International Journal of Neutrosophic Science

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2690-6805ISSN (Online) 2692-6148ISSN (Print)

Plıthogenıc Combıned Dısjoınt Block Fuzzy Cognıtıve Maps (Pcdbfcm)

S. Gomathy , A. Rajkumar , D.Nagarajan , Broumi Said

This research article represents an innovative concept in Plithogenic Combined Disjoint Block Fuzzy Cognitive Maps (PCDBFCM) and its applications. PCDBFCM is a very useful tool in grouping the factors with contradiction degree of multiple attributes. A plithogenic fuzzy matrix is used to represent the connection matrix. The resultant vector is obtained while using plithogenic fuzzy operators. The produced results are very useful in making decisions since they include the degree of conceptual node contradiction with respect to the dominant node. For the plithogenic aggregation operators, the degree of dissimilarity between each attribute value and the main attribute value of the attribute leads to increased accuracy.

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Vol. 20 Issue. 1 PP. 08-16, (2023)

New Operators Using Neutrosophic Crisp Open Set

Riad K. Al-Hamido

In this paper, we introduce new sets  in neutrosophic crisp topology called neutrosophic crisp frontier, neutrosophic crisp border and neutrosophic crisp exterior with the help of neutrosophic crisp open sets in neutrosophic crisp topological space. Also, we discuss the basic and important properties of them and the relations between them. Finally, many examples are presented. 

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Vol. 20 Issue. 1 PP. 17-26, (2023)

Neutrosophic Number Sequences: An introductory Study

Hasan Gökbas , Selçuk Topal , Florentin Smarandache

In this paper, Neutrosophic definitions and properties of some special number sequences which are frequently found in the science literature, called Neutrosophic Number Sequences (NNSq) via Horadam sequence are studied for the first time. Especially for Neutrosophic Fibonacci (NFNq) and Neutrosophic Lucas (NLNq) number sequences, fundamental properties and identities such as Ruggles, Honsberger, Cassini, Catalan, d’Ocagne, and Tagiuri are given. In addition, Neutrosophic definitions of the sequences of Pell (NPNq), Pell-Lucas (NPLNq), Jacobsthal (NJNq), Jacobsthal-Lucas (NJLNq), Mersenne (NMNq), Mersenne-Lucas (NMLNq), Balancing (NBNq), and Lucas-Balancing (NLBNq) numbers are introduced. Besides defining these numbers and their sequences, since fuzzy and intuitionistic fuzzy sets are restrictions of neutrosophic sets, sequences of numbers within these sets are naturally and indirectly revealed.

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Vol. 20 Issue. 1 PP. 27-48, (2023)

New approach towards (ζ1, ζ2)-interval valued Q1 neutrosophic subbisemirings of bisemirings and its extension

M. Palanikumar , Aiyared Iampan , K. Arulmozhi , D. Iranian , A. Seethalakshmy , R. Raghavendran

We introduce the notions of (τ1, τ2)-interval valued Q1 neutrosophic subbisemirings (IVQ1NSBSs), level sets of a (τ1, τ2)-IVQ1NSBS, and (τ1, τ2)-interval valued Q1 neutrosophic normal subbisemirings ((τ1, τ2)- IVQ1NNSBS) of a bisemiring. Let cZ1 be a (τ1, τ2)-IVQ1NSBS of a bisemiring M and bV be the strongest (τ1, τ2)-interval valued Q1 neutrosophic relation of M. To illustrate cZ1 is a (τ1, τ2)-IVQ1NSBS of M if and only if bV is a (τ1, τ2)-IVQ1NSBS of M ⋇ M. We show that homomorphic image of (τ1, τ2)-IVQ1NSBS is again a (τ1, τ2)-IVQ1NSBS. To determine homomorphic pre-image of (τ1, τ2)-IVQ1NSBS is also a (τ1, τ2)- IVQ1NSBS. Examples are given to strengthen our results.

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Vol. 20 Issue. 1 PP. 49-58, (2023)

Special Single Valued Decagonal Neutrosophic Number and its Applications

M. U. Jayanth Sastri , I. Paulraj Jayasimman , A. Rajkumar , D. Nagarajan , Broumi Said

The Neutrosophic number is defined to solve the vagueness of the real-life problem and to analysis the indeterminacy of the problem, the paper defines a special single valued Decagonal Neutrosophic number and De-Neutrosophication formula are formulated using the removal area method and a numerical practical example is illustrated of network path edges using Neutrosophic number.

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Vol. 20 Issue. 1 PP. 59-67, (2023)

Analyses the least cost using Travelling Salesman problem through Neutrosophic Fuzzy system

S. Ghousia Begum , N. Jose Parvin Praveena , A. Rajkumar , D. Nagarajan , Broumi Said

The following paper introduces a methodology to calculate the least cost for a directed network through Travelling salesman problem. Dynamic programming method is used to find the minimum Cost. The recursion formula is used. The edge weights of the networks are being taken in terms of Triangular, Trapezoidal and Pentagonal Neutrosophic set. Score function for the Triangular, Trapezoidal and Pentagonal Neutrosophic sets are being defined for deneutrosophication. The least cost is estimated using all the above said Neutrosophic sets and the result is compared

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Vol. 20 Issue. 1 PP. 68-76, (2023)