FUZZY SETS (THEORY of)
Charles François (2004). FUZZY SETS (THEORY of), International Encyclopedia of Systems and Cybernetics, 2(1): 1377.
| Collection | International Encyclopedia of Systems and Cybernetics |
|---|---|
| Year | 2004 |
| Vol. (num.) | 2(1) |
| ID | ◀ 1377 ▶ |
| Object type | Epistemology, ontology or semantics, Methodology or model |
L.A. ZADEH writes: “The theory of fuzzy sets is, in effect, a step toward a rapprochement between the precision of classical mathematics and the pervasive imprecision of the real world — a rapprochement born of the incessant human quest for a better understanding of mental processes and cognition…
- “We have been slow in coming to the realization that much, perhaps most, of human cognition and interaction with the outside world involves constructs which are not sets in the clasical sense, but rather ”fuzzy sets“ (or subsets), that is, classes with unsharp boundaries in which the transition from membership to non-membership is gradual rather than abrupt. Indeed it can be argued that much of the logic of human reasoning is not the classical two-valued or even multivalued logic, but a logic with fuzzy truths, fuzzy connectives, and fuzzy rules of inference” (1973a & 1973b, p.28).
- “In our view, it is this fuzzy, and as yet not well understood, logic that plays a basic role in what may well be one of the most important facets of human thinking, namely, the ability to summarize information — to extract from the collection of masses of data impinging upon the human brain those and only those subcollections which are relevant to the performance of the task at hand…
- “Thus, the ability to manipulate fuzzy sets and the consequent summarizing capability constitute one of the most important assets of the human mind as well as a fundamental characteristic that distinguishes human intelligence from the type of machine intelligence that is embodied in present-day digital computers” (1973b, p.28-29).
Fuzzy sets theory includes fuzzy subsets, fuzzy functions, fuzzy categories, fuzzy topological spaces, fuzzy structures, etc…