Chebyshev Distance Entropy Combined with TODIM Method in Lq-ROFS Multiattribute Group Decision Making

Abstract

Linguistic q-rung orthopair fuzzy numbers (Lq-ROFNs) are composed of a set of q-rung orthopair fuzzy numbers (q-ROFNs) with membership and nonmembership degrees of linguistic variables, which can be regarded as an extension of linguistic intuitionistic fuzzy numbers (LIFNs) and linguistic Pythagorean fuzzy numbers (LPFNs). Compared with LIFNs and LPFNs, Lq-ROFNs have a wider range of applicability because the value of q can have a wider range, thus allowing to handle more multiattribute group decision making (MAGDM) problems. Based on Lq-ROFS, this paper first proposes the Chebyshev distance metric, then develops the Chebyshev distance entropy for deriving objective solution of decision makers’ (DMs’) weight vector and attribute weight vector by combining the metric and entropy measure. The TODIM method has been widely valued by the society and has achieved good results in many MAGDM problems. Subsequently, the TODIM decision method in Lq-ROFS is presented and combined with the Chebyshev distance entropy model as a new decision method (CDE-TODIM) to solve the MAGDM problems. This method process is objective and direct and takes into account the decision maker’s preferences, and the decision results are more persuasive. Finally, the effectiveness and rationality of this MAGDM method are illustrated by a case as well as comparisons.