Some q‐rung interval‐valued orthopair fuzzy Maclaurin symmetric mean operators and their applications to multiple attribute group decision making

Abstract

In this paper, according to the Maclaurin symmetric mean (MSM) operator, the dual MSM (DMSM) operator and the q-rung interval-valued orthopair fuzzy set (q-RIVOFS), we develop some novel MSM operators under the q-rung interval-valued orthopair fuzzy environment, such as, the q-rung interval-valued orthopair fuzzy MSM operator, the q-rung interval-valued orthopair fuzzy weighted MSM (q-RIVOFWMSM) operator, the q-rung interval-valued orthopair fuzzy DMSM operator, and the q-rung interval-valued orthopair fuzzy weighted DMSM operator. In addition, some precious properties and numerical examples of these new operators are given in detail. These new operators have the advantages of considering the interrelationship of arguments and can deal with multiple attribute group decision-making problems with q-rung interval-valued orthopair fuzzy information. Finally, a reality example for green suppliers selection in green supply chain management is provided to demonstrate the proposed approach and to verify its rationality and scientific. green suppliers selection, multiple attribute group decision making (MAGDM), q-RIVOFWDMSM operator, q-RIVOFWMSM operator, q-rung interval-valued orthopair fuzzy sets (q-RIVOFSs) | INTRODUCTIONIn the study of fuzzy sets (FSs) 1 fields, finding the suitable way to express evaluation information is a hot topic. Although the intuitionistic FSs (IFSs) 2-7 and Pythagorean FSs (PFSs) [8][9][10][11][12][13][14][15][16] have emerged as useful tools to deal with actual decision-making problems, however, the scope of their assessment information remains limited. Thus, to overcome this limitation, the q-rung orthopair fuzzy set (q-ROFS), 17 which is characterized by the sum of q-th power of membership and nonmembership is less or equal to 1, was proposed for MADM problems. Since that, the q-ROFS has aroused the attention of a large number of scholars since its appearance. 18-21 Based on the weighted average (WA) operator and the weighted geometric (WG) operator, [22][23][24][25][26] Liu and Wang 27 developed two q-rung orthopair fuzzy aggregation operator to fuse q-rung orthopair fuzzy numbers. Combined q-rung orthopair fuzzy information and MSM operators, Wei, Wei, Wang, Gao, and Wei 28 proposed some new q-rung orthopair fuzzy aggregation operators and studied their applications to potential evaluation of emerging technology commercialization. Liu, Wang and Liu 29 proposed some q-rung orthopair fuzzy Heronian mean operators and q-rung orthopair fuzzy partitioned Heronian mean operators for MADM, and then some special cases about these operators were discussed. Based on the cosine similarity measure and cotangent similarity measure, Wang, Wang, Wei, and Wei 30 defined some novel q-rung orthopair fuzzy cosine and cotangent similarity measures. Bai, Zhu, Wang, and Zhang 31 defined some q-rung orthopair fuzzy partitioned Maclaurin symmetric mean (MSM) operators for MADM. Xu, Shang, Wang, Wu, and Huang 32 combined the q-ROFS and the dual hesitant fuzzy set to propose the q-rung dual hesitant orthopair fuzz...

Picture Fuzzy Maclaurin Symmetric Mean Operators and Their Applications in Solving Multiattribute Decision-Making Problems

“…Now, we present some MSM operators that are discussed already and analyze their weaknesses. e notion of MSM operator has been discussed by several authors including Qin and Liu [30], Liu et al [31], Wei and Lu [32], Yang and Pang [33], Wei et al [34], Liu et al [35], Wang et al [36], Qin et al [37], Liu and Qin [38], Wang et al [39], Yu et al [40], and Ju et al [41]. We already discussed the significance of the MSM operators earlier.…”

“…Liu et al [35] proposed power QROFMSM operators by merging power AO with QROFMSM operators for decision-making approaches. Wang et al [36] extended the notion of QROFMSM operators to the frame of interval-valued qROFSs by expressing the DM and the DNM using a closed subinterval of [0, 1]. e MSM operators in hesitant fuzzy settings were proposed by Qin et al [37] while the MSM operators for linguistic variables in the intuitionistic fuzzy layout were discussed by Liu and Qin [38].…”

Multi-Attribute Group Decision-Making Based on Interval-Valued q-Rung Orthopair Fuzzy Power Generalized Maclaurin Symmetric Mean Operator and Its Application in Online Education Platform Performance Evaluation

“…MAGDM methods based on q-ROFSs have received much attention [50][51][52]. Similarly, some MAGDM methods under IVq-ROFSs have been proposed [53][54][55][56]. Nevertheless, these methods still have a drawback, i.e., they fail to handle the complicated interrelationship between attributes and simultaneously eliminate the bad influence of decision-makers' evaluation values.…”

A new possibility degree measure for interval‐valued q‐rung orthopair fuzzy sets in decision‐making

“…To incorporate the features of interrelation between the pairs of the attributes, Xu et al 42 presented Muirhead mean AOs for IV‐ROFS with dual hesitant fuzzy information. Wang et al 43 presented Maclaurin symmetric mean (MSM) operators for IV‐ROFS for solving the DMPs. Wang and Li 28 presented some hybrid AO.…”