Solution to a Soft Fuzzy Group Decision-Making Problem Involving a Soft Fuzzy Number Valued Information System

Abstract

In this paper, we introduce an operation union on the collection of soft fuzzy numbers [1] related to multi-parameter set and elucidated with a hypothetical example. For a given soft fuzzy number valued information system ((Formula presented.)), we define a strict partial ordering and a fuzzy number valued utility function on the initial universal set relating to each attribute, which in turn yields a utility soft information corresponding to each entity. We also define a finite collection of soft fuzzy number valued information systems, soft fuzzy number valued hierarchical information systems and their corresponding soft unions. A group decision-making problem with individual attribute set for decision makers wherein the perceptions are expressed using soft fuzzy numbers is modelled involving the collection of soft fuzzy number valued information systems. Such a problem is called soft fuzzy group decision-making problem. A new procedure to solve the problem of finding importance (weights) of the decision makers in such a situation is also proposed in which utility soft information plays a major role. An algorithm is developed to solve the same. Validation of the methodology is shown with an illustration of real life situation.