Interval-valued intuitionistic fuzzy parameterized soft set theory and its application in decision-making

Decision-making is a technique which all of us do every day in different contexts. In Decision-making several alternates are there from which the best one is to be selected. But the alternates may not be crisp many times. So, uncertainty based techniques are necessary to solve these problems. Among the different models of uncertainty, we have fuzzy sets, intuitionistic fuzzy sets and soft sets. There are other variations of fuzzy sets like the interval valued fuzzy sets. Also, we have hybrid models obtained by combining two or more of these models. Molodtsov introduced the notion of soft set in 1999, which has better parameterization capability than most of the other such models. The hybrid model of interval valued fuzzy set and soft set was introduced by Yang in 2009. In this paper, we extend it to define interval valued intuitionistic fuzzy parameterized soft set (IVIFPSS) and establish their properties. Continuing the earlier works on using hybrid models in decision-making, in this paper we use IVIFPSS to put forth two algorithms on decision-making. Out of these two one is on individual decision-making and the other one is on group decision making, which we illustrate through examples.