Axiomatic approach to implication for approximate reasoning with fuzzy logic

This paper aims to give greater understanding than hitherto, to the choice of implications rules when modelling a given situation using approximate reasoning with fuzzy logic. The approach does not limit itself to any particular root multi-valued logic, but rather asserts properties of implication w...

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Bibliographic Details
Published in:Fuzzy sets and systems 1980-01, Vol.3 (2), p.193-219
Main Authors: Baldwin, J.F., Pilsworth, B.W.
Format: Article
Language:English
Subjects:
Approximate reasoning
Fuzzy logic
Fuzzy sets Implication
Modelling
Multi-valued logic
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Summary:This paper aims to give greater understanding than hitherto, to the choice of implications rules when modelling a given situation using approximate reasoning with fuzzy logic. The approach does not limit itself to any particular root multi-valued logic, but rather asserts properties of implication which satisfy an intuitive understanding of the nature of fuzzy deduction. On this basis, various rules of implication which commonly occur in the literature are investigated and a number of these are rejected as unsuitable. Four axioms are stated which cover the desirable properties of implication postulated. Then several classes of implication relations are derived which satisfy the axioms and which are based on the Lukasiewicz logical rule and a modification of another well-known rule.
ISSN:0165-0114
1872-6801
DOI:10.1016/0165-0114(80)90054-8