Conference Program

Document provides a list of the sessions, speakers, workshops, and committees of the 32nd Summer Conference on Topology and Its Applications

Generalized Fuzzy Soft Connected Sets in Generalized Fuzzy Soft Topological Spaces

In this paper we introduce some types of generalized fuzzy soft separated sets and study some of their properties. Next, the notion of connectedness in fuzzy soft topological spaces due to Karata et al, Mahanta et al, and Kandil  et al., extended to generalized fuzzy soft topological spaces. The relationship between these types of connectedness in generalized fuzzy soft topological spaces is investigated with the help of number of counter examples

A Study of Fuzzy Continuous Mappings

The paperndeals with the conceptnof semi-compactness in thengeneralized setting of a fuzzyntopological space.We achievena number of characterizationsnof a fuzzynsemi-compact space.The notionnof semi-compactness is furthernextended to arbitrary fuzzyntopological sets.Such fuzzynsets are formulated inndifferent ways and a fewnpertinent properties are discussed.Finallynwe compare semi-compact fuzzynsets with some ofnthe existing types ofncompact-like fuzzynsets.We ultimately shownthat so far as thenmutual relationships among differentnexisting allied classes of fuzzynsets are concerned,thenclass of semi-compact fuzzynsets occupies a naturalnposition in the hierarchy.Thenpurpose of this papernis to introduce thenconcepts of semi*-connectednspaces, semi*compactnspaces.We investigate theirnbasic properties. We alsondiscuss their relationship withnalready existing concepts

Bifuzzy topological spaces

Separation axioms for bifuzzy topological spaces namely : P-Ri, P-Tj,P-Tjw (i=l,2,j=0,l,2,2 l/2),P-regular and P-normal spaces are defined and many related results are proved such as a bfts (X,τ1, τ2) Is P-normal iff for every τi-closed fuzzy set λ and τj-open fuzzy set μ such that λ C μ there exists a continuous function f : (X,τ1,τ2)—>([0,1]f, L,R) such that λ(x)≤f(x)(l -)≤ f(x)(0+)≤μ(x), for all x ∈ X.Bifuzzy connected topological spaces are defined such as S-connected,Sw-connected ,P-connected and Pw-connected .We have shown that connectedness is preserved under P-continuity and we have shown that the connectedness of (X,τ1,τ2) is not governed by the connectedness of (X, τ1) and (X, τ2). Many types of compactness were defined such as S-compact, P-compact, S-α-compact, S-weakly compact, S-α-weakly compact, P-weakly compact, P-α-weakly compact, S-C- compact, P-C-compact, S-C weakly compact, P-C-weakly compact, P-U- compact and P-S-compact .We have proved that P-S-compactness => P-C-compactness => P-U-compactness but P-U-compactness does not imply neither P-C-compactness nor P-S-compactness. Also we have shown that bifuzzy compactness is preserved under continuous surjection. Bifuzzy Lindelof spaces are also defined. We have shown that there are no analogous definitions of S-weakly compact and S-C- compact in Lindelof spaces. Finally we introduce induced and weakly induced bifuzzy topological spaces and prove that a P-Hausdorff compact bfts is P-weakly induced and a P-topological P-weakly induced bfts is P-induced. Lowen's goodness criterion is extended and then used to test the goodness of these definitions. We have proved that (X,T1,T2) is P-Ti, P-Tiw,P-regular and P-normal iff the bifuzzy topological space (X,ω(T1), ω(T2)) is P-Ti,P-Tiw (i=0,l,2,2 1/2), P- regular and P-normal respectively. We have shown that S- connectedness, P-connectedness are good extensions while Sw- connectedness and Pw-connectedness are not. Moreover we have also shown that S-α-compactness is a good extension of S-compactness if it is good for some α∈ [0,l); while P-α-compactness is a good extension of P-compactness only for α=0. Finally we prove a bitopological space (X,T1,T2) has P-f.p.p iff (X,ω(T1),ω(T2)) has P-f.p.p . [Please see inside the thesis for a better view of equations

A framework for fuzzy topology with particular reference to sequentiality and countability

Pu and Liu's Q-theory is combined with Lowen's goodness criterion for fuzzy extensions to provide a framework for fuzzifying topology. This framework is used for the study of fuzzy countability properties and for the fuzzification of classical sequentiality. In extending classical notions to fuzzy theory care is taken to ensure that they are a special case of the emerging fuzzy concepts. An examination of convergence in the sense of Pu and Liu in special fuzzy topological spaces demonstrates the advantage of Chang's definition of fuzzy topology, which is therefore adopted. A new criterion (called excellence) for the suitability of the fuzzy extensions of classical topological properties is introduced. In addition to passing Lowen's goodness test, an excellent property is expected to behave, under fuzzy extensions of induction and coinduction, in a way resembling that of the original classical property under these constructions. Fuzzy second countability, quasi-first countability and fuzzy sequentiality are found to be excellent extensions of classical second countability, first countability and sequentiality respectively

New Development of Neutrosophic Probability, Neutrosophic Statistics, Neutrosophic Algebraic Structures, and Neutrosophic & Plithogenic Optimizations

This Special Issue puts forward for discussion state-of-the-art papers on new topics related to neutrosophic theories, such as neutrosophic algebraic structures, neutrosophic triplet algebraic structures, neutrosophic extended triplet algebraic structures, neutrosophic algebraic hyperstructures, neutrosophic triplet algebraic hyperstructures, neutrosophic n-ary algebraic structures, neutrosophic n-ary algebraic hyperstructures, refined neutrosophic algebraic structures, refined neutrosophic algebraic hyperstructures, quadruple neutrosophic algebraic structures, refined quadruple neutrosophic algebraic structures, neutrosophic image processing, neutrosophic image classification, neutrosophic computer vision, neutrosophic machine learning, neutrosophic artificial intelligence, neutrosophic data analytics, neutrosophic deep learning, neutrosophic symmetry, and their applications in the real world. This book leads to the further advancement of the neutrosophic and plithogenic theories of NeutroAlgebra and AntiAlgebra, NeutroGeometry and AntiGeometry, Neutrosophic n-SuperHyperGraph (the most general form of graph of today), Neutrosophic Statistics, Plithogenic Logic as a generalization of MultiVariate Logic, Plithogenic Probability and Plithogenic Statistics as a generalization of MultiVariate Probability and Statistics, respectively, and presents their countless applications in our every-day world

Study of covering properties in fuzzy topology

This work is devoted to the study of covering properties both in L-fuzzy topological spaces and in smooth L-fuzzy topological spaces , that is the fuzzy spaces in Sostak's sense, where L is a fuzzy lattice . Based on the satisfactory theory of L-fuzzy compactness build up by Warner, McLean and Kudri, good definitions of feeble compactness and P-closedness are introduced and studied. A unification theory for good L-fuzzy covering axioms is provided. Following the lines of L-fuzzy compactness, we suggest two kinds of L-fuzzy relative compactness as in general topology, study some of their properties and prove that these notions are good extensions of the corresponding ordinary versions. We also present L-fuzzy versions of R-compactness , weak compactness and 0-rigidity and discuss some of their properties. By introducing 'a-Scott continuous functions', a 'goodness of extension' criterion for smooth fuzzy topological properties is established. We propose a good definition of compactness, which we call 'smooth compactness' in smooth L-fuzzy topological spaces. Smooth compactness turns out to be an extension of L-fuzzy compactness to smooth L-fuzzy topological spaces. We study some properties of smooth compactness and obtain different characterizations. As an extension of the fuzzy Hausdorffness defined by Warner and McLean, 'smooth Hausdorffness' is introduced in smooth L-fuzzy topological spaces. Good definitions of smooth countable compactness, smooth Lindelofness and smooth local compactness are introduced and some of their properties studied