An Approach for Multi-criteria Decision Making Problems with Unknown Weight Information using GRA Method Under the Picture Linguistic Fuzzy Environment

Year 2019, Issue: 28, 5 - 19, 07.05.2019

Muhammad Qiyas , Saleem Abdullah Shahzaib Ashraf , Saifullah Khan

Abstract

In this article we used picture linguistic fuzzy Choquet integral weighted averaging (PLFCIWA) operator for multi-attribute group decision making problem, where the attribute weight information are completely unknown. Firstly, we utilized the PLFCIWA operator to aggregate the total preference value of each alternative by decision makers. An optimization model are used to obtain the weighting vector of the criteria, using the basic ideal of traditional grey relational analysis (GRA) method. The degree of grey relation between every alternative and positive-ideal solution and negative-ideal solution is computed. Then, a relative relational degree is defined to find the ranking order of all alternatives by calculating the degree of grey relation to both the positive-ideal solution (PIS) and negative ideal solution (NIS) simultaneously. Finally, a descriptive example is solved to satisfy effectiveness and practicality of the proposed techniques.

Keywords

Picture linguistic fuzzy set, Picture linguistic fuzzy Choquet integral weighted averaging (PLFCIWA) operator, GRA method

References

• K. T. "Atanassov, Intuitionistic fuzzy sets". Fuzzy Sets Syst; 20(1):87–96,(1986)
• G. I. Adamopoulos and G. P. Pappis, "A fuzzy linguistic approach to a multi-criteria sequencing problems", European Journal of operational Research, 92:628-636, (1996).
• K. T. Atanassov, "More on intuitionistic fuzzy sets", Fuzzy Sets and System,33: 37-46, (1989)
• M. J. Bolaños et al, "Convergence properties of the monotone expectation and its application to the extension of fuzzy measures", Fuzzy Sets and Systems,Vol. 33: No. 2, pp. 201-212, November, (1989)