Fuzzy Sets and Fuzzy Reasoning: An Introduction

Fuzzy set theory was initiated by Zadeh in 1965 xc1 and permits the treatment of vague, uncertain, imprecise and ill defined knowledge and concepts in an exact mathematical way. Throughout the years this theory was fully studied and used for the analysis, modelling and control of technological and nontechnological systems xc2–21. Actually, our life and world obey the priciple of compatibility of Zadeh, according to which "the closer one looks at a ‘real’ problem, the fuzzier becomes its solution". Stated informally, the essence of this principle is that, as the complexity of a system increases, out ability to make precise and yet significant statements about its behavior diminishes until a threshold beyond which precision and significance (relevance) become almost exclusive characteristics.