Algorithms for complex interval-valued q-rung orthopair fuzzy sets in decision making based on aggregation operators, AHP, and TOPSIS
Corresponding Author
Harish Garg
School of Mathematics, Thapar Institute of Engineering & Technology, Deemed University, Patiala, Punjab, India
Correspondence
Harish Garg, School of Mathematics, Thapar Institute of Engineering & Technology, Deemed University, Patiala 147004, Punjab, India.
Email: [email protected]; https://sites.google.com/site/harishg58iitr/home
Search for more papers by this authorZeeshan Ali
Department of Mathematics and Statistics, International Islamic University Islamabad, Islamabad, Pakistan
Search for more papers by this authorTahir Mahmood
Department of Mathematics and Statistics, International Islamic University Islamabad, Islamabad, Pakistan
Search for more papers by this authorCorresponding Author
Harish Garg
School of Mathematics, Thapar Institute of Engineering & Technology, Deemed University, Patiala, Punjab, India
Correspondence
Harish Garg, School of Mathematics, Thapar Institute of Engineering & Technology, Deemed University, Patiala 147004, Punjab, India.
Email: [email protected]; https://sites.google.com/site/harishg58iitr/home
Search for more papers by this authorZeeshan Ali
Department of Mathematics and Statistics, International Islamic University Islamabad, Islamabad, Pakistan
Search for more papers by this authorTahir Mahmood
Department of Mathematics and Statistics, International Islamic University Islamabad, Islamabad, Pakistan
Search for more papers by this authorAbstract
The interval-valued q-rung orthopair fuzzy set (IVq-ROFS) and complex fuzzy set (CFS) are two generalizations of the fuzzy set (FS) to cope with uncertain information in real decision making problems. The aim of the present work is to develop the concept of complex interval-valued q-rung orthopair fuzzy set (CIVq-ROFS) as a generalization of interval-valued complex fuzzy set (IVCFS) and q-rung orthopair fuzzy set (q-ROFS), which can better express the time-periodic problems and two-dimensional information in a single set. In this article not only basic properties of CIVq-ROFSs are discussed but also averaging aggregation operator (AAO) and geometric aggregation operator (GAO) with some desirable properties and operations on CIVq-ROFSs are discussed. The proposed operations are the extension of the operations of IVq-ROFS, q-ROFS, interval-valued Pythagorean fuzzy, Pythagorean fuzzy (PF), interval-valued intuitionistic fuzzy, intuitionistic fuzzy, complex q-ROFS, complex PF, and complex intuitionistic fuzzy theories. Further, the Analytic hierarchy process (AHP) and technique for order preference by similarity to ideal solution (TOPSIS) method are also examine based on CIVq-ROFS to explore the reliability and proficiency of the work. Moreover, we discussed the advantages of CIVq-ROFS and showed that the concepts of IVCFS and q-ROFS are the special cases of CIVq-ROFS. Moreover, the flexibility of proposed averaging aggregation operator and geometric aggregation operator in a multi-attribute decision making (MADM) problem are also discussed. Finally, a comparative study of CIVq-ROFSs with pre-existing work is discussed in detail.
CONFLICT OF INTEREST
The authors declare no potential conflict of interest.
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