CONSTRUCTION THEOREMS FOR INTUITIONISTIC FUZZY-SETS

We will begin presenting a point operator which allows us to associate a family of fuzzy sets with each intuitionistic fuzzy set. We will th en expose two construction theorems of intuitionistic fuzzy sets from one fuzzy set and a theorem which allows us to construct an intuitioni stic fuzzy set from two fuzzy sets. We will also prove that it is poss ible to recover the fuzzy sets used in the construction from the intui tionistic fuzzy set constructed by means of different operators. All t he theorems shown let us generate intuitionistic fuzzy sets with fixed beforehand entropy and it is easy to construct algorithms to implemen t these processes. We conclude by proving a theorem relative to the wa y of recuperating from an intuitionistic fuzzy set built with two fuzz y sets, the mio fuzzy sets used in its construction and a third fuzzy set included among them. Finally, we expose the importance the constru ction theorems will have in our future research relative to the obtain ment of the conclusion of the generalized modus ponens when the antece dents of the generalized modus ponens are perturbed in the way indicat ed in the theorems developed.