Hakeem A. Othman

On fuzzy sp -open sets

A new class of generalized fuzzy open sets in fuzzy topological space, called fuzzy sp-open sets, are introduced, and their properties are studied and the relationship between this new concept and other weaker forms of fuzzy open sets we discussed. Moreover, we introduce the fuzzy sp-continuous (resp., fuzzy sp-open) mapping and other stronger forms of sp-continuous (resp., fuzzy spopen) mapping and establish their various characteristic properties. Finally, we study the relationships between all these mappings and other weaker forms of fuzzy continuous mapping and introduce fuzzy sp-connected. Counter examples are given to show the noncoincidence of these sets and mappings.

On fuzzy \(\theta\)-generalized-semi-closed sets

This paper is set to, introduce new notions of the fuzzy generalized closed sets called fuzzy (theta)-generalized semi-closed (semi -open) sets. Using these new notions, we introduce fuzzy (theta)-generalized semi-continuous, fuzzy (theta)-generalized semi-irresolute and fuzzy (theta)-generalized semi-closed (semi -open) mappings. Then, we establish their various properties. Moreover, we illustrate and explain the relations between these new concepts and others. Counterexamples are given to show the non-coincidence of these different class of fuzzy generalized closedsets and fuzzy generalized continuous mappings.