Fuzzy sets and t-norms in the light of fuzzy logic

Vilém Novák; Witold Pedrycz

doi:10.1016/S0020-7373(88)80041-5

Fuzzy sets and t-norms in the light of fuzzy logic

Vilém Novák
, Witold Pedrycz

Department of Measurements and Control Systems (RAU/RAU2)

Czech Academy of Sciences

Research output: Contribution to journal › Article › peer-review

14 Citations (Scopus)

Abstract

The paper is a discussion of the many-valued fuzzy logic, which is syntactico-semantically complete and its impact on the fuzzy set theory, namely on the operations with fuzzy sets. Arguments that all the operations with membership grades must fulfil the so called fitting condition are given. It follows that general t-norms are not suitable to be basis of the operations with fuzzy sets. Some general classes of operations with membership grades are presented.

Original language	English
Pages (from-to)	113-127
Number of pages	15
Journal	International Journal of Man-Machine Studies
Volume	29
Issue number	2
DOIs	https://doi.org/10.1016/S0020-7373(88)80041-5
Publication status	Published - 1988

ASJC Scopus subject areas

General Engineering

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10.1016/S0020-7373(88)80041-5

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abstract = "The paper is a discussion of the many-valued fuzzy logic, which is syntactico-semantically complete and its impact on the fuzzy set theory, namely on the operations with fuzzy sets. Arguments that all the operations with membership grades must fulfil the so called fitting condition are given. It follows that general t-norms are not suitable to be basis of the operations with fuzzy sets. Some general classes of operations with membership grades are presented.",

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AB - The paper is a discussion of the many-valued fuzzy logic, which is syntactico-semantically complete and its impact on the fuzzy set theory, namely on the operations with fuzzy sets. Arguments that all the operations with membership grades must fulfil the so called fitting condition are given. It follows that general t-norms are not suitable to be basis of the operations with fuzzy sets. Some general classes of operations with membership grades are presented.

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Fuzzy sets and t-norms in the light of fuzzy logic

Abstract

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