(p,q) - Fuzzy αm-Closed Sets in Double Fuzzy Topological Spaces

Abstract

In this submitted article, we defined new notions of closed sets and called it (p, q)-fuzzy α m -closed sets in double fuzzy topological spaces. Also, we investigate some characterizations and properties of the sets mentioned above. As a result, we discussed some new and more general relationship between (p, q)-fuzzy α m -closed set and it's generalized which is called an (p, q)-generalized fuzzy α m -closed sets which was obtained and compared.

SOME TYPES OF CONTIONUOUS FUNCTION VIA (r0, s1)-FUZZY αm- CLOSED SETS

“…The expression "intuitionistic" evaporate used in literature until 2005, when Gutierrez Garcia and Rodabaugh [5], they suggested that the double fuzzy set is a more appropriate name than intuitionistic and completed that their research project under the name " double" rather than intuitionistic. The goal of this present is to continue and to the allocation study of Fatimah et al [6,7]. Also, we will give new definitions of double fuzzy α mcontinuous function, double fuzzy α m -open function and double fuzzy-α m generalized-continuous function.…”

“…λ 1 is called (r 0 , s 1 )-fα m -open iff 1 ̅ -λ 1 an (r 0 , s 1 )fα m -closed. Definition 2.6 [7] If X is a dfts, for each λ 1 , μ 1 ∈ Ӏ X , r 0 ∈ I r0 and s 1 ∈ I s1 then, the 𝛼 𝑚 -Closure and 𝛼 𝑚 -Interior operator of λ 1 is defined as: 𝛼 𝑚 𝐶 τ X ,τ X * (λ 1 , 𝑟 0 , 𝑠 1 ) = ⋀{ μ 1 ∈ Ӏ X : λ 1 ≤ μ 1 , μ 1 is (r 0 , s 1 )-f𝛼 𝑚 -closed}. 𝛼 𝑚 I τ X ,τ X * (λ 1 , 𝑟 0 , 𝑠 1 ) = ⋁ {μ 1 ∈ Ӏ X : λ 1 ≥ μ 1 , μ 1 is (r 0 , s 1 )-f𝛼 𝑚 -open}.…”

Double Intuitionistic Open Sets with Some Applications

“…Generalization of the concept of double set was first introduced by Kandil, Tantawy, and Wafaie on flou intuitionistic topological spaces [9]. In Mohammed, F. M., Abdullah, S. I., & Obaid, S. H. [10] investigated (p, q)fuzzy αm-closed sets in double fuzzy topological spaces. The concept of on intuitionistic gradation of openness.…”