The logical content of triangular bases of fuzzy sets in {\L}ukasiewicz infinite-valued logic
Logic in Computer Science
2013-11-26 v1 Logic
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.
Keywords
Cite
@article{arxiv.1210.8302,
title = {The logical content of triangular bases of fuzzy sets in {\L}ukasiewicz infinite-valued logic},
author = {Pietro Codara and Ottavio M. D'Antona and Vincenzo Marra},
journal= {arXiv preprint arXiv:1210.8302},
year = {2013}
}
Comments
Preprint submitted to Fuzzy Sets and Systems