Abstract

The proposed q-rung orthopair fuzzy set (q-ROFS) and picture fuzzy set (PIFS) are two powerful tools for depicting fuzziness and uncertainty. This paper proposes a new tool, called q-rung picture linguistic set (q-RPLS) to deal with vagueness and impreciseness in multi-attribute group decision-making (MAGDM). The proposed q-RPLS takes full advantages of q-ROFS and PIFS and reflects decision-makers’ quantitative and qualitative assessments. To effectively aggregate q-rung picture linguistic information, we extend the classic Heronian mean (HM) to q-RPLSs and propose a family of q-rung picture linguistic Heronian mean operators, such as the q-rung picture linguistic Heronian mean (q-RPLHM) operator, the q-rung picture linguistic weighted Heronian mean (q-RPLWHM) operator, the q-rung picture linguistic geometric Heronian mean (q-RPLGHM) operator, and the q-rung picture linguistic weighted geometric Heronian mean (q-RPLWGHM) operator. The prominent advantage of the proposed operators is that the interrelationship between q-rung picture linguistic numbers (q-RPLNs) can be considered. Further, we put forward a novel approach to MAGDM based on the proposed operators. We also provide a numerical example to demonstrate the validity and superiorities of the proposed method.

Highlights

  • Decision-making is a common activity in daily life, aiming to select the best alternative from several candidates

  • Motivated by the ideas of q-rung orthopair fuzzy set (q-ROFS) and PIFS, we propose the concept of q-rung picture fuzzy set (q-RPFS), which takes the advantages of both q-ROFS and PIFS

  • We provide some operations for q-rung picture linguistic numbers (q-RPLNs)

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Summary

Introduction

Decision-making is a common activity in daily life, aiming to select the best alternative from several candidates. As one of the most important branches of modern decision-making theory, multi-attribute group decision-making (MAGDM) has been widely investigated and successfully applied to economics and management due to its high capacity to model the fuzziness and uncertainty of information [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]. Owing to the complicacy of decision-making problems, the precondition is to represent the fuzzy and vague information appropriately in the process of MAGDM. Atanassov [16] originally proposed the concept of intuitionistic fuzzy set (IFS), characterized by a membership degree and a non-membership degree. Thereafter, Yager [21] proposed the concept of Pythagorean fuzzy set (PYFS)

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