Theory of Bijective Hypersoft Set with Application in Decision Making

Abstract

Hypersoft set (an extension of soft set) is a new mathematical tool to tackle the inadequacy of soft set for attribute-valued sets. In this study, concept of bijective hypersoft set is proposed and some of its set theoretic operations like restricted-AND and relaxed-AND, are characterized. Moreover, new operations of bijective hypersoft set such as dependency, decision system, significance of decision system, reduced decision system and decision rules in decision system, are discussed with illustrated examples. A decision making algorithm and application are discussed with the support of these proposed operations.