Maclaurin symmetric mean operators and their applications in the environment of complex q-rung orthopair fuzzy sets
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Maclaurin symmetric mean operators and their applications in the environment of complex q-rung orthopair fuzzy sets Zeeshan Ali1 · Tahir Mahmood1 Received: 14 May 2019 / Revised: 13 January 2020 / Accepted: 17 March 2020 © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2020
Abstract The Maclaurin symmetric mean (MSM) and dual Maclaurin symmetric mean (DMSM) operators are two aggregation operators to aggregate the q-rung orthopair fuzzy numbers (q-ROFNs) into a single element. The complex q-rung orthopair fuzzy framework is more effective to describe fuzzy information in real decision-making problems. The complex qrung orthopair fuzzy sets (Cq-ROFSs) are more superior to the complex intuitionistic fuzzy sets (CIFSs) and complex pythagorean fuzzy sets (CPFSs) to cope with uncertain and difficult information in the environment of fuzzy set theory. Thus, this manuscript proposes some complex q-rung orthopair fuzzy Maclaurin symmetric mean (Cq-ROFMSM), complex qrung orthopair fuzzy weighted Maclaurin symmetric mean (Cq-ROFWMSM), complex qrung orthopair fuzzy dual Maclaurin symmetric mean (Cq-ROFDMSM) and complex q-rung orthopair fuzzy weighted dual Maclaurin symmetric mean (Cq-ROFWDMSM) operators. Moreover, some properties and special cases of our proposed methods are also introduced. Then we present a multi-attributive group decision-making based on proposed methods. Further, a numerical example is provided to illustrate the flexibility and accuracy of the proposed operators. Last, the proposed methods are compared with existing methods to examine the best emerging technology enterprises. Keywords q-Rung orthopair fuzzy sets · Complex q-rung orthopair fuzzy sets · Maclaurin symmetric mean operators · Dual Maclaurin symmetric mean operators Mathematics Subject Classification 03E72 · 03A72 · 90B50 · 94D05
Communicated by Regivan Hugo Nunes Santiago.
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Tahir Mahmood [email protected] Zeeshan Ali [email protected]
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Department of Mathematics and Statistics, International Islamic University Islamabad, Islamabad, Pakistan 0123456789().: V,-vol
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Z. Ali, T. Mahmood
1 Introduction MAGDM is one of the most important activities in real life to select the best alternative from the set of possible alternatives. Typically, MAGDM problem often requires decision-makers to provide evaluation information about the criteria and the alternatives with a fuzzy set (FS) (Zadeh 1965; Chen and Klein 1997; Roubens 1997; Kahraman 2008; Xiao et al. 2009; Huang 2008; Roy and Maji 2007). The notion of FS proved to be an important tool to cope with difficult information. Further, Atanassove (1999) extended the notion of FS to intuitionistic fuzzy set (IFS) by including the non-membership degree in the concept of FS. The concept of IFS is more reliable than FS to describe effectively the opinion of human beings. Basically, the IFS is characterized by membership and non-membership grade with their sum less than or equal to one. Moreover, Yager (2009) proposed ordered weighted aggregati
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