Optimizing Quasi-Interior Ideals and Fuzzy Soft Quasi-Interior Ideals of Ternary Semirings

Abstract

This study explores the algebraic structure of Ternary semirings and introduces the novel concepts of “quasi-interior ideals” (QIIs) and “fuzzy soft quasi-interior ideals” (FS QIIs). It starts with an overview of semirings, elaborating on their development and relevance in algebra and computer science—the job ventures into QIIs and their properties, including FS QIIs in T-semirings. The definitions, examples, and theorems clarify the conditions when such ideals work and their roles in characterizing regular T-semirings. Fuzzy set theory is further explored through its application to algebraic structures and problems in logic, set theory, and optimization. Such extensive analysis considerably expands the knowledge about semirings and their practical use in different mathematics and theoretical fields.