International Journal of Neutrosophic Science

In this paper we give a comprehensive presentation of the notions of filter base, filter and ultrafilter on single valued neutrosophic set and we investigate some of their properties and relationships. More precisely, we discuss properties related to filter completion, the image of neutrosophic filter base by a neutrosophic induced mapping and the infimum and supremum of two neutrosophic filter bases.  

In this paper we have defined the concept of neutrosophic queueing systems and defined its neutrosophic performance measures. An important application of neutrosophic logic in queueing systems we face in real life were discussed, that is the neutrosophic events accuring times, because of its wide applications in networking and simulating communication systems specialy when probability distribution is not known, and because it’s more realistic to consider and to not ignore the imprecise events times. Event-based table of a neutrosophic queueing system was presented and its neutrosophic performance measures were derived, i.e. neutrosophic mean waiting time in queue, neutrosophic mean waiting time in system, neutrosophic expected number of customers in queue and neutrosophic expected number of customers in system. Neutrosophic Little’s Formulas (NLF) were also defined which is a main tool in queueing systems problems to make it easier finding performance measures from each other.

The objective of this paper is to formally present the concept of NeutroGroups by considering three NeutroAxioms (NeutroAssociativity, existence of NeutroNeutral element and existence of NeutroInverse element). Several interesting results and examples of NeutroGroups, NeutroSubgroups, NeutroCyclicGroups, NeutroQuotientGroups and NeutroGroupHomomorphisms are presented. It is shown that generally, Lagrange’s theorem and 1st isomorphism theorem of the classical groups do not hold in the class of NeutroGroups.

The main goal of this paper is to propose a new type of separation axioms via neutrosophic crisp semi open sets and neutrosophic crisp points in neutrosophic crisp topological spaces, namely neutrosophic crisp semi separation axioms. Finally, we examine the relationship between them in details. And also includes the study of the connections between these neutrosophic crisp semi separation axioms and the existing neutrosophic crisp separation axioms. Moreover, many examples are presented, to illustrate the concepts introduced in this paper. and investigate their fundamental properties, relationships and characterizations.

It is customary in mathematics that almost all new developments maintain compatibility with what is already proved and accepted. Following this way, neutrosophic logic has the classical logic as subset. However, in mathematics, all the affirmations must be proved first to be accepted, so the claim that the neutrosophic logic encompass classical logic must be also proved. Thus, this paper show that the main properties of the classical logic hold when translated to neutrosophic form at propositional level.