The Bijective N-soft set decision system

Abstract

The characteristics of many decision-making problems in an N-soft set environment are that the parameters consist of condition and decision parameters of which each alternative is only related to one parameter, and the union of partition by parameter sets is a universe. We propose a new method called a Bijective N-soft set for handling such problems. The Bijective N-soft set is a particular case of an N-soft set. The complement of the Bijective N-soft set, the restricted AND operation on Bijective N-soft sets and the dependence between two Bijective N-soft sets are discussed. Then, the properties associated with existing operations are further examined in this paper; among other things, the complement and AND operations satisfy the closed properties. Furthermore, related to the decision system, the reduction of the Bijective N-soft set is also proposed, and an algorithm to group condition parameters that influence the decision parameter as an application in the decision-making process whose cases can be represented as a Bijective N-soft set is also given in this paper.

Keywords

• n-soft sets
• bijective fuzzy soft sets
• bijective n-soft sets