HYBRID RIGHT AND LEFT BI-QUASI IDEALS OF SEMIRINGS - Meenakshi, S; Muhiuddin, G; Porselvi, K; Elavarasan, B (TWMS journal of applied and engineering mathematics, 2025)
The fuzzy set is an excellent tool for dealing with indeterminacy that can be clearly and effectively analysed from the decision-maker's viewpoint, and it is extremely helpful for showing people's hesitations in their everyday interactions. In order to deal with practical problems, soft set theory has recently been created. By combining the fuzzy and soft sets, Jun et al. created hybrid structures. Hybrid structures are soft-set and fuzzy-set speculations. The concepts of hybrid bi-quasi ideal, hybrid right bi-quasi ideal, and hybrid left bi-quasi ideal of semirings are addressed in this paper. We also explore the equivalent conditions for a subset of a semiring to be a right bi-quasi ideal and for the semiring to be regular. Hybrid right (left) bi-quasi ideals in semirings are used to characterise the regular semiring. Keywords: Semiring, ideal, right (left) bi-quasi ideal, hybrid structure, hybrid ideal, hybrid right (left) bi-quasi ideal. AMS Subject Classification: 16Y60, 08A72