The Best Interval Representation of Fuzzy S-Implications and Automorphisms

The aim of this work is to analyze interval fuzzy S-implications and interval automorphisms. Starting from any fuzzy S-implication, it is shown how to obtain an interval fuzzy S-implication canonically. We proved that such interval fuzzy S-implications meet the optimality property and preserve the s...

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Bibliographic Details
Main Authors: Bedregal, B.C., Santiago, R.H.N., Reiser, R.H.S., Dimuro, G.P.
Format: Conference Proceeding
Language:English
Subjects:
Accuracy
Control systems
Fuzzy control
Fuzzy logic
Fuzzy set theory
Fuzzy sets
Humans
Mathematics
Optimal control
Uncertainty
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Summary:The aim of this work is to analyze interval fuzzy S-implications and interval automorphisms. Starting from any fuzzy S-implication, it is shown how to obtain an interval fuzzy S-implication canonically. We proved that such interval fuzzy S-implications meet the optimality property and preserve the same properties satisfied by fuzzy S-implications. In addition, commutative diagrams are used in order to relate fuzzy S-implications to interval fuzzy S-implications, and to understand how interval automorphisms act on interval S-implications, generating other interval fuzzy S-implications.
ISSN:1098-7584
DOI:10.1109/FUZZY.2007.4295636