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arXiv · 1210.8302

The logical content of triangular bases of fuzzy sets in {\L}ukasiewicz infinite-valued logic

Pietro Codara·Ottavio M. D'Antona·Vincenzo Marra
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Abstract

Continuing to pursue a research direction that we already explored in connection with G\"odel-Dummett logic and Ruspini partitions, we show here that {\L}ukasiewicz logic is able to express the notion of pseudo-triangular basis of fuzzy sets, a mild weakening of the standard notion of triangular basis. En route to our main result we obtain an elementary, logic-independent characterisation of triangular bases of fuzzy sets.

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Pietro Codara, Ottavio M. D'Antona, Vincenzo Marra. 2012-10-31. The logical content of triangular bases of fuzzy sets in {\L}ukasiewicz infinite-valued logic. https://doi.org/10.1016/j.fss.2013.11.004

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