Kimberling, C.: On a class of associative functions. Publ. Math. Debrecen 20 (1973), 21--39.  Home/Search   Document Not in Database   Summary   Related Articles

....the support of the project no. VS 96049 of the Czech Ministry of Education, COST Action 15, the grants no. 201 97 0437 and 402 96 0414 of the Grant Agency of the Czech Republic and the grant VEGA 1 4064 97. 1 The first investigation of diagonals of continuous t norms is due to Kimberling [3], namely for the case of strict t norms. We recall his result in a slightly modified version in Section 2. Section 3 is devoted to the diagonals of nilpotent and Archimedean t norms. In Section 4, we characterize the diagonals of general continuous t norms. In each case, the class of all t norms ....

....x for all x 2 ]0; 1[ We shall prove that the necessary conditions from the latter proposition are also sufficient. Let ffi be an automorphism of [0; 1] such that ffi(x) x for all x 2 ]0; 1[ We shall construct an additive generator, f , of a strict t norm with the given diagonal ffi (see also [3]) We denote by id the identity on [0; 1] and by Z the set of all integers. We define functions ffi n , n 2 Z, recursively by ffi n = 8 : id if n = 0; ffi ffi ffi n Gamma1 if n 0; ffi Gamma1 ffi ffi n 1 if n 0: We start the construction of f at an arbitrary point s 2 ]0; ....

Kimberling, C.: On a class of associative functions. Publ. Math. Debrecen 20 (1973), 21--39.

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