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A note on a nilpotent lower bound of ilpotent triangular norms [Fuzzy Sets and Systems 104 (1999) 27–34]
FUZZY
sets and systems ELSEVIER
Fuzzy Sets and Systems 104 (1999) 137
Corrigendum
A note on a nilpotent lower bound ofnilpotent triangular norms [Fuzzy Sets and Systems 104 (1999) 27-34] 1 Radko Mesiar 2 Slovak Technical 65dversity, Department 0[' Matlwmatics. Radlinsk~ho 11. 813 68 Bratisla~:a, SIo~,akia
We are grateful to Prof. E. Pap, University Novi Sad, for a remark concerning Theorem 1 of this paper. Actually, the superadditivity of composite h o f and h o g was shown (and not of f o h and g o h as required). Consequently, all results remain valid, but reversing the relevant inequalities, i.e., we have shown the existence of an upper nilpotent bound of a finite system of nilpotent triangular norms. However,
we have in preparation a new paper with a general solution of continuous Archimedean bounds for a finite system of continuous Archimedean t-norms (both for upper and lower bounds). Therefore, all conclusions and applications described in Section 4 are still valid with exception of Example 1, where the relevant tnorm T is an upper bound of both T. and TI, (and not a lower bound as claimed).
I PIl of original article: S0165-0114(98)00255-3. 2 E-mail: [email protected] 0165-0114/99/$ see front matter @ 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 5 - 0 1 1 4 ( 9 8 ) 0 0 4 2 0 - 5
sets and systems ELSEVIER
Fuzzy Sets and Systems 104 (1999) 137
Corrigendum
A note on a nilpotent lower bound ofnilpotent triangular norms [Fuzzy Sets and Systems 104 (1999) 27-34] 1 Radko Mesiar 2 Slovak Technical 65dversity, Department 0[' Matlwmatics. Radlinsk~ho 11. 813 68 Bratisla~:a, SIo~,akia
We are grateful to Prof. E. Pap, University Novi Sad, for a remark concerning Theorem 1 of this paper. Actually, the superadditivity of composite h o f and h o g was shown (and not of f o h and g o h as required). Consequently, all results remain valid, but reversing the relevant inequalities, i.e., we have shown the existence of an upper nilpotent bound of a finite system of nilpotent triangular norms. However,
we have in preparation a new paper with a general solution of continuous Archimedean bounds for a finite system of continuous Archimedean t-norms (both for upper and lower bounds). Therefore, all conclusions and applications described in Section 4 are still valid with exception of Example 1, where the relevant tnorm T is an upper bound of both T. and TI, (and not a lower bound as claimed).
I PIl of original article: S0165-0114(98)00255-3. 2 E-mail: [email protected] 0165-0114/99/$ see front matter @ 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 5 - 0 1 1 4 ( 9 8 ) 0 0 4 2 0 - 5