Fuzzy Sets and Fuzzy Systems: A Brief Introduction
Janusz Kacprzyk · Studies in fuzziness and soft computing · 2000
We present a brief introduction to the theory of fuzzy sets and systems for readers who are not yet familiar with this powerful formal apparatus meant for the representation and processing of imprecisely specified (vague) concepts, descriptions, relations, etc. We show basic elements related to: the very concept of a fuzzy set, properties of fuzzy sets, operations on fuzzy sets, fuzzy relations, linguistic variables, fuzzy conditional statements and the compositional rule of inference, fuzzy numbers, probabilities of fuzzy events, defuzzification, approaches to fuzzy logic, and the essence of Bellman and Zadeh’s (1970) approach to decision making under fuzziness.