Fuzzy Linmap Method for Multiattribute Group Decision Making With Linguistic Variables and Incomplete Information

Abstract

The aim of this paper is to develop a fuzzy linear programming technique for multidimensional analysis of preference (FLINMAP) in multiattribute group decision making problems with linguistic variables and incomplete preference information. In this paper, linguistic variables are used to assess an alternative on qualitative attributes using fuzzy ratings corresponding to some triangular fuzzy numbers. Each alternative is assessed on the basis of its distance to a fuzzy positive ideal solution (FPIS) which is unknown a priori. The FPIS and the weights of attributes are calculated by constructing a new linear programming model based on the group consistency and inconsistency indices defined on the basis of preferences between alternatives given by the decision makers. The distance of each alternative to the FPIS can be calculated to determine the ranking order of all alternatives. The implementation process of this methodology is demonstrated with an example.

On optimal decision for QoS-aware composite service selection

“…The proposed approach enables decision makers to select OoSaware services from the marketplace. In the multiple attribute decision-making applications, our approach is a complement way to the extension works of Srinivasan and Shocker (1973) and Li and Sun (2007). Table 10 The optimal solution of Simplex method for rating of decision maker d3.…”

Managing incomplete preference relations in decision making: A review and future trends

“…(ii) LPRs based on virtual linguistic term sets [42,85]; and (iii) LPRs based on a cardinal approach [47,68].…”

Consistency based completion approaches of incomplete preference relations in uncertain decision contexts

“…In this subsection we present the methodologies classified depending on the linguistic frameworks they use: (i) 2-tuple LPRs [35], [41], [42]; (ii) LPRs based on virtual linguistic term sets [43], [44]; and (iii) LPRs based on a cardinal approach [45], [25].…”

“…(iii) LPRs based on a cardinal approach. a) Li et al [45] propose an extension of the well known LINMAP method [48] to deal with decision making problems with fuzzy linguistic information. Each alternative is assessed on the basis of its distance to a fuzzy positive ideal solution (FPIS) which is unknown, using a new method to calculate the distance between trapezoidal fuzzy number scores.…”