Title :
Copula-Like Operations on Finite Settings
Author :
Mayor, Gaspar ; Suner, Jaume ; Torrens, Joan
Author_Institution :
Dept. of Math. & Comput. Sci., Univ. of the Balearic Islands, Illes Balears, Spain
Abstract :
This paper deals with discrete copulas considered as a class of binary aggregation operators on a finite chain. A representation theorem by means of permutation matrices is given. From this characterization, we study the structure of associative discrete copulas and a theorem of decomposition of any discrete copula in terms of associative discrete copulas is obtained. Finally, some aspects concerning their extension to copulas are dealt with.
Keywords :
fuzzy logic; fuzzy set theory; statistical distributions; associative discrete copula; binary aggregation operators; finite chain; fuzzy logic; fuzzy sets; permutation matrices; Computer science; Concrete; Distribution functions; Fuzzy logic; Fuzzy set theory; Fuzzy sets; Mathematics; Matrix decomposition; Performance evaluation; Uncertainty; Aggregation operator; copula; discrete binary operation; divisibility; permutation matrix; triangular norm;
Journal_Title :
Fuzzy Systems, IEEE Transactions on
DOI :
10.1109/TFUZZ.2004.840129
