Minimal decomposition theorems and minimal extension principle for picture fuzzy sets

Mohammad Kamrul Hasan, Md. Yasin Ali, Abeda Sultana, Nirmal Kanti Mitra

Abstract


Picture fuzzy set theory was originally proposed as a mathematical tool to deal with uncertainty by taking yes, no, neutral memberships of an element of a universal set. It has been studied by a host of researchers theoretically and practically. But still now, the structural properties of picture fuzzy sets are not widely studied. In this article, we propose lower (𝛼, 𝛾, 𝛽)-cut and strong lower (𝛼, 𝛾, 𝛽)-cut of a picture fuzzy set and illustrate some of their properties. Three minimal decomposition theorems for picture fuzzy sets are introduced by lower (𝛼, 𝛾, 𝛽)-cut, strong lower (𝛼, 𝛾, 𝛽)-cut and level set of picture fuzzy sets with illustrations by a numerical example. Some properties of minimal extension principle are also described by using the lower (𝛼, 𝛾, 𝛽)-cut and the strong lower (𝛼, 𝛾, 𝛽)-cut of picture fuzzy sets. Finally, arithmetic operations for picture fuzzy sets are illustrated by using the minimal extension principle.

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Published: 2022-03-28

How to Cite this Article:

Mohammad Kamrul Hasan, Md. Yasin Ali, Abeda Sultana, Nirmal Kanti Mitra, Minimal decomposition theorems and minimal extension principle for picture fuzzy sets, J. Math. Comput. Sci., 12 (2022), Article ID 120

Copyright © 2022 Mohammad Kamrul Hasan, Md. Yasin Ali, Abeda Sultana, Nirmal Kanti Mitra. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

 

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