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In this paper, the notion of Neutrosophic fuzzy ideals of near-rings are introduced and discussed some algebraic properties like nion ,intersection , homomorphic image and preimage of neutrosophic fuzzy ideals of near-rings. Further we discuss about the direct product of Neutrosophic fuzzy ideals of near-rings.
In this paper, the notion of Neutrosophic fuzzy ideals of near-rings are introduced and discussed some algebraic properties like union ,intersection , homomorphic image and preimage of neutrosophic fuzzy ideals of near-rings. Further we discuss about the direct product of Neutrosophic fuzzy ideals of near-rings .
“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).
“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).
This article enriches the idea of neutrosophic soft ideal (NSI). The notion of neutrosophic soft prime ideal (NSPI) is also introduced here. The characteristics of both NSI and NSPI are investigated. Their relations are drawn with the concept of ideal and prime ideal in crisp sense. Any neutrosophic soft set (Nss) can be made into NSI or NSPI using the respective cut set under a situation. The homomorphic characters of ideal and prime ideal in this new class are also drawn critically.
The aim of this paper is to introduce and study some new neutrosophic fuzzy pairwise notions via neutrosophic fuzzy ideals. Relationships between the above new neutrosophic fuzzy pairwise notions and there other relevant classes are investigated.
Single valued neutrosophic set also known as the subclass of neutrosophic set is one of the mighty tool to deal with inexact, indefinite, unsure information, vagueness etc. In this study we have prolonged the theory of neutrosophic rings to SVNS and formed single valued neutrosophic rings.
“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).
“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.
The motivation of the present paper is to extend the concept of neutrosophic soft prime ideal over a ring. In this paper the concept of neutrosophic soft completely prime ideals, neutrosophic soft completely semi-prime ideals and neutrosophic soft prime k - ideals have been introduced. These are illustrated with suitable examples also. Several related properties, theorems and structural characteristics of each are studied here.