Fuzzy logic: intelligence, control, and information
Fuzzy logic: intelligence, control, and information
Poset representation for gödel and nilpotent minimum logics
ECSQARU'05 Proceedings of the 8th European conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
A characterisation of bases of triangular fuzzy sets
FUZZ-IEEE'09 Proceedings of the 18th international conference on Fuzzy Systems
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By a Ruspini partition we mean a finite family of fuzzy sets {f"1,...,f"n},f"i:[0,1]-[0,1], such that @?"i"="1^nf"i(x)=1 for all x@?[0,1], where [0,1] denotes the real unit interval. We analyze such partitions in the language of Godel logic. Our first main result identifies the precise degree to which the Ruspini condition is expressible in this language, and yields inter alia a constructive procedure to axiomatize a given Ruspini partition by a theory in Godel logic. Our second main result extends this analysis to Ruspini partitions fulfilling the natural additional condition that each f"i has at most one left and one right neighbour, meaning that min"x"@?"["0","1"]{f"i"""1(x),f"i"""2(x),f"i"""3(x)}=0 holds for i"1i"2i"3.