Decision-theoretic rough fuzzy set model and application

In this paper, we define soft ω -open sets and strongly soft ω -open sets as two new classes of soft sets. We study the natural properties of these types of soft sets and we study the validity of the exact versions of some known results in ordinary topological spaces regarding ω -open sets in soft topological spaces. Also, we study the relationships between the ω -open sets of a given indexed family of topological spaces and the soft ω -open sets (resp. strongly soft ω -open sets) of their generated soft topological space. These relationships form a biconditional logical connective which is a symmetry. As an application of strongly soft ω -open sets, we characterize soft Lindelof (resp. soft weakly Lindelof) soft topological spaces.

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On Two Classes of Soft Sets in Soft Topological Spaces

Covering-based rough sets are important generalizations of the classical rough sets of Pawlak. In this paper, by means of j-neighborhoods, complementary j-neighborhoods and j-adhesions, we build some new different types of j-covering approximations based rough sets and study related properties. Also, we explore the relationships between the considered j-covering approximations and investigate the properties of them. Using different neighborhoods, some different general topologies are generated as topologies induced from a binary relation. Finally, an interesting application of the new types of covering-based rough sets to the rheumatic fever is given.

Certain types of coverings based rough sets with application

Abstract In this paper, we introduce a topological method to produce new rough set models. This method is based on the idea of “somewhat open sets” which is one of the celebrated generalizations of open sets. We first generate some topologies from the different types of $$N_\rho $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>N</mml:mi> <mml:mi>ρ</mml:mi> </mml:msub> </mml:math> -neighborhoods. Then, we define new types of rough approximations and accuracy measures with respect to somewhat open and somewhat closed sets. We study their main properties and prove that the accuracy and roughness measures preserve the monotonic property. One of the unique properties of these approximations is the possibility of comparing between them. We also compare our approach with the previous ones, and show that it is more accurate than those induced from open, $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> -open, and semi-open sets. Moreover, we examine the effectiveness of the followed method in a problem of Dengue fever. Finally, we discuss the strengths and limitations of our approach and propose some future work. 

/pdf/topological-approach-to-generate-new-rough-set-models-1zgk8ryf.pdf

Topological approach to generate new rough set models

The current work concentrates on generating different topologies by using the\n concept of the ideal. These topologies are used to make more thorough\n studies on generalized rough set theory. The rough set theory was first\n proposed by Pawlak in 1982. Its core concept is upper and lower\n approximations. The principal goal of the rough set theory is reducing the\n vagueness of a concept to uncertainty areas at their borders by increasing\n the lower approximation and decreasing the upper approximation. For the\n mentioned goal, different methods based on ideals are proposed to achieve\n this aim. These methods are more accurate than the previous methods. Hence\n it is very interesting in rough set context for removing the vagueness\n (uncertainty).

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Idealization of j-approximation spaces

On rough approximations via ideal

Some types of pairwise soft sets and the associated soft topologies

Pairwise soft separation axioms in soft bitopological spaces

Generalization of Pawlak’s rough approximation spaces by using ij- χ-open sets and its applications

− In [34] we introduced the notion of r-(τi, τj)-θ-generalized fuzzy closed sets in smoothbitopological spaces by using (τiθ-fuzzy closure, denoted Cθon smooth bitopological spaces by using smooth supra topological space(X, τ12) which is generated from smooth bitopological space (X, τ1, τ) [1], such that Cθ≤ Tτi. Inthis paper, we introduce a new class of r-θ-generalized fuzzy closed sets, namely, r-τ12-θ-gfc in smoothbitopological spaces via Cθ-fuzzy closure operator. The basic properties of these sets are studied.Furthermore, the relationship with other notions of r-generalized fuzzy closed sets in [31, 32, 33, 34]are investigated and we give many examples for reverse. In addition, by using r-τ12-θ-gfc sets, wedefine a new fuzzy closure operator which generates a new smooth topology. Finally, generalized fuzzyθ-continuous (resp. irresolute) and fuzzy strongly θ-continuous mappings are introduced and some oftheir properties are studied

/pdf/r-t12-th-generalized-fuzzy-closed-sets-in-smooth-1hzyxr0s7m.pdf

Osama A. E. Tantawy

Papers

On rough approximations via ideal

Some types of pairwise soft sets and the associated soft topologies

Pairwise soft separation axioms in soft bitopological spaces

Generalization of Pawlak’s rough approximation spaces by using ij- χ-open sets and its applications

r-τ12-θ-GENERALIZED FUZZY CLOSED SETS IN SMOOTH BITOPOLOGICAL SPACES