Interval Type-2 Trapezoidal Fuzzy Decision- Making Method with Consistency-Improving Algorithm and DEA Model

Abstract

Interval type-2 fuzzy sets (IT2FSs) are useful and valuable tool to describe the decision makers' qualitative evaluation information. This paper designs a novel interval type-2 trapezoidal fuzzy decision-making (IT2TFDM) method, in which the local consistency adjustment strategy (LCAS) and interval type-2 fuzzy data envelopment analysis (DEA) are presented. First, in order to sufficiently describe the uncertain evaluation information, the definition of IT2TrFPRs is introduced, which is followed by the presentation of order consistency and multiplicative consistency for IT2TrFPRs. Then, an approach is proposed to check whether an IT2TrFPR is multiplicative consistent, and we construct a convergent consistency-improving algorithm, wherein the LCAS is utilized to retain the preference evaluation information of decision makers as much as possible. Furthermore, in order to determine the interval type-2 trapezoidal fuzzy priority weight vector, we investigate an interval type-2 trapezoidal fuzzy DEA model. An IT2TFDM method is proposed to obtain the reliable ranking of the alternatives. Finally, a fog-haze influence factor selection problem is given to show the practicality of the proposed IT2TFDM method, and the comparative analysis is carried out to clarify its validity and merits.