What is it about?

The Archimedean t-conorm and t-norm (ATT) are well-known for having the capability to generate versatile and flexible operational rules for fuzzy numbers, while the Muirhead mean (MM) operator is an all-in-one aggregation operator for capturing the interrelationships of the aggregated arguments. To this end, the MM operator and the ATT for PHFNs are combined to present a Pythagorean hesitant fuzzy Archimedean MM (PHFAMM) operator and a weighted PHFAMM operator and a new MCDM method based on the presented operators is proposed in this paper.

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Why is it important?

To describe the values of criteria and to generate a sort of alternatives are two important issues in multi-criteria decision-making (MCDM). A superior tool for the former issue is the Pythagorean hesitant fuzzy number (PHFN) and an effective tool for the latter issue is aggregation operator. So far, a number of aggregation operators of PHFNs have been presented within the academia. Each aggregation operator has its own characteristics and can work well for its specific purpose. But there is not yet an aggregation operator of PHFNs that can provide satisfying generality and flexibility in aggregating the values of criteria and capturing the interactions of criteria. The proposed method makes up for this vacancy and can provide desirable generality and flexibility in the aggregation of criterion values and capturing of criterion relationships.

Perspectives

Writing this article was a great pleasure as it has co-authors with whom I have had long-standing admiration for. This article also takes me into the field of fuzzy decision making in artificial intelligence. I hope this article makes what people might think is a boring, slightly abstract area like fuzzy control of artificial intelligence and fuzzy decision making in artificial intelligence, kind of interesting and maybe even exciting.

Xiuyan Guo
Guangxi Key Laboratory of Intelligent Processing of Computer Images and Graphic, Guilin University of Electronic Technology, Guilin, PR China

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This page is a summary of: A new multi-criteria decision-making method based on Pythagorean hesitant fuzzy Archimedean Muirhead mean operators1, Journal of Intelligent & Fuzzy Systems, October 2019, IOS Press, DOI: 10.3233/jifs-190704.
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