Slightly double fuzzy continuous functions

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.…”

“…The triplex (X, 𝜏 X , 𝜏 X * ) is called a double fuzzy topological spaces (dfts, for short), and denoted by X. Definition 2.2 [5,6] If X is a dfts. Then a double fuzzy closure operator and double fuzzy interior operator of λ 1 ∈ I X are defined by: 𝐶 𝜏 𝑥 ,𝜏 𝑥 * (λ 1 ,r 0 , s 1 ) = ∧ {μ 1 ∈ I X , λ 1 ≤ μ 1 , 𝜏 X ( 1 ̅ − μ 1 ) ≥ 𝑟 0 , 𝜏 X * (1 ̅ − μ 1 ) ≤ 𝑠 1 }, I 𝜏 𝑥 ,𝜏 𝑥 * ( λ 1 , (r 0 , s 1 ) = ⋁ {μ 1 ∈ I X , μ 1 ≤ λ 1 , 𝜏 X (μ 1 ) ≥ 𝑟 0 , 𝜏 X * (μ 1 ) ≤ 𝑠 1 }.…”

“…1. An (r 0 , s 1 )-fuzzy open set (r 0 , s 1 )-fo, for short) [6] if 𝜏 X (λ 1 ) ≥ r 0 and 𝜏 X * (λ 1 ) ≤ s 1 , whenever r 0 ∈ I ro and s 1 ∈ I s1 . A fuzzy set λ 1 is called an (r 0 , s 1 )-fuzzy closed set ((r 0 , s 1 )-fc, for short), whenever 𝜏 X (1 ̅ -λ 1 ) ≥ r 0 and 𝜏 X * (1 ̅ -λ 1 ) ≤ s 1 .…”

“…λ 1 is called (r 0 , s 1 )-generalized fuzzy open ((r 0 , s 1 )-gf open, for short) if (1 ̅ -λ 1 ) is an (r 0 , s 1 )-gfc set. Definition 2.4 [6] Let X and Y be two dfts , s. A function f : X → Y is said to be a double fuzzy continuous function iff τ…”

Approximations of ∈ , ∈ ∨ q Abughazalah1, Yaqoob2, Ashraf3 2021Mathematical Problems in Engineering1000View full textAdd to dashboardCite

“…Fuzzy set theory is a classical application of set theory. Applications of fuzzy sets in some algebraic structures and other structures can be seen in [10][11][12][13]. Zdzisław Pawlak [14] introduced the notion of rough sets, in the year 1982.…”