In this paper we define the soft set Product as a product of many soft sets and afterwards we extend it to the Hypersoft set. Similarly, the Indetermsoft Product is extended to the IndetermHypersoft set. We also present several applications of the soft set Product to Fuzzy (and fuzzy-extensions)  soft set Product and to Indetermsoft set and IndetermHypersoft set.

In this paper, the notion of generalized neutrosophic soft open set (GNSOS) in neutrosophic soft open set (GNSOS) in neutrosophic soft topological structures relative to neutrosophic soft points is introduced. The concept of generalized neutrosophic soft separation axioms in neutrosophic soft topological spaces with respect to

Abstract. In this work, we de ne a fuzzy soft set theory and its related properties. We then de ne fuzzy soft aggregation operator that allows constructing more efficient decision making method. Finally, we give an example which shows that the method can be successfully applied to many problems that contain uncertainties.

In our paper, we continue the study of the theory of fuzzy soft sets and their properties. Based on the singular values of the corresponding matrix, we define the energy of a fuzzy soft set, as well as the $\lambda$-energy of a fuzzy soft set, allowing us to introduce an effective method for decision-making. Then, we consider the limits of the defined energies, which are essentially non-negative numerical values. The paper demonstrates through examples how the introduced method can be successfully applied to many problems containing uncertainties. Additionally, the paper includes comparisons of the introduced method with other methods addressing similar problems.

soft set theory has been well-known as an innovative approach to managing uncertainty-related problems and modelling uncertainty since Molodtsov introduced it in 1999. It has been applied in a variety of contexts, both theoretical and practical. The core concept of the theory, soft set operations, has piqued the curiosity of researchers ever since it was developed. A number of restricted and extended soft set operations have been defined, and their characteristics have been investigated. In this study, we present a new restricted and extended soft set operation, which we refer to as extended gamma and restricted gamma operation, and we study their fundamental algebraic properties in detail. Additionally, this operation's distributions over other soft-set operations are examined. Considering the algebraic properties of the extended gamma operation and its distribution rules, we show that when combined with other types of soft sets, it forms several important algebraic structures, like semirings and near-semirings, in the collection of soft sets over the universe. This theoretical study is highly significant from both a theoretical and practical standpoint, as the main notion of the theory is the operations of soft sets, which provide the basis for many applications, such as cryptology and optimal decision-making procedures.

In this paper, the notion of vague soft hypermodules is introduced, which is an extension of the notions of vague soft hypergroups and vague soft hyperrings. Also, some basic properties of vague soft hypermodules and homomorphisms between vague soft hypermodules are presented and the image and pre-image of a vague soft hypermodule under a vague soft hypermodule homomorphism are studied.

In this paper we discuss some basic properties of rough soft sets and hence we introduce the notion of rough soft group. Basic properties of rough soft group are presented and supported by some illustrative examples.