International Journal of Neutrosophic Science

The neutrosophic idea is a fertile environment adaptable to different mathematical tools. This paper aims to introduce the mapping of complex interval neutrosophic soft sets (MI-CNSSs). Further, the images and inverse images of complex interval neutrosophic soft sets and their properties are explored. These will be supported by concrete examples, and this paper will present some theorems about complex interval neutrosophic soft images and inverse images.

Several others have already discussed various types of new techniques in multi-criteria decision-making problems. De-fuzzification, De-eutrophication, and De-Bipolarisation all of these are new approaches that have been established. But this work depicts the concept and features of the Neutrosophic Bipolar Pentagonal Fuzzy number. The relationships and products of the picture fuzzy set, as well as their associated results, are investigated. The different kinds of neutrosophic single-typed bipolar pentagonal numbers (nbpnum) were also discussed. A multi-criteria choice is also done in a triangular Bipolar Neutrosophic Fuzzy Set to identify the ideal output depending on several attributes. A multi-criteria choice is also done in a triangular Bipolar Neutrosophic Fuzzy Set to identify the ideal output depending on several attributes.

Structural health monitoring (SHM) tries to determine the status of substances, elements, and the life expectancy of any aircraft building. It also serves as a vital tool for ensuring the structural integrity and safety of the aircraft. This research used a neutrosophic-Entropy model to assess the structural cracks in the reinforced concrete aircraft to evaluate its structural performance. For example, Entropy may be used in the civil engineering profession to pick subcontractors, manage traffic, and monitor the structural integrity of a structure, among other things. SHM in reinforced concrete aircraft buildings is examined in this research using the suggested technology. Expert groups were consulted to help determine the level of significance among the parameters used to monitor the aircraft's structural integrity. To further understand the structures' actual improvement, the Entropy approach given here would be quite beneficial. Also, we presented some neutrosophic multiplications. Neutrosophic multiplication module (NMM)  (a.k.a. ) (commulative group (A))has produced some surprising new findings, which we explore in this article. As a bonus, we'll shed some light on a few related topics to the NMM itself. Since the Neutrosophic Jacobson radical of the A multiplication modules is a Neutrosophic small submodule of , then  must be a Neutrosophic cyclic module, as we demonstrate. Last but not least, we prove that E (Universal) is a NMM only if and only when it's Neutrosophic divided modules more than a Neutrosophic integral domain.

We introduce the notion of Diophantine neutrosophic subbisemiring (DioNSBS), level sets of DioNSBS of a bisemiring. The concept of DioNSBS is a generalization of fuzzy subbisemiring over bisemiring. We interact the theory for (λ, μ)-DioNSBS over bisemiring. Let α be the Diophantine neutrosophic subset in S , we show that α = ⟨(ΞT α , ΞI α , ΞF α ), (Γα, ∆α, Θα)⟩ is a DioNSBS of S if and only if all non empty level set α(t,s) is a subbisemiring of S for t, s ∈ [0, 1]. Let α be the DioNSBS of a bisemiring S and W be the strongest Diophantine neutrosophic relation of S , we observe that α is a DioNSBS of S if and only if W is a DioNSBS of S × S . Let α1, α2, ..., αn be the family of DioN SBSs of S1, S2, ..., Sn respectively. We show that α1× α2 × ... × αn is a DioNSBS of S1 × S2 × ... × Sn. The homomorphic image of DioNSBS is a DioNSBS. The homomorphic preimage of DioNSBS is a DioNSBS. Examples are provided to illustrate our results.

The paper focuses on neutrosophic algebraic structures and operations applicability to the study of classical al-gebraic structures, particularly the R-module. The definition of neutrosophic submodules P and Q was further developed upon in this work in order to create neutrosophic submodules of P + Q. In this study, the neutrosophic submodule of the direct sum M ⊕ N is constructed, analyzed, and its associated results are examined. Additionally, several algebraic results of the neutrosophic submodule’s direct sum of a non-empty arbitrary family of submodules are examined.

Square root Diophantine neutrosophic interval-valued set (SRDioNIVS) approaches to multiple attribute decisionmaking (MADM) problems. The square root neutrosophic sets, interval-valued Diophantine neutrosophic sets are both extensions of square root Diophantine neutrosophic sets. In this section, we discuss aggregating operations and how those interprtautions have evolved over time. The paper is focused on a novel idea known as square root neutrosophic interval-valued weighted averaging (SRDioNIVWA), square root neutrosophic interval-valued weighted geometric (SRDioNIVWG), generalized square root neutrosophic interval-valued weighted averaging (GSRDioNIVWA), and generalized square root neutrosophic interval-valued weighted geometric (GSRDioNIVWG). We also begin an algorithm using these operators. The use of the euclidean and hamming distances is described, and examples from real-world problems are inserted. As a result, the defined models are more accurate and closely tied to Ξ. In order to show the reliability and usefulness of the models under examination, we also compare a few of the proposed and current models. The study’s results are also fascinating and intriguing.