Fuzzy Counterparts of Fischer Diagonal Condition in ⊤-Convergence Spaces

Abstract

Fischer diagonal condition plays an important role in convergence space since it precisely ensures a convergence space to be a topological space. Generally, Fischer diagonal condition can be represented equivalently both by Kowalsky compression operator and Gähler compression operator. ⊤-convergence spaces are fundamental fuzzy extensions of convergence spaces. Quite recently, by extending Gähler compression operator to fuzzy case, Fang and Yue proposed a fuzzy counterpart of Fischer diagonal condition, and proved that ⊤-convergence space with their Fischer diagonal condition just characterizes strong L-topology—a type of fuzzy topology. In this paper, by extending the Kowalsky compression operator, we present a fuzzy counterpart of Fischer diagonal condition, and verify that a ⊤-convergence space with our Fischer diagonal condition precisely characterizes topological generated L-topology—a type of fuzzy topology. Hence, although the crisp Fischer diagonal conditions based on the Kowalsky compression operator and the on Gähler compression operator are equivalent, their fuzzy counterparts are not equivalent since they describe different types of fuzzy topologies. This indicates that the fuzzy topology (convergence) is more complex and varied than the crisp topology (convergence).

CHFS: Complex hesitant fuzzy sets‐their applications to decision making with different and innovative distance measures

“…The fuzzy counterparts of the Fischer diagonal condition in T‐diverges space were explored by Jin et al. [10]. Sanchez‐Roger et al.…”

“…Recently, a fuzzy collaborative approach for examining the suitability of smart health was established by Chen et al [9]. The fuzzy counterparts of the Fischer diagonal condition in T-diverges space were explored by Jin et al [10]. Sanchez-Roger et al [11] investigated the fuzzy logic and its uses in finance.…”