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 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.

Interval-valued Pythagorean fuzzy set (IVPFS), originally proposed by Peng and Yang, is a novel tool to deal with vagueness and incertitude. As a generalized set, IVPFS has close relationship with interval-valued intuitionistic fuzzy set (IVIFS). IVPFS can be reduced to IVIFS satisfying the condition $\mu^++\nu^+ \leq 1$. However, the related operations of IVPFS do not take different conditions into consideration. In this paper, we initiate some new interval-valued Pythagorean fuzzy operators ($\diamondsuit, \Box, \spadesuit, \clubsuit, \maltese, \rightarrow, \$ $) and discuss their properties in relation with some existing operators $(\cup, \cap, \oplus, \otimes)$ in detail. It will promote the development of interval-valued Pythagorean fuzzy operators. Later, we propose an algorithm to deal with multi-attribute decision making (MADM) problem based on proposed $\spadesuit$ operator. Finally, the effectiveness and feasibility of approach is demonstrated by mine emergency decision making example.

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.

Man and how to play his role in various fields is the main issue of governance. Therefore, the study of various governance issues should be done according to this factor. The social sciences and humanities owe engineering sciences the application of systems methodologies, especially soft methodology over the past few decades. The purpose of this study was to evaluate the capabilities of various research methods in soft operations in governance studies and according to the research questions based on the method adopted (qualitative approach using meta-analysis) in the period from 2000 to 2021, it was found that the use of soft methods is on the rise. "soft systems methodology, scenario-based planning, and viable systems model" being used for governance studies, corporate governance, public governance, and information technology governance. The studies led to the extraction of a model for selecting the type of soft research method for governance studies. Therefore, considering that, this study with these dimensions has not been done in the country so far and has not led to pattern design, it is new. It was also found that methods such as heaven-to-earth approach methodology, futures studies, analysis and development of strategic options, and the method of revealing and testing strategic assumptions have been less used in governance studies.

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.