ON THE STRUCTURE OF TWO - FOLD FUZZY SET

The traditional fuzzy set deals with single degree of membership which cannot capture matters exhibited by multi-dimensional uncertainty. This gap motivate is the motivation to our work. We extend the existing Boolean algebra of the traditional fuzzy set to the two-fold fuzzy set., to further make its application wider and easier. The results show the conformity of the two-fold fuzzy sets with the existing Boolean algebra in the theory of the traditional fuzzy sets. The basic operations of the traditional fuzzy set were investigated against the two-fold fuzzy sets. The axioms of fuzzy union, fuzzy intersection and fuzzy complement of the traditional fuzzy set were investigated and extended to that of the two-fold fuzzy set. Furthermore, the set having satisfied the axioms was proved to be commutative, associative, distributive, involutivity, absorptive point-wise, and in concord with De Morgan’s law. With this the two fold fuzzy set will be more relevant in modelling vagueness and imprecision than the traditional fuzzy set.