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A New Approach to Evaluate Regular Semirings in terms of Bipolar Fuzzy k-Ideals Using k-Products

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  • Shahida Bashir
  • Ahmad N. Al-Kenani
  • Tanzila Kausar
  • Rabia Mazhar
  • Ching-Feng Wen

Abstract

In this paper, we provide a generalized form of ideals that is k-ideals of semirings with the combination of a bipolar fuzzy set (BFS). The BFS is a generalization of fuzzy set (FS) that deals with uncertain problems in both positive and negative aspects. The main theme of this paper is to present the idea of α,β-bipolar fuzzy k-subsemiring (k-BFSS), α,β-bipolar fuzzy k-ideals (k-BFIs), and α,β-bipolar fuzzy k-bi-ideals (k-BFbIs) in semirings by applying belongingness ∈ and quasi-coincidence q of the bipolar fuzzy (BF) point. After that, upper and lower parts of k-product of BF subsets of semirings are introduced. Lastly, the notions of k-regular and k-intraregular semirings in terms of ∈,∈∨q-k–BFIs and ∈,∈∨q-k–BFbIs are characterized.

Suggested Citation

  • Shahida Bashir & Ahmad N. Al-Kenani & Tanzila Kausar & Rabia Mazhar & Ching-Feng Wen, 2022. "A New Approach to Evaluate Regular Semirings in terms of Bipolar Fuzzy k-Ideals Using k-Products," Journal of Mathematics, Hindawi, vol. 2022, pages 1-12, June.
    • Handle: RePEc:hin:jjmath:5759130
    DOI: 10.1155/2022/5759130
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