An Introduction to the Theory of Imprecise Soft Sets

This paper aims to introduce the theory of imprecise soft sets which is a hybrid model of soft sets and imprecise sets. It has been established that two independent laws of randomness are necessary and sufficient to define a law of fuzziness. Further, in case of fuzzy sets, the set theoretic axioms of exclusion and contradiction are not satisfied. Accordingly, the theory of imprecise sets has been developed where these mistakes arising in the literature of fuzzy sets are absent. Our work is an endeavor to combine imprecise sets with soft sets resulting in imprecise soft sets. We have put forward a matrix representation of imprecise soft sets. Finally we have studied the notion of similarity of two imprecise soft sets and put forward an application of similarity in a decision problem.