Abstract Fuzzy set (FS) theory and rough sets (RSs) are constructed to accommodate the data uncertainty. In contrast, bipolar FS (BFS) can tackle uncertainty bipolarity of in different circumstances. This article aims introduce idea fuzzy ideals semigroup (SG), which is a generalization concept BFSs (RBFSs) an SG. We also investigate roughness subsemigroup (BF-SSG) with help congruence relation...

In a large fuzzy rule-based system, a great dealof computation time is required for a fuzzy inference engine. A given fuzzy rule-based system is modeled as a fuzzy inference graph where each node in the graph corresponds to a relation representing a rule in the rule-based system. This paper presents algorithms to minimize the number of nodes in the graph using fuzzy operations as well as their ...

We give various reformulations of the Strong Perfect Graph Conjecture, based on a study of forced coloring procedures, uniquely colorable subgraphs and ! ? 1-cliques in minimal imperfect graphs.

We will extend Reed's Semi-Strong Perfect Graph Theorem by proving that unbreakable C 5-free graphs diierent from a C 6 and its complement have unique P 4-structure.

The Strong Perfect Graph Conjecture, suggested by Claude Berge in 1960, had a major impact on the development of graph theory over the last forty years. It has led to the definitions and study of many new classes of graphs for which the Strong Perfect Graph Conjecture has been verified. Powerful concepts and methods have been developed to prove the Strong Perfect Graph Conjecture for these spec...