Hesitant Intuitionistic Fuzzy Strongly Prime Submodule

Abstract

In this paper, we investigate the concept of hesitant intuitionistic ʄ-strongly prime submodules of an module M. The fundamental properties of this concept are systematically investigated. In particular, it is proved that the intersection of any two hesitant intuitionistic ʄ-strongly prime submodules is again a hesitant intuitionistic ʄ-strongly prime submodule. Furthermore, it is shown that every hesitant intuitionistic ʄ-strongly prime submodule is necessarily a hesitant intuitionistic ʄ-prime submodule. A characterization of hesitant intuitionistic ʄ-strongly prime submodules is also obtained, and their connection with classical strongly prime submodules is examined through the characteristic hesitant intuitionistic ʄ-set. The obtained results extend existing theories on ʄ -intuitionistic ʄ-submodules and provide a broader theoretical framework for studying algebraic structures under hesitant intuitionistic ʄ-environments.