Sugeno and Shilkret integrals, and T- and S-evaluators

At SISY 2008 conference we studied the Sugeno, Shilkret and Cho-quet integrals and some of their level-dependent modifications as TL-(SL-) evaluators. In this contribution we give an overview of possible level-dependent generalizations of Sugeno and Shilkret integrals. We show under which conditions these integrals and their generalizations are T- and/or S-evaluators for an arbitrary t-norm T and t-conorm S.

[1]  S. Bodjanova,et al.  Self-duality of fuzzy integral-based TL- and SL-evaluators , 2008, 2008 6th International Symposium on Intelligent Systems and Informatics.

[2]  Radko Mesiar,et al.  Domination of Aggregation Operators and Preservation of Transitivity , 2002, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[3]  Radko Mesiar,et al.  Comonotone maxitivity and extended Sugeno integral , 2008 .

[4]  E. Pap Null-Additive Set Functions , 1995 .

[5]  Salvatore Greco,et al.  The Choquet integral with respect to a level dependent capacity , 2011, Fuzzy Sets Syst..

[6]  Radko Mesiar,et al.  Domination of ordered weighted averaging operators over t-norms , 2004, Soft Comput..

[7]  Martin Kalina,et al.  T-evaluators and S-evaluators , 2009, Fuzzy Sets Syst..

[8]  Radko Mesiar,et al.  Level-Dependent Sugeno Integral , 2009, IEEE Transactions on Fuzzy Systems.