notions of bipolar fuzzy numbers, trapezoidal bipolar fuzzy numbers, triangular bipolar fuzzy numbers and bipolar fuzzy linguistic variables are introduced. Ranking function on the set of all bipolar fuzzy numbers, and the expressions for the ranking of trapezoidal and triangular bipolar fuzzy numbers are derived. A group decision making method based on trapezoidal bipolar fuzzy TOPSIS method is proposed, and the implementation of the proposed method in the selection of best project proposal is presented. Finally, a theoretical comparison of the proposed trapezoidal bipolar fuzzy TOPSIS method with other multi-criteria decision making methods such as TOPSIS, bipolar fuzzy TOPSIS and bipolar fuzzy ELECTRE I is discussed.
KeywordsBipolar fuzzy numbers Trapezoidal bipolar fuzzy numbers Triangular bipolar fuzzy numbers Bipolar fuzzy linguistic values Trapezoidal bipolar fuzzy TOPSIS
The authors are highly thankful to the Associate Editor, and the anonymous referees for their valuable comments and suggestions.
Compliance with ethical standards
Conflict of interest
The authors declare that they have no conflict of interest regarding the publication of the research article.
- Akram M, Alshehri NO, Davvaz B, Ashraf A (2016) Bipolar fuzzy digraphs in decision support systems. J Mult Valued Log Soft Comput 27(5–6):531–551Google Scholar
- Akram M, Feng F, Borumand Saeid A, Fotea V (2017) A new multiple criteria decision-making method based on bipolar fuzzy soft graphs. Iran J Fuzzy Syst 15(4):73–92Google Scholar
- Benayoun R, Roy B, Sussman N (1966) Manual de Reference du Programme Electre. Note de Synthese et Formation, No. 25 Direction Scientific SEMA Paris, FranceGoogle Scholar
- Burillo P, Bustince H, Mohedano V (1994) Some definition of intuitionistic fuzzy number. Fuzzy based expert systems, fuzzy Bulgarian enthusiasts, Sofia, Bulgaria, 28–30Google Scholar
- Dey PP, Pramanik S, Giri BC (2016) TOPSIS for solving multi-attribute decision making problems under bipolar neutrosophic environment. In: Smarandache F, Pramanik S (eds) New trends in neutrosophic theory and applications. Pons Editions, Brussels, pp 65–77Google Scholar
- Lee KM (2000) Bipolar-valued fuzzy sets and their operations. In: Proceheeding the international conference on intelligent technologies, Bangkok, Thailand, pp 307–312Google Scholar
- Roszkowska E (2011) Multi-criteria decision making models by applying the TOPSIS method to crisp and interval data. Mult Crit Decis Mak Univ Econ Katow 6:200–230Google Scholar
- Selvachandran G, Salleh AR (2014) Intuitionistic fuzzy linguistic variables and intuitionistic fuzzy hedges. Far East J Math Sci 95(2):221–233Google Scholar
- Zhang WR (1994) Bipolar fuzzy sets and relations. A computational framework for cognitive modeling and multiagent decision analysis. In: Proceedings of IEEE conference fuzzy information processing society biannual conference, pp 305–309Google Scholar
- Zhang WR (1998) Bipolar fuzzy sets. Fuzzy Syste Proc IEEE World Congr Comput Intell 1:835–840Google Scholar