Handbook of fuzzy computation by Enrique H Ruspini; Piero Patrone Bonissone; Witold Pedrycz

By Enrique H Ruspini; Piero Patrone Bonissone; Witold Pedrycz

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Fundamental studies are also required to gain a better understanding of the conceptual bases of fuzzy logic, particularly as they relate to important notions of similarity and utility and to cognitive processes of analogical reasoning. , why a typical ‘small dog’ is neither a typical dog nor a typical small animal) and from a deeper philosophical consideration of the notion of typicality itself. Another area worthy of special attention-particularly when considering the philosophical concern of fuzzy-set-based methods for the abstraction of essential aspects of system behavior-is that of automated abstraction and summarization: a field of application that has become increasingly important because of the recent explosion in the amount of information accessible through networked computer systems.

For example, in the conceptual frame of a Euclidean plane, to understand the theorem of Pythagoras many earlier mathematical concepts that can be translated by precise terms are needed. This theorem, once established and made explicit by a precise rule, is definitive knowledge for triangles in a Euclidean plane. However, for example, in the conceptual frame of social life, the rule ‘After receiving the bill in a restaurant, give a tip of 15%, but if the food and drink were good and the service excellent, then give at least 20%’ describes knowledge that is neither precise nor definitive.

The interpretation of such statements-rooted in notions of generalized similarityfalls outside the scope of this introductory chapter but is discussed elsewhere in this Handbook. It will suffice to say here that these statements describe the degree of ‘ease’ by which certain concepts match certain situations. The ability to represent vague concepts by possibility distributions is central to the developments of fuzzy set theory, which was conceived, to some extent, as a way to represent and manipulate linguistic utterances as they are commonly found in everyday discourse.

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