A Note on Strongly Lower Semi-Continuous Functions and the Induced Fuzzy Topological Space Generated by Them

A new class of functions called strongly lower semi-continuous (SLSC) functions is defined and its properties are studied. It is shown that the arbitrary supremum and finite infimum of SLSC functions are again SLSC. Using these functions, an induced fuzzy topological space, called s-induced fuzzy topological space on a topological space (X, T), is introduced. Moreover, some incorrect results on fuzzy topological spaces obtained previously by some authors are identified and modified accordingly. Examples of the newly defined induced space are given and their various properties are investigated. Interrelationships between a fuzzy topological space (X, F) and the s-induced fuzzy topological space generated by the crisp members of F are examined. In this process, different lower semi-continuities and induced fuzzy spaces generated by them have been defined in a general set up and their few properties have been studied

Neutrosophic Bitopological Spaces

WOS: 000502521500006In this study, bitopological structure which is a more general structure than topological spaces is built on neutrosophic sets. The necessary arguments which are pairwise neutrosophic open set, pairwise neutrosophic closed set, pairwise neutrosophic closure, pairwise neutrosophic interior are defined and their basic properties are presented. The relations of these concepts with their counterparts in neutrosophic topological spaces are given and many examples are presented

Countable Fuzzy Topological Space and Countable Fuzzy Topological Vector Space

This paper deals with countable fuzzy topological spaces, a generalization of the notion of fuzzy topological spaces. A collection of fuzzy sets F on a universe X forms a countable fuzzy topology if in the definition of a fuzzy topology, the condition of arbitrary supremum is relaxed to countable supremum. In this generalized fuzzy structure, the continuity of fuzzy functions and some other related properties are studied. Also the class of countable fuzzy topological vector spaces as a generalization of the class of fuzzy topological vector spaces has been introduced and investigated

Supra Soft b-Compact and Supra Soft b-Lindle÷F Spaces

The purpose of this paper is to introduce and study the concepts of supra soft b-compact and supra soft b-Lindelˆf spaces. Also we study several of their properties and characterizations in details. Furthermore, the invariance of these kinds of spaces under some types of supra soft mappings and their hereditary properties are also investigate

New Trends in Neutrosophic Theory and Applications Volume II

Neutrosophic set has been derived from a new branch of philosophy, namely Neutrosophy. Neutrosophic set is capable of dealing with uncertainty, indeterminacy and inconsistent information. Neutrosophic set approaches are suitable to modeling problems with uncertainty, indeterminacy and inconsistent information in which human knowledge is necessary, and human evaluation is needed. Neutrosophic set theory was proposed in 1998 by Florentin Smarandache, who also developed the concept of single valued neutrosophic set, oriented towards real world scientific and engineering applications. Since then, the single valued neutrosophic set theory has been extensively studied in books and monographs introducing neutrosophic sets and its applications, by many authors around the world. Also, an international journal - Neutrosophic Sets and Systems started its journey in 2013. Single valued neutrosophic sets have found their way into several hybrid systems, such as neutrosophic soft set, rough neutrosophic set, neutrosophic bipolar set, neutrosophic expert set, rough bipolar neutrosophic set, neutrosophic hesitant fuzzy set, etc. Successful applications of single valued neutrosophic sets have been developed in multiple criteria and multiple attribute decision making. This second volume collects original research and application papers from different perspectives covering different areas of neutrosophic studies, such as decision making, graph theory, image processing, probability theory, topology, and some theoretical papers. This volume contains four sections: DECISION MAKING, NEUTROSOPHIC GRAPH THEORY, IMAGE PROCESSING, ALGEBRA AND OTHER PAPERS. First paper (Pu Ji, Peng-fei Cheng, Hongyu Zhang, Jianqiang Wang. Interval valued neutrosophic Bonferroni mean operators and the application in the selection of renewable energy) aims to construct selection approaches for renewable energy considering the interrelationships among criteria. To do that, Bonferroni mean (BM) and geometric BM (GBM) are employed

Initial Characterized L-spaces and Characterized L- topological Groups

In this research work, new topological notions are proposed and investigated. The notions are named initial characterized L-spaces and characterized L-topological groups. The properties of such notions are deeply studied. We show that the intitial characterized L-space for an characterized L-spaces exists. By this notion, the notions of characterized L-subspace and characterized product L-space are introduced and studied. More information can be found in the full paper

On Initial and Final Characterized L- topological Groups

In this research work, new topological notions are proposed and investigated. The notions are named finalcharacterized L-spaces and initial and final characterized L-topological groups. The properties of such notionsare deeply studied. We show that all the final lefts and all the final characterized L-spaces are uniquely exist inthe category CRL-Sp and hence CRL-Sp is topological category over the category SET of all sets. By the notion offinal characterized L-space, the notions of characterized qoutien pre L-spaces and characterized sum L-spacesare introduced and studied. The characterized L-subspaces together with their related inclusion mappings andthe characterized quotient pre L-spaces together with their related canonical surjections are the equalizers andco-equalizers, respectively in CRL-Sp. Moreover, we show that the initial and final lefts and then the initial andfinal characterized L-topological groups uniquely exist in the category CRL-TopGrp. Hence, the category CRLTopGrpis topological category over the category Grp of all groups. By the notion of initial and finalcharacterized L-topological groups, the notions of characterized L-subgroups, characterized product Ltopologicalgroups and characterized L-topological quotient groups are introduced and studied., we show that thecategory CRL-TopGrp is concrete and co-concrete category of the category L-Top. More details can be found in the full paper