Level-Dependent Sugeno Integral

In this paper, a new concept of level-dependent Sugeno integral is introduced, and it is used to represent comonotone maxitive aggregation functions acting on a complete scale K. The relationship between the level-dependent Sugeno integral and some other types of fuzzy integrals is shown, and properties of the level-dependent Sugeno integral are discussed. Several examples show that the level-dependent Sugeno integral can have different aggregation attitudes for low input values than for high input values, and thus, overcome problems that arise while using the Sugeno integral.

[1]  Steven Greenberg,et al.  Syllable-proximity evaluation in automatic speech recognition using fuzzy measures and a fuzzy integral , 2003, The 12th IEEE International Conference on Fuzzy Systems, 2003. FUZZ '03..

[2]  R. Mesiar,et al.  Aggregation operators: properties, classes and construction methods , 2002 .

[3]  Endre Pap,et al.  Handbook of measure theory , 2002 .

[4]  D. Denneberg.  Non-additive measure and integral , 1994 .

[5]  D. Schmeidler.  Integral representation without additivity , 1986 .

[6]  Yi-Chung Hu,et al.  Functional-link net with fuzzy integral for bankruptcy prediction , 2007, Neurocomputing.

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

[8]  Michel Grabisch,et al.  Fuzzy Measures and Integrals , 1995 .

[9]  Doretta Vivona,et al.  Aggregation operators and associated fuzzy measures , 2001 .

[10]  Tuan D. Pham,et al.  An image restoration by fusion , 2001, Pattern Recognit..

[11]  S. Weber.  Two integrals and some modified versions-critical remarks , 1986 .

[12]  Martin Kalina,et al.  Fuzzy Preference Relations and Lukasiewicz Filters , 2007, EUSFLAT Conf..

[13]  Michio Sugeno,et al.  Canonical Hierarchical Decomposition of Choquet Integral Over Finite Set with Respect to Null Additive Fuzzy Measure , 1998, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[14]  H.T. Nguyen,et al.  A modification of Sugeno integral describes stability and smoothness of fuzzy control , 1998, 1998 IEEE International Conference on Fuzzy Systems Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98CH36228).

[15]  Andrey Temko,et al.  Fuzzy integral based information fusion for classification of highly confusable non-speech sounds , 2008, Pattern Recognit..

[16]  Radko Mesiar,et al.  A Universal Integral as Common Frame for Choquet and Sugeno Integral , 2010, IEEE Transactions on Fuzzy Systems.

[17]  Olivier Strauss,et al.  Variable structuring element based fuzzy morphological operations for single viewpoint omnidirectional images , 2007, Pattern Recognit..

[18]  G. Choquet.  Theory of capacities , 1954 .

[19]  R. Mesiar,et al.  CHAPTER 33 – Monotone Set Functions-Based Integrals , 2002 .

[20]  Jean-Luc Marichal,et al.  On Sugeno integral as an aggregation function , 2000, Fuzzy Sets Syst..

[21]  Radko Mesiar,et al.  A concept of universal integral based on measures of level sets , 2009, 2009 7th International Symposium on Intelligent Systems and Informatics.

[22]  Vicenç Torra,et al.  Generalized transformed t-conorm integral and multifold integral , 2006, Fuzzy Sets Syst..

[23]  Andrea Mesiarová-Zemánková,et al.  Construction of aggregation operators: new composition method , 2003, Kybernetika.

[24]  Vicenç Torra,et al.  Twofold integral and multi-step Choquet integral , 2004, Kybernetika.

[25]  Radko Mesiar,et al.  Weighted ordinal means , 2007, Inf. Sci..

[26]  N. Shilkret.  Maxitive measure and integration , 1971 .

[27]  Patricia Melin,et al.  A hybrid modular neural network architecture with fuzzy Sugeno integration for time series forecasting , 2007, Appl. Soft Comput..

[28]  Congxin Wu,et al.  Generalized fuzzy integrals of fuzzy-valued functions , 1998, Fuzzy Sets Syst..

[29]  Radko Mesiar,et al.  A Universal Integral , 2007, EUSFLAT Conf..

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