Theory And Application Of Hypersoft Set

Florentin Smarandache generalize the soft set to the hypersoft set by transforming the function 𝐹 into a multi-argument function. This extension reveals that the hypersoft set with neutrosophic, intuitionistic, and fuzzy set theory will be very helpful to construct a connection between alternatives and attributes. Also, the hypersoft set will reduce the complexity of the case study. The Book “Theory and Application of Hypersoft Set” focuses on theories, methods, algorithms for decision making and also applications involving neutrosophic, intuitionistic, and fuzzy information. Our goal is to develop a strong relationship with the MCDM solving techniques and to reduce the complexion in the methodologies. It is interesting that the hypersoft theory can be applied on any decision-making problem without the limitations of the selection of the values by the decision-makers. Some topics having applications in the area: Multi-criteria decision making (MCDM), Multi-criteria group decision making (MCGDM), shortest path selection, employee selection, e-learning, graph theory, medical diagnosis, probability theory, topology, and some more.

Smarandache developed the idea of hypersoft set (HSS) theory as an extension of soft set (SS) theory. HSS provides a general mathematical framework for handling data that can be formulated as several trait-valued disjoint sets which blend to various traits. The major goal of this article is to lay the footing for supplying a new model called bipolar fuzzy hypersoft sets (BFHSSs) by linking both fuzzy sets (FSs) and HSSs under bipolarity property. By using positive and negative membership functions and multi-argument functions, these structures work best for testing uncertainty. This makes them better at solving real-world problems, especially ones that have both good and bad sides. This paper also has different operations for BFHSSs, such as absolute BFHSS, null BFHSS, complement, subset, union, intersection, and their related properties. Moreover, operations like OR and AND for BFHSS have been instituted. Some properties are demonstrated, and some numerical examples are given to illustrate the mechanism of using these tools. Finally, these tools are applied in the decision-making process based on an algorithm that is built.

Hypersoft set is an emerging knowledge of study which is projected to address the limitations of soft set for the entitlement of multi-argument approximate function. This function maps sub-parametric tuples to power set of universe. It emphasizes the partitioning of each attribute into its respective attribute-valued set that is missing in existing soft set-like structures.

In this article, some essential aspects of plithogenic hypersoft algebraic structures have been analyzed. Here the notions of plithogenic hypersoft subgroups i.e. plithogenic fuzzy hypersoft subgroup, plithogenic intuitionistic fuzzy hypersoft subgroup, plithogenic neutrosophic hypersoft subgroup have been introduced and studied. For doing that we have rede ned the notions of plithogenic crisp hypersoft set, plithogenic fuzzy hypersoft set, plithogenic intuitionistic fuzzy hypersoft set, and plithogenic neutrosophic hypersoft set and also given their graphical illustrations. Furthermore, by introducing function in di erent plithogenic hypersoft environments, some homomorphic properties of plithogenic hypersoft subgroups have been analyzed.

The aim of this paper is to introduce the concept of intuitionistic fuzzy hypersoft topology. Certain properties of intuitionistic fuzzy hypersoft (IFH) topology like IFH b asis, IFH subspace, IFH interior and IFH cloure are investigated. Furthermore, the multicriteria decision making (MCDM) algorithms with aggregation operators based on IFH topology are developed. In Algorithm 1 and Algorithm 2, MCDM problem is applied for IFH sets and IFH topology, respectively. Any real-life implementations of the proposed MCDM algorithms are demonstrated by numerical illustrations.

In computational intelligence, machine learning, image processing, neural networks, medical diagnostics, and decision analysis, the ideas of correlation coefficients and entropy have practical applications. By applying hypersoft set (HSS) in neutrosophic environment provides a good model for describing and addressing uncertainties. In statistics, the correlation coefficient between two variables is crucial.

The aim of this paper is to initiat formal study of hypersoft sets. We first, present basic operations like union, intersection and difference of hypersoft sets; basic ingredients for topological structures on the collection of hypersoft sets.