HYBRID BI-IDEALS AND HYBRID QUASI-IDEALS IN ORDERED SEMIRINGS

HYBRID BI-IDEALS AND HYBRID QUASI-IDEALS IN ORDERED SEMIRINGS

B. Elavarasan, S. Meenakshi, K. Porselvi

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Abstract

Fuzzy set theory has been proven to be a powerful tool for dealing with uncertainty in decision-making processes. This theory addresses uncertain parameters. Soft set theory is another mathematical concept used for managing uncertainty in decisionmaking processes and imprecision. Integrating the ideas of a fuzzy set and a soft set, Jun et al. established the concept of hybrid structure. We should emphasize that hybrid structures combine soft and fuzzy set theories. The main objective of this paper is to explore the concept of hybrid bi-ideals and hybrid quasi-ideals in ordered semirings. In addition, we construct an example of hybrid bi-ideal and hybrid quasi-ideal in an ordered semiring. We provide various properties of hybrid bi-ideal and hybrid quasi-ideal in ordered semirings.

Keywords

Ordered semiring, regular, hybrid structure, hybrid bi-ideal, and hybrid quasiideal.