Jiří Močkoř

Mathematical principles of fuzzy logic

Preface. 1. Fuzzy Logic: What, Why, for Which? 2. Algebraic Structures for Logical Calculi. 3. Logical Calculi and Model Theory. 4. Fuzzy Logic in Narrow Sense. 5. Functional Systems in Fuzzy Logic Theories. 6. Fuzzy Logic in Broader Sense. 7. Topoi and Categories of Fuzzy Sets. 8. Few Historical and Concluding Remarks. References. Index.

Fuzzy and non-deterministic automata

Abstract The existence of isomorphism between the category of fuzzy automata and the category of chains of non-deterministic automata is proved and some relationships between output fuzzy sets of these systems are investigated.

Semigroup homomorphisms and fuzzy automata

Abstract A generalized Ω-fuzzy automaton over a complete residuated lattice Ω and a monoid (M,*) and with a set S of states is introduced as a monoid homomorphism F:(M,*)→(?,∘), where (?,∘) is a monoid of Ω-fuzzy sets in a set S×S. An extension principle depending of proper filters Φ in Ω is introduced which then enables to introduce morphisms between generalized Ω-fuzzy automata and to introduce the category ℱΦ of these automata. It is proved that categories of classical fuzzy automata, non-deterministic automata and some other systems are equivalent to subcategories of ℱΦ for a suitable filter Φ.

Fuzzy sets and cut systems in a category of sets with similarity relations

Let

A CATEGORY OF FUZZY AUTOMATA

\Upomega

Fuzzy objects in spaces with fuzzy partitions

be a complete residuated lattice. Let

Fuzzy logic models in a category of fuzzy relations

{\mathbf{SetR}}(\Upomega)