Some q-Rung Picture Fuzzy Dombi Hamy Mean Operators with Their Application to Project Assessment

Jiahuan He,Xindi Wang,Runtong Zhang,Li Li

doi:10.3390/math7050468

Abstract

The recently proposed q-rung picture fuzzy set (q-RPFSs) can describe complex fuzzy and uncertain information effectively. The Hamy mean (HM) operator gets good performance in the process of information aggregation due to its ability to capturing the interrelationships among aggregated values. In this study, we extend HM to q-rung picture fuzzy environment, propose novel q-rung picture fuzzy aggregation operators, and demonstrate their application to multi-attribute group decision-making (MAGDM). First of all, on the basis of Dombi t-norm and t-conorm (DTT), we propose novel operational rules of q-rung picture fuzzy numbers (q-RPFNs). Second, we propose some new aggregation operators of q-RPFNs based on the newly-developed operations, i.e., the q-rung picture fuzzy Dombi Hamy mean (q-RPFDHM) operator, the q-rung picture fuzzy Dombi weighted Hamy mean (q-RPFDWHM) operator, the q-rung picture fuzzy Dombi dual Hamy mean (q-RPFDDHM) operator, and the q-rung picture fuzzy Dombi weighted dual Hamy mean (q-RPFDWDHM) operator. Properties of these operators are also discussed. Third, a new q-rung picture fuzzy MAGDM method is proposed with the help of the proposed operators. Finally, a best project selection example is provided to demonstrate the practicality and effectiveness of the new method. The superiorities of the proposed method are illustrated through comparative analysis.

Highlights

In the framework of multi-attribute group decision-making (MAGDM), decision-makers evaluate all alternatives from multiple aspects
We present some properties of the q-RPFDDHM operator
We propose novel operational rules of q-rung picture fuzzy numbers (q-RPFNs) on the basis of Dombi t-norm and t-conorm

Summary

Introduction

In the framework of multi-attribute group decision-making (MAGDM), decision-makers evaluate all alternatives from multiple aspects. When using MAGDM models to deal with real decision-making problems, a very important issue is to express decision-makers’ evaluation information over alternatives properly. Due to the complexity of decision-making problems and the inherent fuzziness information, it is almost impossible for decision-makers to express their decision opinions in crisp numbers. Atanassov [1] provided a new methodology to deal with fuzzy information, called intuitionistic fuzzy sets (IFSs). IFSs are constructed by a series of order pairs, called intuitionistic fuzzy numbers (IFNs), having a membership and a non-membership degree. An obvious fact is that in IFSs, once the membership and non-membership degrees are determined, the indeterminacy degree or hesitancy degree is a default.

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Conclusion