Uogólnione schematy i reguły wnioskowania w logice rozmytej

Abstract

In Chapter 1 we recall the most important notions in the theory of fuzzy sets. In Chapter 2 we give some basic facts regarding approximate reasoning. In the main part of the thesis we consider functional equations and inequalities mentioned above when one function is given - usually a t-norm T (or a semicopula or any other generalization of a classical conjunction). Therefore we show some solutions for chosen families of fuzzy im- plications. In Chapter 3 we focus on hypothetical syllogism - there are solutions for (CRI-GHS), (BK-GHS) and (HS), but also we present here some algebraic properties of a composition sup-T. Chapter 4 contains information regarding solutions of (CRI-GMP), (BK-GMP) and (MP). In Chapter 5 analogous facts for (CRI-GMT), (BK-GMT) and (MT) can be found. Solutions for (CRI-GRA), (BK-GRA) and (RA) have been described in Chapter 6. In Chapter 7 we shortly give some remarks concerning some other possible functional equa- tions that might be received when combinig rules of inference and different fuzzy relations. In last Chapter 8, we present a different method of reasoning - similarity based reasoning. Also we give some remarks for two main strategies in approximate reasoning - FITA (First Infer Then Aggregate) and FATI (First Aggregate Then Infer) with respect to some proven theorems.