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The logical content of triangular bases of fuzzy sets in Łukasiewicz infinite-valued logic (1210.8302v1)
Published 31 Oct 2012 in cs.LO and math.LO
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.