Bipolar Fuzzy Supra Topological Spaces

Abstract

In the present work, we introduce bipolar fuzzy supra topological space as a generalization of fuzzy supra topological space, investigate the basic properties, give the concepts of interior and closure and encouraged them by examples and counterexamples. Moreover, we study the concepts of bipolar fuzzy supra continuity and 𝑆 * bipolar fuzzy supra continuity and see that composition of two 𝑆 * bipolar fuzzy supra continuous functions may not be a 𝑆 * bipolar fuzzy supra continuous function. Also, we attempt to define the concept of compactness on bipolar fuzzy supra topology.

Bipolar Fuzzy Supra Topology via (Q-) Neighborhood and Its Application in Data Mining Process

“…Since then, many authors have studied supra topology and its extensions such as (intuitionistic) fuzzy supra topology [30][31][32]. In 2022, Hami et al [33] discussed bipolar fuzzy supra topological spaces as a generalization of supra topologies to bipolar fuzzy topologies.…”

On Certain Properties of Bipolar Fuzzy Supra Preopen Sets

“…9. 𝑖𝑛𝑡 𝜏 (𝑖𝑛𝑡 𝜏 (𝒬)) = 𝑖𝑛𝑡 𝜏 (𝒬), 𝑐𝑙 𝜏 (𝑐𝑙 𝜏 (𝒬)) = 𝑐𝑙 𝜏 (𝒬). Definition 2.15: [14] Let 𝜏 ∈ 𝐵𝑃𝐹𝑆𝑇(𝑈 1 ), 𝜎 ∈ 𝐵𝑃𝐹𝑆𝑇(𝑈 2 ) and 𝜑: (𝑈 1 , 𝜏) ⟶ (𝑈 2 , 𝜎) be a mapping. Then, 𝜑 is called a BF supra continuous mapping if 𝜑 −1 (𝒬) ∈ 𝜏 for every 𝒬 ∈ 𝜎.…”

“…Using the notion of intuitionistic fuzzy sets, Turanlı [13] defined intuitionistic fuzzy supra topology in 2003. Malkoç and Pazar Varol [14] discussed BF supra topological spaces as a generalization of supra topologies to bipolar fuzzy topologies.…”

“…Let 𝜏 * be a BF topology and 𝜏 be a BF supra topology on 𝑈. Then, 𝜏 * is named to be associated BF topology with the 𝜏 if and only if 𝜏 * ⊂ 𝜏 [14]. Let (𝑈, 𝜏) be a BF supra topological space and 𝒦 be the family of all BF supra closed sets in 𝑈.Then the followings are true; i.…”