Fuzzy Sets.

Zadeh, L. A. (1965). Fuzzy Sets. Information and Control, 8(3), 338-353.

Type

Journal article

Intellectual base

Primary research

Year

1965

Volume

8

Issue

3

Pages

338-353

ISSN

0019-9958

DOI

10.1016/s0019-9958(65)90241-x

DOI registrant

Elsevier

Link

https://doi.org/10.1016/S0019-9958(65)90241-X

Cited from

mathematics, philosophy

Cited by

5 citations across 5 artifacts.

Each citation links to the sentence it supports in the citing article.

Primes

• Classification
  • The same property has a shadow side: the sharp boundaries that enable consistent, scalable application also flatten continuous underlying variation, treating cases just inside and just outside a category as categorically different when they may be near-identical—the very mismatch Zadeh (1965) addressed by introducing fuzzy sets, in which membership is graded rather than crisp.

    This sourceIntroduces graded membership as a generalization of crisp set membership, addressing the mismatch between sharp classification boundaries and continuous underlying variation.

• Fuzzy Set
  • Zadeh's 1965 paper introduced exactly this graded-membership structure and extended inclusion, union, intersection, complement, relation, and convexity to it.
• Set and Membership
  • Fuzzy-set

    This sourceIntroduces graded membership as a generalization of crisp set membership, addressing the mismatch between sharp classification boundaries and continuous underlying variation.

Domain-specific

• Fuzzy rule
  • Its operational meaning depends on declared choices for antecedent connectives, fuzzy implication or firing, consequent representation, aggregation with other rules, and, when a crisp action is required, defuzzification or weighted output.
• Vague set
  • … that the universe, truth and false membership functions, unit-interval codomain, t(x)+f(x) no greater than one and resulting membership interval and hesitation interpretation are explicit. to An applied instance preserves the same invariant under a changed scale, notation, jurisdiction, dataset, or implementation..

Verification

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