A study on generalizations of soft sets

Abstract

Most of the problems in economics, environment, science and engineering are deals with uncertainty and decision making. The uncertainty arises in the form of ambiguity and lack of information about the data. Decision making is the problem of choosing the optimal choice which suits the physical nature of the problem. In these situations a tool such as soft set, which deals with uncertainty and rich in handling the parameters will analyze the problem effectively and gives a much better solutions. The objective of this research is to study the generalization of soft sets like, intuitionistic fuzzy soft sets, generalized fuzzy soft rough sets, fuzzy parameterized soft fuzzy sets, and ordered intuitionistic fuzzy soft sets, and applied them in multi-criteria decision making problems. Further, investigate the properties of these sets and developing some useful algorithms which can be applied in a decision making problems. In addition, the effectiveness of the proposed techniques is established with a numerical illustration. A new similarity measure and a weighted similarity measure on Intuitionistic Fuzzy Soft Sets (IFSSs) are proposed and some of their basic properties are discussed. Further, the optimality criteria for the decision making problem using the proposed method are stated and performance analysis of the method is discussed through a measure of performance and measure of error. The effectiveness of the proposed method is demonstrated with UCI Machine Learning Repository datasets to the diagnostic problem and their interested parameters are presented. newline newline newline