Estructuras algebraicas para la lógica fuzzy

Abstract

Finalmente, utilizando la noción de jerarquía de conceptos clásica y fuzzy, damos una aplicación a la economía determinando una función de pertenencia asociada al contexto.

In this dissertation, we give the basic notions of fuzzy sets, as presented by Zadeh, and the we study the underlying algebraic structure. This structure, essentially a lattice endowed with a Galois connection formed by a product and a residuation, appears in many forms, according to the properties of the product and its relation to the lattice structure. We present these cases going from the general to the specific, including the one introduced by Zadeh. For these particular cases we analyze the associated logics. We also expand of the concepts of homomorphisms, subalgebras and products of residuated lattices. Finally, using both, the classic and fuzzy notions of formal concepts analysis, we give an application to Economic Sciences that helps determine membership functions associated to a context.