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Intuitionistic Neutrosophic Crisp Sets And Their Application To Topology


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Intuitionistic neutrosophic crisp sets and their application to topology


Intuitionistic neutrosophic crisp sets and their application to topology

Author: J. Kim

language: en

Publisher: Infinite Study

Release Date:


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In this paper, we introduce the new notion of intuitionistic neutrosophic crisp sets as a tool for approximating undefinable or complex concepts in real world. First, we deal with some of its algebraic structures. Next, we define an intuitionistic neutrosophic crisp topology, base (subbase) and interior (closure), respectively and investigate some of each properties, and give some examples. Finally, we discussed various intuitionistic neutrosophic crisp continuities.

Neutrosophic Sets and Systems, vol. 54/2023 {Special Issue on Neutrosophic Algebraic Structures, NeutroAlgebra & AntiAlgebra and SuperHyperAlgebra & Neutrosophic SuperHyperAlgebra. Contributions of Researchers from the Arab World}


Neutrosophic Sets and Systems, vol. 54/2023 {Special Issue on Neutrosophic Algebraic Structures, NeutroAlgebra & AntiAlgebra and SuperHyperAlgebra & Neutrosophic SuperHyperAlgebra. Contributions of Researchers from the Arab World}

Author: Florentin Smarandache

language: en

Publisher: Infinite Study

Release Date: 2024-02-01


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“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc. Neutrosophy is a new branch of philosophy that studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. This theory considers every notion or idea together with its opposite or negation and with their spectrum of neutralities in between them (i.e. notions or ideas supporting neither nor ). The and ideas together are referred to as . Neutrosophy is a generalization of Hegel's dialectics (the last one is based on and only). According to this theory every idea tends to be neutralized and balanced by and ideas - as a state of equilibrium. In a classical way , , are disjoint two by two. But, since in many cases the borders between notions are vague, imprecise, Sorites, it is possible that , , (and of course) have common parts two by two, or even all three of them as well. Neutrosophic Set and Neutrosophic Logic are generalizations of the fuzzy set and respectively fuzzy logic (especially of intuitionistic fuzzy set and respectively intuitionistic fuzzy logic). In neutrosophic logic a proposition has a degree of truth (T), a degree of indeterminacy (I), and a degree of falsity (F), where T, I, F are standard or non-standard subsets of ]-0, 1+[. Neutrosophic Probability is a generalization of the classical probability and imprecise probability. Neutrosophic Statistics is a generalization of the classical statistics. What distinguishes the neutrosophics from other fields is the , which means neither nor . , which of course depends on , can be indeterminacy, neutrality, tie game, unknown, contradiction, ignorance, imprecision, etc.

New Neutrosophic Sets via Neutrosophic Topological Spaces


New Neutrosophic Sets via Neutrosophic Topological Spaces

Author: Wadei Al-Omeri

language: en

Publisher: Infinite Study

Release Date:


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In Geographical information systems (GIS) there is a need to model spatial regions with indeterminate boundary and under indeterminacy. The purpose of this chapter is to construct the basic concepts of the so-called "neutrosophic sets via neutrosophic topological spaces (NTs)".