Neutrosophic Set and Neutrosophic Topological Spaces
A. A. Salama,S. A. Alblowi +1 more
TLDR
In this paper, a new set theory called neutrosophic set is proposed, which is based on fuzzy topological space and intuitionistic fuzzy topology space, and its properties are discussed.Abstract:
Neutrosophy has been introduced by Smarandache (7, 8) as a new branch of philosophy. The purpose of this paper is to construct a new set theory called the neutrosophic set. After given the fundamental definitions of neutrosophic set operations, we obtain several properties, and discussed the relationship between neutrosophic sets and others. Finally, we extend the concepts of fuzzy topological space (4), and intuitionistic fuzzy topological space (5, 6) to the case of neutrosophic sets. Possible application to superstrings and read more
Citations
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Complex Neutrosophic Set
TL;DR: The dominancy of complex neutrosophic set to all current methods through the graph is showed, and the drawbacks and failure of the current methods are shown.
Journal ArticleDOI
Generalized Neutrosophic Set and Generalized Neutrosophic Topological Spaces
A. A. Salama,S. A. Alblowi +1 more
TL;DR: In this article, the authors introduce definitions of generalized neutrosophic sets and obtain several properties, and discuss the relationship between generalized neutro-scores and GIS topology rules.
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Multi-criteria decision-making method based on single-valued neutrosophic linguistic Maclaurin symmetric mean operators
Jian-qiang Wang,Yu Yang,Lin Li +2 more
TL;DR: This study centers on multi-criteria decision-making (MCDM) issues in which criteria are weighed differently and criteria values are expressed as single-valued neutrosophic linguistic numbers.
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Complex neutrosophic set
Mumtaz Ali,Florentin Smarandache +1 more
TL;DR: In this article, a complex neutrosophic set is introduced to handle imprecise, indeterminate, inconsistent, and incomplete information of periodic nature, which is an extension of the complex intuitionistic fuzzy sets.
Book
Neutrosophic Precalculus and Neutrosophic Calculus
TL;DR: In this book, the author presents a few examples of indeterminacies and several methods to deal with these specific indeterminacy, but many other ind determinacies there exist in the authors' everyday life, and they have to be studied and resolved using similar of different methods.
References
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Book
Fuzzy sets
TL;DR: A separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.
Journal ArticleDOI
Intuitionistic fuzzy sets
TL;DR: Various properties are proved, which are connected to the operations and relations over sets, and with modal and topological operators, defined over the set of IFS's.
Book
A unifying field in logics: neutrosophic logic. neutrosophy, neutrosophic set, neutrosophic probability and statistics
TL;DR: In this article, Smarandache generalized the fuzzy logic and introduced two new concepts: a) "neutrosophy" -study of neutralities as an extension of dialectics; b) and its derivative, such as Neutrosophic logic, NeUTrosophistic set, Neutroscophic probability, and NEUTrosophy statistics, thus opening new ways of research in four fields: philosophy, logics, set theory, and probability/statistics.
Journal ArticleDOI
An introduction to intuitionistic fuzzy topological spaces
TL;DR: The basic concepts of the so-called “intuitionistic fuzzy topological spaces” are constructed, the definitions of fuzzy continuity, fuzzy compactness, fuzzy connectedness and fuzzy Hausdorff space are introduced, and several preservation properties and some characterizations concerning fuzzy compactity and fuzzyconnectedness are obtained.