Decision-making algorithmic technique based on bijective hypersoft set
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Date
2021-09
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UMT Lahore
Abstract
Hypersoft set is an emerging field of study which is meant to address the insufficiency and the limitation of existing soft set-like models regarding the consideration and the entitlement of multi-argument approximate function. This type of function maps the multi-sub parametric tuples to power set of universe. It fully focuses on the partitioning of each attribute into its attribute-valued set that is missing in existing soft set-like structures. It replaces single-argument approximate function of soft set with multi-argument approximate function. Hypersoft set considers the cartesian product of disjoint attribute-valued sets as domain of multi-argument approximate function rather than taking the single set of attributes. In this sense, hypersoft set has distinction and upper hand than existing soft set model. This study mainly aims to discuss the distinctive properties of hypersoft set under bijective setting which is novel and useful addition in fuzzy set-/ soft set-like literature. Therefore through this view-point, this research is aiming to align existing literature on bijective soft sets with the need for such a multi-argument function. In chapter 2, a bird’s view is presented from existing literature regarding fuzzy set, intuitionistic fuzzy set, neutrosophic set, soft set and hypersoft set with the support of illustrative numerical examples. In chapter 3, the fundamentals i.e. properties, axiomatic operations, set-theoretic operations and operational laws and results of bijective hypersoft set are discussed with self-explanatory numerical examples. In chapter 4, a decision-making algorithm is proposed which is based on decision-support aggregation operators viii and decision-support set of bijective hypersoft set. This proposed algorithm is validated and elaborated with the help of real world application for optimal product selection. Moreover, the proposed study is compared with the some existing relevant models with the discussion of generalization of the proposed structure. Finally, the whole research is summarized with suitable future directions.