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The article focuses on combining the near set theory with plithogenic hypersoft sets. In addition, near plithogenic hypersoft sets on different environments have been discussed.
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 ingrediants for topological structures on the collection of hypersoft sets.
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.
Plithogenic Hypersoft sets was introduced by Florentin Smarandache, who has extended crisp sets, fuzzy sets, intuitionistic sets, neutrosophic sets to plithogenic sets. The plithogenic sets considers the degree of appurtenance of the elements with respect to the attribute system. Smarandache has presented the classification of the plithogenic hypersoft sets and the applications of plithogenic fuzzy whole hypersoft sets in multi attribute decision making. Inspired by these research works, the concept of combined plithogenic hypersoft sets is introduced in this article. The representations of the degree of appurtenance of the elements determines the type of plithogenic hypersoft set, if it takes a combination of values then the new archetype of plithogenic hypersoft sets gets emerged into decision making scenario. This research work is put forth to project the realistic perception of the experts in the construction process of optimal conclusions.
In this paper, we generalize the soft set to the hypersoft set by transforming the function F into a multi-attribute function. Then we introduce the hybrids of Crisp, Fuzzy, Intuitionistic Fuzzy, Neutrosophic, and Plithogenic Hypersoft Set.
In this paper, we advance the study of plithogenic hypersoft set (PHSS).We present four classifications of PHSS that are based on the number of attributes chosen for application and the nature of alternatives or that of attribute value degree of appurtenance. These four PHSS classifications cover most of the fuzzy and neutrosophic cases that can have neutrosophic applications in symmetry. We also make explanations with an illustrative example for demonstrating these four classifications. We then propose a novel multi-criteria decision making (MCDM) method that is based on PHSS, as an extension of the technique for order preference by similarity to an ideal solution (TOPSIS).
Plithogenic Hypersoft sets (PHS) introduced by Smarandache are the extensions of soft sets and hypersoft sets and it was further protracted to plithogenic fuzzy whole Hypersoft set to make it more applicable to multi attribute decision making environment.
The main objective of this study is to introduce the notion of plithogenic neutrosophic hypersoft almost topological group. We have defined some new concepts and investigated properties of regularly open set and regularly closed set and then we observed the definitions of plithogenic neutrosophic hypersoft closed mapping, open mapping and finally we have defined the definition of plithogenic neutrosophic hypersoft almost continuous mapping. By observing the definition of plithogenic neutrosophic hypersoft almost continuous mapping we have studied neutrosophic hypersoft topological group and plithogenic neutrosophic hypersoft almost topological group and some of their properties.
The theory of plithogeny developed by Smarandache is described as a more generalized form of representing sets of different nature such as crisp, fuzzy, intuitionistic and neutrosophic. Plithogenic set comprises degree of appurtenance and contradiction degree with respect only to the dominant attribute. This paper introduces extended plithogenic sets comprising degrees of appurtenance and contradiction with respect to both dominant and recessive attributes. The extension of the 5-tuple Plithogenic sets to a 7- tuple plithogenic sets helps in developing a more comprehensive kind of Plithogenic sociogram. The newly developed plithogenic sets and its implications in Plithogenic sociogram is validated by the decision making problem on food processing industries. The obtained results using extended plithogenic sets are more promising in comparison to the conventional plithogenic sets. The proposed kind of plithogenic sets will benefit the decision makers to make optimal decisions based on both optimistic and pessimistic approaches.
Convexity plays an imperative role in optimization, pattern classiffication and recognition, image processing and many other relating topics in different fields of mathematical sciences like operation research, numerical analysis etc. The concept of soft sets was first formulated by Molodtsov as a completely new mathematical tool for solving problems dealing with uncertainties. Smarandache conceptualized hypersoft set as a generalization of soft set. Deli introduced the concept of convexity cum concavity on soft sets to cover above topics under uncertain scenario. In this study, a theoretic and analytical approach is employed to develop a conceptual framework of convexity concavity on hypersoft set which is generalized and more effective concept to deal with optimization relating problems.