On the properties of sequences of fuzzy-valued Choquet integrable functions

Fuzzy Optimization and Decision Making - Tập 7 - Trang 417-431 - 2008
Rui-Sheng Wang1, Ming-Hu Ha2
1School of Information, Renmin University of China, Beijing, China
2College of Mathematics and Computers, Hebei University, Baoding, China

Tóm tắt

In this paper, we focus on investigating the properties of sequences of fuzzy-valued Choquet (for short, (C)-) integrable functions. Firstly, the concept of uniform (C)-integrabiliy and other new concepts like uniform absolute continuity and uniform boundedness for sequences of fuzzy-valued (C)-integrable functions are introduced and then the relations among them are discussed. As the applications of these concepts, we also present several convergence theorems for sequences of fuzzy-valued (C)-integrable functions by using uniform (C)-integrability.

Tài liệu tham khảo

Choquet G. (1953/1954) Theory of capacities Annals of Institute of Fourier 5:131–295. de Campos L.M., Bolanos M.J. (1992) Characterization and comparison of Sugeno and Choquet integrals. Fuzzy Sets and Systems 52: 61–67 Denneberg D. (1994) Nonadditive measure and integral. Kluwer Academic Publishers, Boston Fang J.X. (2007) Some properties of sequences of generalized fuzzy integrable functions. Fuzzy Sets and Systems 158: 1832–1842 Ha M.H., Wang X.Z., Yang L.Z., Y. Li. (2003) Sequences of (S) fuzzy integrable functions. Fuzzy Sets and Systems 138: 507–522 Ha M.H., Wu C.X. (1998) Fuzzy measure and fuzzy integral theory. Science Press, Beijing Meyera P., Roubensb M. (2006) On the use of the Choquet integral with fuzzy numbers in multiple criteria decision support. Fuzzy Sets and Systems 157: 927–938 Murofushi T., Sugeno M. (1993) Some quantities represented by Choquet integral. Fuzzy Sets and Systems 56: 229–235 Pap E. (1995) Null-ddditive set functions. Kluwer Academic Publishers, Dordrecht Ralescu D., Adams G. (1980) The fuzzy integral. Journal of Mathematical Analysis and Applications 75: 562–570 Sugeno, M. (1974). Theory of fuzzy integrals and its applications. Ph.D. Thesis, Tokyo Institute of Technology. Wang G.J., Li X.P. (1999) On the convergence of the fuzzy valued functional defined by μ-integrable fuzzy valued functions. Fuzzy Sets and Systems 107: 219–226 Wang R.S., Ha M.H. (2006) On Choquet integrals of fuzzy-valued functions. The Journal of Fuzzy Mathematics 14(1): 89–102 Wang Z., Klir G. (1992) Fuzzy measure theory. Plenum Press, New York Wang Z., Klir G.J., Wang W. (1996) Monotone set functions defined by Choquet integrals. Fuzzy Sets and Systems 81: 241–250 Wang Z., Yang R., Heng P.A., Leung K.S. (2006) Real-valued Choquet integrals with fuzzy-valued integrand. Fuzzy Sets and Systems 157: 256–269 Wu C., Sun B. (2007) A note on the extension of the null-additive set function on the algebra of subsets. Applied Mathematics Letters 20(7): 770–772 Wu C., Wang S., Ma M. (1993) Generalized fuzzy integrals: Part 1. Fundamental concepts. Fuzzy Sets and Systems, 57: 219–226 Yan J.A. (1998) Measure theory. Science Press, Beijing Yang R., Wang Z., Heng P.A., Leung K.S. (2005) Fuzzy numbers and fuzzification of the Choquet integral. Fuzzy Sets and Systems 153: 95–113 Zhang G. (1998) Fuzzy-valued measure theory. Tsinghua University Press, Beijing Zhang D., Wang Z. (1993) On set-valued fuzzy integrals. Fuzzy Sets and Systems 56: 63–67