α- separation axioms based on Lukasiewicz logic
نویسنده
چکیده
In the present paper, we introduce topological notions defined by means of α-open sets when these are planted into the framework of Ying’s fuzzifying topological spaces (by Lukasiewicz logic in [0, 1]). We introduce T 0 −, T 1 −, T 2 (αHausdorff)-, T 3 (α-regular)and T 4 (αnormal)-separation axioms. Furthermore, the R 0− and R 1− separation axioms are studied and their relations with the T 1 − and T 2 − separation axioms are introduced. Moreover, we clarify the relations of these axioms with each other as well as the relations with other fuzzifying separation axioms.
منابع مشابه
SOFT TOPOLOGY AND SOFT PROXIMITY AS FUZZY PREDICATES BY FORMULAE OF LUKASIEWICZ LOGIC
In this paper, based in the L ukasiewicz logic, the definition offuzzifying soft neighborhood structure and fuzzifying soft continuity areintroduced. Also, the fuzzifying soft proximity spaces which are ageneralizations of the classical soft proximity spaces are given. Severaltheorems on classical soft proximities are special cases of the theorems weprove in this paper.
متن کاملα∗−RT0 Intuitionistic Fuzzy Topological Spaces
In this paper we introduce the gradation of separation axioms ST 0 , RT 0 in an intuitionistic fuzzy topological space in the sense of Mondal and Samanta [7]. Using these concepts we have introduced and studied α-and α *-RT 0 intuitionistic fuzzy topological spaces.
متن کاملThe Liar Paradox and Fuzzy Logic
Can one extend crisp Peano arithmetic PA by a possibly many-valued predicate Tr(x) saying \x is true" and satisfying the \dequotation schema" ' Tr(') for all sentences '? This problem is investigated in the frame of Lukasiewicz innnitely valued logic.
متن کاملTractability of the Crisp Representations of Tractable Fuzzy Description Logics
An important line of research within the field of fuzzy DLs is the computation of an equivalent crisp representation of a fuzzy ontology. In this short paper, we discuss the relation between tractable fuzzy DLs and tractable crisp representations. This relation heavily depends on the family of fuzzy operators considered. Introduction. Despite the undisputed success of ontologies, classical onto...
متن کامل