Selectivity analysis of parameters in soft set and its effect on decision making

Abstract

Binary relations between alternatives and parameters in a soft set have a vital role in the analysis of configuration of this soft set. All of the studies on the soft set approach focus on the parameters and their images under the approximate function. Recently, by approaching the soft set from a different perspective, a pseudo soft set has been introduced. This approach associates the alternatives and their images under the approximate function. In this paper, we first discuss the transition from a soft set to a pseudo soft set and vice versa. Later on, we endeavor to analyze the selectivity of parameters in the structure of a (fuzzy parameterized) soft set. This analysis focuses on the binary relations with boolean values between a parameter and its associated alternatives rather than on the specific values of alternatives with respect to a parameter. Relatedly, the concepts of selectivity ratio and coverage selectivity ratio of parameters under the (fuzzy parameterized) soft sets are introduced and some basic properties are presented. Also, by using the transition between the soft set and the pseudo soft set, it is investigated the effect of selectivity analysis of parameters on decision making. As a result of this attempt, new decision making algorithms are proposed. The outputs of these algorithms are compared with those of some of the existing decision making algorithms based on the (fuzzy parameterized) soft sets. Thus, the performance of each of the proposed algorithms is displayed.