Fuzzy measures and integrals

We present fuzzy measures and fuzzy integrals as special poset homeomorphisms. Besides general fuzzy integrals, regular fuzzy integrals are introduced and some of their properties are discussed. State of art of fuzzy measure and fuzzy integral theory are briefly summarized and some further streaming is sketched.

[1]  Michel Grabisch,et al.  The symmetric Sugeno integral , 2003, Fuzzy Sets Syst..

[2]  R. Mesiar,et al.  Aggregation operators: new trends and applications , 2002 .

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

[4]  L. Zadeh Probability measures of Fuzzy events , 1968 .

[5]  S. T. Wierzcho An algorithm for identification of fuzzy measure , 1983 .

[6]  F. García,et al.  Two families of fuzzy integrals , 1986 .

[7]  Radko Mesiar,et al.  Measure-based aggregation operators , 2004, Fuzzy Sets Syst..

[8]  George J. Klir,et al.  Fuzzy sets, uncertainty and information , 1988 .

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

[10]  Peter Struk,et al.  Extremal fuzzy integrals , 2006, Soft Comput..

[11]  M. Grabisch,et al.  Bi-capacities for decision making on bipolar scales , 2002 .

[12]  Ivan Kramosil Probabilistic analysis of belief functions , 2001 .

[13]  Didier Dubois,et al.  Possibility Theory - An Approach to Computerized Processing of Uncertainty , 1988 .

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

[15]  G. Vitali,et al.  Sulla definizione di integrale delle funzioni di una variabile , 1925 .

[16]  Zhenyuan Wang,et al.  A new genetic algorithm for nonlinear multiregressions based on generalized Choquet integrals , 2003, The 12th IEEE International Conference on Fuzzy Systems, 2003. FUZZ '03..

[17]  Elena García Barriocanal,et al.  Choquet integral-based aggregation of interface usability parameters: identification of fuzzy measure , 2004 .

[18]  G. Klir,et al.  Fuzzy Measure Theory , 1993 .

[19]  Zhang Guang-Quan On fuzzy number-valued fuzzy measures defined by fuzzy number-valued fuzzy integrals II , 1992 .

[20]  Anna Kolesárová,et al.  Triangular norm-based iterative compensatory operators , 1999, Fuzzy Sets Syst..

[21]  Michel Grabisch,et al.  Identification of non-additive measures from sample data , 2003, Planning Based on Decision Theory.

[22]  S. Greco Bipolar Sugeno and Choquet integrals , 2002 .

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

[24]  Jun Li,et al.  On Egoroff's theorems on finite monotone non-additive measure space , 2005, Fuzzy Sets Syst..

[25]  Haruki Imaoka,et al.  On a Subjective Evaluation Model by a Generalized Fuzzy Integral , 1997, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

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

[27]  Deli Zhang,et al.  On set-valued fuzzy measures , 2004, Inf. Sci..

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