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Computational Complexity pp 1177–1200Cite as

Fuzzy Logic

  • Reference work entry

Article Outline

Glossary

Definition of the Subject

Introduction

Conceptual Structure of Fuzzy Logic

The Basics of Fuzzy Set Theory

The Concept of Granulation

The Concepts of Precisiation and Cointensive Precisiation

The Concept of a Generalized Constraint

Principal Contributions of Fuzzy Logic

A Glimpse of What Lies Beyond Fuzzy Logic

Bibliography

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Abbreviations

Cointension:

A qualitative measure of proximity of meanings/input‐output relations.

Extension principle:

A principle which relates to propagation of generalized constraints.

f‑validity:

fuzzy validity.

Fuzzy if‑then rule:

A rule of the form: if X is A then Y is B. In general, A and B are fuzzy sets.

Fuzzy logic (FL):

A precise logic of imprecision, uncertainty and approximate reasoning.

Fuzzy logic gambit:

Exploitation of tolerance for imprecision through deliberatem‑imprecisiation followed by mm‐precisiation.

Fuzzy set:

A class with a fuzzy boundary.

Generalized constraint:

A constraint of the form X isr R, where X is the constrained variable, R is the constraining relation and r is an indexical variable which defines the modality of the constraint, that is, its semantics. In general, generalized constraints have elasticity.

Generalized constraint language:

A language generated by combination and propagation of generalized constraints.

Graduation:

Association of a scale of degrees with a fuzzy set.

Granuland:

Result of granulation.

Granular variable:

A variable which takes granules as variables.

Granulation:

Partitioning of an object/set into granules.

Granule:

A clump of attribute values drawn together by indistinguishability, equivalence, similarity, proximity or functionality.

Linguistic variable:

A granular variable with linguistic labels of granular values.

m‑precision:

Precision of meaning.

mh‐precisiand:

m‑precisiand which is described in a natural language (human‐oriented).

mm‐precisiand:

m‑precisiand which is described in a mathematical language (machine‐oriented).

p‑validity:

provable validity.

Precisiand:

Result of precisiation.

Precisiend:

Object of precisiation.

v‑precision:

Precision of value.

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Authors and Affiliations

  1. Department of EECS, University of California, Berkeley, USA

    Lotfi A. Zadeh

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  1. RAMTECH LIMITED, 122 Escalle Lane, Larkspur, CA, 94939, USA

    Robert A. Meyers Ph. D. (Editor-in-Chief) (Editor-in-Chief)

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Zadeh, L.A. (2012). Fuzzy Logic . In: Meyers, R. (eds) Computational Complexity. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1800-9_73

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