view full paper - International Journal of Scientific and Research

... Definition2.7: A crisp subset B of a fuzzy topological space (X,) is said to be fuzzy w-compact if B is fuzzy w-compact as a fuzzy subspace of X. Theorem2.10: A fuzzy w-closed crisp subset of a fuzzy w-compact space is fuzzy w-compact relative to X. Proof: Let A be a fuzzy w-closed crisp set of fuz ...

... Definition2.7: A crisp subset B of a fuzzy topological space (X,) is said to be fuzzy w-compact if B is fuzzy w-compact as a fuzzy subspace of X. Theorem2.10: A fuzzy w-closed crisp subset of a fuzzy w-compact space is fuzzy w-compact relative to X. Proof: Let A be a fuzzy w-closed crisp set of fuz ...

On Fuzzy δ-I-Open Sets and Decomposition of Fuzzy α-I

... for some x∈X will be denoted by A(x). For any two fuzzy sets A and B in (X,τ), A≤B if and only if A(x)≤B(x) for each x∈X. A fuzzy set in (X,τ) is said to be quasi-coincident with a fuzzy set B, denoted by AqB, if there exists x∈X such that A(x) + B(x) >1 [16]. A fuzzy set V in (X,τ) is called a q-ne ...

... for some x∈X will be denoted by A(x). For any two fuzzy sets A and B in (X,τ), A≤B if and only if A(x)≤B(x) for each x∈X. A fuzzy set in (X,τ) is said to be quasi-coincident with a fuzzy set B, denoted by AqB, if there exists x∈X such that A(x) + B(x) >1 [16]. A fuzzy set V in (X,τ) is called a q-ne ...

UTILIZING SUPRA α-OPEN SETS TO

... In 1965, Njastad [13] presented and investigated a notion of α-open sets in topological spaces. Mildly compact (Mildly Lindelöf) spaces [15] were introduced in 1974 and almost compact spaces [9] were introduced in 1975 by Staum and Lambrinos, respectively. Mashhour et al.[11] introduced a concept o ...

... In 1965, Njastad [13] presented and investigated a notion of α-open sets in topological spaces. Mildly compact (Mildly Lindelöf) spaces [15] were introduced in 1974 and almost compact spaces [9] were introduced in 1975 by Staum and Lambrinos, respectively. Mashhour et al.[11] introduced a concept o ...

Gδ–SEPARATION AXIOMS IN ORDERED FUZZY TOPOLOGICAL

... Definition 3. A fuzzy set µ is a fuzzy topological space (X, T ) is called a fuzzy Gδ -neighbourhood of x ∈ X if there exists a fuzzy Gδ -set µ1 with µ1 ≤ µ and µ1 (x) = µ(x) > 0. It is easy to see that a fuzzy set is fuzzy Gδ - if and only if µ is a fuzzy Gδ neighbourhood of each x ∈ X for which µ( ...

... Definition 3. A fuzzy set µ is a fuzzy topological space (X, T ) is called a fuzzy Gδ -neighbourhood of x ∈ X if there exists a fuzzy Gδ -set µ1 with µ1 ≤ µ and µ1 (x) = µ(x) > 0. It is easy to see that a fuzzy set is fuzzy Gδ - if and only if µ is a fuzzy Gδ neighbourhood of each x ∈ X for which µ( ...

Some types of fuzzy open sets in fuzzy topological groups

... C.L.CHANG, Fuzzy topological spaces, 45, 182-190 (1968). A. ROSENFELD, Fuzzy groups, Journal of Mathematical Analyses and Applications. 35, 512-517 (1971). B. HUTTON, Normality in Fuzzy Topological Spaces, Journal of Mathematical Analyses and Applications. 50, 74-79 (1975). R. LOWEN, Fuzzy Topologic ...

... C.L.CHANG, Fuzzy topological spaces, 45, 182-190 (1968). A. ROSENFELD, Fuzzy groups, Journal of Mathematical Analyses and Applications. 35, 512-517 (1971). B. HUTTON, Normality in Fuzzy Topological Spaces, Journal of Mathematical Analyses and Applications. 50, 74-79 (1975). R. LOWEN, Fuzzy Topologic ...

b − I-OPEN SETS AND DECOMPOSITION OF CONTINUITY VIA

... sets which is weaker than that of I-open sets. At last Hatir at all [5] have introduced the notions of BI -sets, CI -sets, α − I-sets, semi-I-sets and β − I-sets. By using this sets, they provided decompositions of continuity. In this paper, we introduced the notions b − I-open and strong BI -sets t ...

... sets which is weaker than that of I-open sets. At last Hatir at all [5] have introduced the notions of BI -sets, CI -sets, α − I-sets, semi-I-sets and β − I-sets. By using this sets, they provided decompositions of continuity. In this paper, we introduced the notions b − I-open and strong BI -sets t ...

ON PRE-I-OPEN SETS, SEMI-I-OPEN SETS AND bI

... [13] of K with respect to τ and I is defined as follows: for K ⊂ X, K ∗ (I, τ ) = {x ∈ X : U ∩K ∈ / I for every U ∈ τ (x)} where τ (x) = {U ∈ τ : x ∈ U }. A Kuratowski closure operator Cl∗ (.) for a topology τ ∗ (I, τ ), called the ?-topology, finer than τ , is defined by Cl∗ (K) = K ∪ K ∗ (I, τ ) [ ...

... [13] of K with respect to τ and I is defined as follows: for K ⊂ X, K ∗ (I, τ ) = {x ∈ X : U ∩K ∈ / I for every U ∈ τ (x)} where τ (x) = {U ∈ τ : x ∈ U }. A Kuratowski closure operator Cl∗ (.) for a topology τ ∗ (I, τ ), called the ?-topology, finer than τ , is defined by Cl∗ (K) = K ∪ K ∗ (I, τ ) [ ...

Soft separation axioms in soft topological spaces

... and theory of measurement. Maji et. al [20] applied soft sets in a multicriteria decision making problems. It is based on the notion of knowledge reduction of rough sets. They applied the technique of knowledge reduction to the information table induced by the soft set. In [21], they defined and stu ...

... and theory of measurement. Maji et. al [20] applied soft sets in a multicriteria decision making problems. It is based on the notion of knowledge reduction of rough sets. They applied the technique of knowledge reduction to the information table induced by the soft set. In [21], they defined and stu ...

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... The fuzzy set A is fuzzy-supper closed if A+ = A and fuzzy supper open if A−=A. A is fuzzy supper-open if and only if A is fuzzy supper-closed. Definition 3.2: A mapping f: X → Y from a fuzzy topological space (X, δ1) to a fuzzy topological space (Y, δ2) is said to be fuzzy supper-continuous if the ...

... The fuzzy set A is fuzzy-supper closed if A+ = A and fuzzy supper open if A−=A. A is fuzzy supper-open if and only if A is fuzzy supper-closed. Definition 3.2: A mapping f: X → Y from a fuzzy topological space (X, δ1) to a fuzzy topological space (Y, δ2) is said to be fuzzy supper-continuous if the ...