Exploration of pre-open sets in a fuzzy bitopological space via operation approach

Abstract

In this article, we propose an operation $(i,j)^*_\gamma$ on the set of all $(i,j)^*$-fuzzy pre-open set in a given fuzzy bitopological space $(X,\tau_i,\tau_j )$. Using the newly introduced operation, we initiate the $(i,j)^*_\gamma$-fuzzy preopen set and characterize it upto some extent. Also, we explore $(i,j)^*$-fuzzy pre-open set in the light of minimality. Finally, we study locally finiteness of a fuzzy bitopological space via $(i,j)^*_\gamma$-fuzzy open set.