Continuing to pursue a research direction that we already explored in connection with Gödel–Dummett logic and Ruspini partitions, we show here that Łukasiewicz 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.

The logical content of triangular bases of fuzzy sets in Łukasiewicz infinite-valued logic / P. Codara, O.M. DʼAntona, V. Marra. - In: FUZZY SETS AND SYSTEMS. - ISSN 0165-0114. - 247(2014), pp. 38-50. [10.1016/j.fss.2013.11.004]

The logical content of triangular bases of fuzzy sets in Łukasiewicz infinite-valued logic

P. Codara;O.M. DʼAntona;V. Marra
2014

Abstract

Continuing to pursue a research direction that we already explored in connection with Gödel–Dummett logic and Ruspini partitions, we show here that Łukasiewicz 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.
Abstract Schauder bases; Axiomatisations; Fuzzy partitions; Fuzzy sets; Triangular bases; Łukasiewicz logic
Settore MAT/01 - Logica Matematica
Settore INF/01 - Informatica
2014
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/232253
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