A Hybrid Multiple-Attribute Decision-Making Model Under Complex Q-Rung Orthopair Fuzzy Hamy Mean Aggregation Operators

Introduction

One of the most common and influential research fields in decision science is MADM. It indicates that there is a set of alternatives that decision makers (DMs) need to assess with multiple attributes. The objective of MADM is to select from a finite number of alternatives the optimal one. It is the vital branch of the decision-making theory which has been extensively used in human activities. To describe the uncertainties, Zadeh (1965) put forward the concept of fuzzy sets (FSs) which has the membership degree (MD) only. Later on, to describe the fuzzy information, Atanassov (1986) introduced intuitionistic fuzzy sets (IFSs) which have the MD as well as non-membership degree (NMD), satisfies the condition that sum of MD and NMD would be less than or equal to 1. In recent decades, Pythagorean fuzzy sets (PFSs) (Yager, 2013) have proved to be very useful for describing uncertainty and complexity of the MADM problems. The PFS is expressed by the functions of membership and non-membership, which fulfils the condition that sum of squares of them is not greater than 1. The PFS is more useful to solve the MADM problems than IFSs, i.e., if MD=0.7 and NMD=0.6 then 0.7²+0.6²=0.85<1, it is Pythagorean fuzzy number but not an intuitionistic fuzzy number. After that Fermatean fuzzy sets (FFSs) were proposed by Senapati and Yager (2020). But FFSs have some drawbacks. To overcome these drawbacks, Yager (2016) set forward the concept of q-rung orthopair fuzzy sets (q-ROFSs) to express complex fuzzy information and have widely been applied to the MADM problems. In q-ROFSs, each element satisfies the condition that the sum of the qth power of membership function and non-membership function is not greater to 1. The q-ROFSs provide more flexibility, stronger model ability and larger freedom for decision makers in expressing their preferences on alternatives. To choose the optimal alternative in generalized fuzzy environment, several decision-making approaches (Akram et al., 2021a,b,c,d; Akram et al., 2020; Akram et al., 2019; Akram and Naz, 2019; Akram et al., 2018; Krishankumar et al., 2017,2018,2019; Naz et al., 2021) have been introduced by researchers. Naz et al. (2018) proposed the concepts of Pythagorean fuzzy relations along with its application in MADM. To deal with the MADM problems, Naz and Akram (2019) developed a new decision-making approach based on graph theory in which the decision information is expressed by hesitant fuzzy elements.