Fuzzy Measures and Choquet Integral on Discrete Spaces

This paper studies some relationships between fuzzy relations, fuzzy graphs and fuzzy measure. It is shown that a fundamental theorem of Discrete Convex Analysis is derived from the theory of fuzzy measures and the Choquet integral.

[1]  Swarup Medasani,et al.  Graph matching by relaxation of fuzzy assignments , 2001, IEEE Trans. Fuzzy Syst..

[2]  Kiran R. Bhutani,et al.  On M-strong fuzzy graphs , 2003, Inf. Sci..

[3]  Yasuo Narukawa,et al.  Choquet integral and Sugeno integral as aggregation functions , 2003 .

[4]  Christian Borgelt,et al.  Learning possibilistic graphical models from data , 2003, IEEE Trans. Fuzzy Syst..

[5]  Christiane Fellbaum,et al.  Book Reviews: WordNet: An Electronic Lexical Database , 1999, CL.

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

[7]  M. Blue,et al.  Unified approach to fuzzy graph problems , 2002, Fuzzy Sets Syst..

[8]  Malcolm J. Beynon,et al.  The introduction and utilization of (l, u)‐graphs in the extended variable precision rough sets model , 2003, Int. J. Intell. Syst..

[9]  László Lovász,et al.  Submodular functions and convexity , 1982, ISMP.

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

[11]  Assia Alaoui,et al.  On fuzzification of some concepts of graphs , 1999, Fuzzy Sets Syst..

[12]  Azriel Rosenfeld,et al.  Strong arcs in fuzzy graphs , 2003, Inf. Sci..

[13]  Kazuo Murota,et al.  Matrices and Matroids for Systems Analysis , 2000 .

[14]  Zhi-Qiang Liu,et al.  On causal inference in fuzzy cognitive maps , 2000, IEEE Trans. Fuzzy Syst..

[15]  A. Boulmakoul Generalized path-finding algorithms on semirings and the fuzzy shortest path problem , 2004 .

[16]  Gabriella Pasi,et al.  Modeling users' preferences in systems for information access , 2003, Int. J. Intell. Syst..

[17]  Pedro Larrañaga,et al.  Learning Bayesian networks in the space of structures by estimation of distribution algorithms , 2003, Int. J. Intell. Syst..

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

[19]  Satoru Fujishige,et al.  Submodular functions and optimization , 1991 .

[20]  Kazuo Murota,et al.  Discrete convex analysis , 1998, Math. Program..

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