Abstract:
: In this thesis, we extend some results obtained by A. Amroune and B. Davvaz in their paper entitled "Fuzzy ordered sets and duality for finite fuzzy distributive lattices". In this way a representation theorem for the infinite fuzzy distributive lattices is given. More precisely, we show that the category of infinite fuzzy Priestley spaces is equivalent to the dual of the category of infinite fuzzy distributive lattices.
We have also developed a representation theory of intuitionistic fuzzy perfect distributive lattices in the finite case. To that end, we have introduced the notion of intuitionistic fuzzy perfect distributive lattices and the one of fuzzy perfect Priestley spaces to show the equivalence between the category of finite intuitionistic fuzzy perfect Priestley spaces and the dual of the category of finite intuitionistic fuzzy perfect distributive lattices
