"RIV/68407700:21230/09:00157777!RIV10-GA0-21230___" . . . "US - Spojen\u00E9 st\u00E1ty americk\u00E9" . . "Convex combinations of nilpotent triangular norms"@en . "P(GA201/07/1136)" . "Nilpotent triangular norm; Reidmeister condition; Convex combination"@en . . "350" . "Convex combinations of nilpotent triangular norms" . "RIV/68407700:21230/09:00157777" . . . "[CAD7E3777247]" . "Convex combinations of nilpotent triangular norms"@en . "0022-247X" . "000261895800025" . . . "Convex combinations of nilpotent triangular norms" . . "Petr\u00EDk, Milan" . . "308313" . "Journal of Mathematical Analysis and Its Applications" . . "21230" . "In this paper we deal with the open problem of convex combinations of continuous triangular norms stated by Alsina, Frank, and Schweizer [C. Alsina, M.J. Frank, B. Schweizer, Problems on associative functions, Aequationes Math. 66 (2003) 128--140, Problems 5 and 6]. They pose a question whether a non-trivial convex combination of triangular norms can ever be a triangular norm. The main result of this paper gives a negative answer to the question for any pair of continuous Archimedean triangular norms with different supports. With the help of this result we show that a non-trivial convex combination of nilpotent t-norms is never a t-norm. The main result also gives an alternative proof to the result presented by Ouyang and Fang [Y. Ouyang, J. Fang, Some observations about the convex combination of continuous triangular norms, Nonlinear Anal., 68 (11) (2008) 3382--3387, Theorem 3.1]. In proof of the main theorem we utilize the Reidmeister condition known from the web geometry."@en . "In this paper we deal with the open problem of convex combinations of continuous triangular norms stated by Alsina, Frank, and Schweizer [C. Alsina, M.J. Frank, B. Schweizer, Problems on associative functions, Aequationes Math. 66 (2003) 128--140, Problems 5 and 6]. They pose a question whether a non-trivial convex combination of triangular norms can ever be a triangular norm. The main result of this paper gives a negative answer to the question for any pair of continuous Archimedean triangular norms with different supports. With the help of this result we show that a non-trivial convex combination of nilpotent t-norms is never a t-norm. The main result also gives an alternative proof to the result presented by Ouyang and Fang [Y. Ouyang, J. Fang, Some observations about the convex combination of continuous triangular norms, Nonlinear Anal., 68 (11) (2008) 3382--3387, Theorem 3.1]. In proof of the main theorem we utilize the Reidmeister condition known from the web geometry." . "1"^^ . . . "5"^^ . . "1" . "2"^^ . .