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Some Novel Interactive Hybrid Weighted Aggregation Operators with Pythagorean Fuzzy Numbers and Their Applications to Decision Making

by Na Li 1, Harish Garg 2,* and Lei Wang 1,*
1
Department of Basic Teaching, Liaoning Technical University, Huludao 125105, China
2
School of Mathematics, Thapar Institute of Engineering and Technology, Deemed University, Patiala 147004, Punjab, India
*
Authors to whom correspondence should be addressed.
Mathematics 2019, 7(12), 1150; https://doi.org/10.3390/math7121150
Received: 29 October 2019 / Revised: 21 November 2019 / Accepted: 21 November 2019 / Published: 24 November 2019
A Pythagorean fuzzy set (PFS) is one of the extensions of the intuitionistic fuzzy set which accommodate more uncertainties to depict the fuzzy information and hence its applications are more extensive. In the modern decision-making process, aggregation operators are regarded as a useful tool for assessing the given alternatives and whose target is to integrate all the given individual evaluation values into a collective one. Motivated by these primary characteristics, the aim of the present work is to explore a group of interactive hybrid weighted aggregation operators for assembling Pythagorean fuzzy sets to deal with the decision information. The proposed aggregation operators include interactive the hybrid weighted average, interactive hybrid weighted geometric and its generalized versions. The major advantages of the proposed operators to address the decision-making problems are (i) to consider the interaction among membership and non-membership grades of the Pythagorean fuzzy numbers, (ii) it has the property of idempotency and simple computation process, and (iii) it possess an adjust parameter value and can reflect the preference of decision-makers during the decision process. Furthermore, we introduce an innovative multiple attribute decision making (MADM) process under the PFS environment based on suggested operators and illustrate with numerous numerical cases to verify it. The comparative analysis as well as advantages of the proposed framework confirms the supremacies of the method. View Full-Text
Keywords: Pythagorean fuzzy sets; aggregation operators; MADM; hybrid operators Pythagorean fuzzy sets; aggregation operators; MADM; hybrid operators
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Li, N.; Garg, H.; Wang, L. Some Novel Interactive Hybrid Weighted Aggregation Operators with Pythagorean Fuzzy Numbers and Their Applications to Decision Making. Mathematics 2019, 7, 1150.

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