Doubly Soft Set Model with Single Fuzzy Parameter at Second Level of Hierarchy for Making Decisions

Abstract

We come across the challenge of uncertainty in making decisions in various real life problems. The intelligence, analytical ability, reasoning and available information is used by us to make these decisions. The imprecise nature of the available information is the main source of uncertainty which makes our task more challenging for making decisions. The available mathematical tools like fuzzy sets, rough sets, vague sets and soft sets etc. which are in use have their own limitations with regard to different types of uncertainty. Thus depending on the kinds of uncertainty involved in a decision problem, it is necessary to explore hybrid approaches to address these issues of uncertainty in making decisions in a real environment. In this paper a doubly soft set with a single fuzzy parameter at the second level of hierarchy is proposed to address the combination of two kinds of uncertainty in a decision problem. The doubly soft set takes care of the relationship of elements of the set with the two levels of parameters involved and fuzzy set takes care of relationships among the elements of the parameters at the second level of hierarchy. The proposed model is illustrated with the help of an example of a decision problem.