Extension principles for picture fuzzy sets

Autor: Mohammad Kamrul Hasan, Md. Yasin Ali, Abeda Sultana, Nirmal Kanti Mitra
Rok vydání: 2023
Předmět:
Zdroj: Journal of Intelligent & Fuzzy Systems. 44:6265-6275
ISSN: 1875-8967
1064-1246
DOI: 10.3233/jifs-220616
Popis: Picture fuzzy set (PFS), is a newly developed apparatus to treaty with uncertainties in problems where the opinions are yes, no, neutral, and refusal types. Extension principle is one of the key tools for describing uncertainties. It provides a general method for existing classical mathematical concepts to address fuzzy quantities. It has numerous applications in various arena of our real life. However, there are less works on extension principle for picture fuzzy sets. In this article, new extension principles namely minimal extension principle and average extension principle are proposed for picture fuzzy sets. Various properties of the minimal extension principle and the average extension principle for PFSs are also established. We also prove some properties of Zadeh’s extension principle for PFSs. Finally, arithmetic operations for PFSs based on the average extension principle are developed with numerical illustrations.
Databáze: OpenAIRE
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