Power Aggregation Operators and VIKOR Methods for Complex q-Rung Orthopair Fuzzy Sets and Their Applications

Harish Garg, Jeonghwan Gwak, Tahir Mahmood and Zeeshan Ali
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Harish Garg: School of Mathematics, Thapar Institute of Engineering and Technology, Deemed University, Patiala 147004, India
Jeonghwan Gwak: Department of Software, Korea National University of Transportation, Chungju 27469, Korea
Tahir Mahmood: Department of Mathematics and Statistics, International Islamic University, Islamabad 44000, Pakistan
Zeeshan Ali: Department of Mathematics and Statistics, International Islamic University, Islamabad 44000, Pakistan

Mathematics, 2020, vol. 8, issue 4, 1-34

Abstract: The aim of this paper is to present the novel concept of Complex q-rung orthopair fuzzy set (Cq-ROFS) which is a useful tool to cope with unresolved and complicated information. It is characterized by a complex-valued membership grade and a complex-valued non-membership grade, the distinction of which is that the sum of q-powers of the real parts (imaginary parts) of the membership and non-membership grades is less than or equal to one. To explore the study, we present some basic operational laws, score and accuracy functions and investigate their properties. Further, to aggregate the given information of Cq-ROFS, we present several weighted averaging and geometric power aggregation operators named as complex q-rung orthopair fuzzy (Cq-ROF) power averaging operator, Cq-ROF power geometric operator, Cq-ROF power weighted averaging operator, Cq-ROF power weighted geometric operator, Cq-ROF hybrid averaging operator and Cq-ROF power hybrid geometric operator. Properties and special cases of the proposed approaches are discussed in detail. Moreover, the VIKOR (“VIseKriterijumska Optimizacija I Kompromisno Resenje”) method for Cq-ROFSs is introduced and its aspects discussed. Furthermore, the above mentioned approaches apply to multi-attribute decision-making problems and VIKOR methods, in which experts state their preferences in the Cq-ROF environment to demonstrate the feasibility, reliability and effectiveness of the proposed approaches. Finally, the proposed approach is compared with existing methods through numerical examples.

Keywords: fuzzy sets; complex fuzzy sets; Pythagorean fuzzy sets; q-rung orthopair fuzzy sets; complex q-rung orthopair fuzzy sets; power aggregation operators (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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