Multiple attribute group decision‐making based on order‐α divergence and entropy measures under q‐rung orthopair fuzzy environment

Abstract

The q‐rung orthopair fuzzy set (qROPFS), proposed by Yager, is a more effective and proficient tool to represent uncertain or vague information in real‐life situations. Divergence and entropy are two important measures, which have been extensively studied in different information environments, including fuzzy, intuitionistic fuzzy, interval‐valued fuzzy, and Pythagorean fuzzy. In the present communication, we study the divergence and entropy measures under the q‐rung orthopair fuzzy environment. First, the work defines two new order‐α divergence measures for qROPFSs to quantify the information of discrimination between two qROPFSs. We also examine several mathematical properties associated with order‐α qROPF divergence measures in detail. Second, the paper introduces two new parametric entropy functions called “order‐α qROPF entropy measures” to measure the degree of fuzziness associated with a qROPFS. We show that the proposed order‐α divergence and entropy measures include several existing divergence and entropy measures as their particular cases. Further, the paper develops a new decision‐making approach to solve multiple attribute group decision‐making problems under the qROPF environment where the information about the attribute weights is completely unknown or partially known. Finally, an example of selecting the best enterprise resource planning system is provided to illustrate the decision‐making steps and effectiveness of the proposed approach.

Undergraduate teaching audit and evaluation using an extended MABAC method under q ‐rung orthopair fuzzy environment

“…Employing the Euclidean distance operator, the distance of each university from the BBA vector G can be computed by Equation (15)…”

“…14 When the rung q increases, more orthopairs can meet the restricted condition and then a wider scope of fuzzy information can be expressed. 15,16 The q-ROFSs offer more flexibility and freedom for decision makers to express their uncertain information by adjusting the value of the parameter q dynamically. 17,18 Given these advantages, the q-ROFSs have been recently utilized to deal with uncertainty in many areas, which include classroom teaching quality assessment, 19 online shopping decision making, 20 investment evaluation, 21 green supplier selection, 16 and enterprise GONG ET AL.…”

“…A q ‐ROFS is characterized by the degrees of membership and nonmembership, whose sum of the q th power is not exceeding one 14 . When the rung q increases, more orthopairs can meet the restricted condition and then a wider scope of fuzzy information can be expressed 15,16 . The q ‐ROFSs offer more flexibility and freedom for decision makers to express their uncertain information by adjusting the value of the parameter q dynamically 17,18 .…”

Uncertainty measures for probabilistic hesitant fuzzy sets in multiple criteria decision making

“…Hence, the future work could be extended to the development of application for PHFE entropy measures in different areas of decision making, especially, those are based on the relationship of entropy measure with distance measure, 22 divergence measure, 23 and belief entropy measure. 24 Moreover, there exist good prospects for the further study of the proposed kinds of entropy measures which can be extended to the other fuzzy sets including neutrosophic sets, 25 picture fuzzy sets, 26 Pythagorean fuzzy sets, 27,28 Pythagorean probabilistic hesitant fuzzy sets, 29 q-rung orthopair fuzzy sets, 30 and so forth.…”

Knowledge measure for the q‐rung orthopair fuzzy sets

“…Peng et al 23 proposed an algorithm for emergency decision making using . Verma 24 explained order‐ divergence and entropy measures for and applied to multiattribute group decision making problems. Mi et al 25 proposed VIKOR method for and used it in hospitality brand management.…”