Construction theorems for intuitionistic fuzzy sets

It is proved that it is possible to recover the fuzzy sets used in the construction from the intuitionistic fuzzy set constructed by means of different operators, and the importance the construction theorems will have in the future research relative to the obtainment of the conclusion of the generalized modus ponens when the antecedents of the normalized modus Ponens are perturbed.

Abstract

We will begin presenting a point operator which allows us to associate a family of fuzzy sets with each intuitionistic fuzzy set. We will then expose two construction theorems of intuitionistic fuzzy sets from one fuzzy set and a theorem which allows us to construct an intuitionistic fuzzy set from two fuzzy sets. We will also prove that it is possible to recover the fuzzy sets used in the construction from the intuitionistic fuzzy set constructed by means of different operators. All the theorems shown let us generate intuitionistic fuzzy sets with fixed beforehand entropy and it is easy to construct algorithms to implement these processes. We conclude by proving a theorem relative to the way of recuperating from an intuitionistic fuzzy set built with two fuzzy sets, the two fuzzy sets used in its construction and a third fuzzy set included among them. Finally, we expose the importance the construction theorems will have in our future research relative to the obtainment of the conclusion of the generalized modus ponens when the antecedents of the generalized modus ponens are perturbed in the way indicated in the theorems developed.