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Mathematical analysis of interval-valued fuzzy relations: Application to approximate reasoning

✍ Scribed by H. Bustince; P. Burillo

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
131 KB
Volume
113
Category
Article
ISSN
0165-0114

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✦ Synopsis

In this paper, interval-valued fuzzy relations between sets X and Y are introduced as fuzzy subsets of the cartesian product X Γ— Y , and t-norms and t-conorms are chosen in such a way that as many properties of relations in 2-valued logic are preserved. Besides, we will see that if we require certain reasonable properties, including distributivity, then we end up with the only possible choice: min and max. Finally, as an example, a method of inference in approximate reasoning for the one-dimensional case based on interval-valued fuzzy sets is considered and discussed using the idea of interval-valued fuzzy relations.

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