The target of this study is to observe some of the algebraic structures of a single valued neutrosophic set. So, we introduce the concept of a neutrosophic submodule of a given classical module and investigate some of the crucial properties and characterizations of the proposed concept.

D. Molodtsov (1999) introduced the concept of a soft set as a new approach for modeling uncertainties. The aim of this work is to define special kinds of soft sets, namely soft, L-fuzzifying soft, L-soft, and L-fuzzy soft neighborhood sets and to use them in order to give an alternative characterization of categories related to topology: crisp topological, L-topological, L-fuzzifying topological and L-fuzzy topological spaces.

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The objective of this paper is to describe the concept of intuitionistic fuzzy metric-like spaces. This space is an extension of metric-like spaces and fuzzy metric spaces, and intuitionistic fuzzy metric spaces. We discuss convergence sequences, contractive mapping and some fixed-point theorems in intuitionistic fuzzy metric-like space. We also give explanations, examples and counterexamples to validate the superiority of these results. Our results provide a substantial extension of several important results from fuzzy metric-like spaces.

In the present work, we introduce bipolar fuzzy supra topological space as a generalization of fuzzy supra topological space, investigate the basic properties, give the concepts of interior and closure and encouraged them by examples and counterexamples. Moreover, we study the concepts of bipolar fuzzy supra continuity and 𝑆 * bipolar fuzzy supra continuity and see that composition of two 𝑆 * bipolar fuzzy supra continuous functions may not be a 𝑆 * bipolar fuzzy supra continuous function. Also, we attempt to define the concept of compactness on bipolar fuzzy supra topology.