The improper fuzzy Riemann integral and its numerical integration

Information Sciences

Volumn 111, Issue 1-4, 1998, Pages 109-137

  Wu, Hsien Chung ^a,b  

^a The University of Texas at Austin   (United States)

^b NONE   (Taiwan)

Author keywords

Closed fuzzy number; Improper fuzzy riemann integral; Least squares; Nonlinear programming; Simpson's rule

Indexed keywords

INTEGRATION; LEAST SQUARES APPROXIMATIONS; NONLINEAR PROGRAMMING; NUMBER THEORY; POLYNOMIALS; PROBLEM SOLVING;

CLOSED FUZZY NUMBER; IMPROPER FUZZY RIEMANN INTEGRAL; SIMPSON'S RULE;

FUZZY SETS;

EID: 0032202946     PISSN: 00200255     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-0255(98)00016-4     Document Type: Article

References (18)

1. M. Sugeno, Theory of Fuzzy Integrals and Its Applications, Ph.D. Dissertation, Tokyo Institute of Technology, 1974.
2. J.R. Sims, Z.Y. Wang, Fuzzy measures and fuzzy integrals: An overview, Int. J. General Systems 17 (1990) 157-189.
3. M.K. Luhandjula, Linear programming under randomness and fuzziness, Fuzzy Sets and Systems 10 (1983) 45-55.
4. Z. Qiao, Y. Zhang, G.-Y. Wang, On fuzzy random linear programming, Fuzzy Sets and Systems 65 (1994)31-49.
5. H. Kwakernaak, Fuzzy random variables I: Definitions and theorems, Inform. Sci. 15 (1978) 1-29.
6. M.L. Puri, D.A. Ralescu, Fuzzy random variables, J. Math. Anal. Appl. 114 (1986) 409-422.
7. T.M. Apostol, Mathematical Analysis, 2nd ed., Addison-Welesy, Reading, MA, 1974.
8. W. Rudin, Real and Complex Analysis, McGraw-Hill, New York, 1986.
9. M.S. Bazarra, C.M. Shetty, Nonlinear Programming, Wiley, New York, 1993.
10. L.A. Zadeh, Fuzzy sets, Inform. Control 8 (1965) 338-353.
11. M. Mizumoto, K. Tanaka, The four operations of arithmetic on fuzzy numbers, Systems Comput. Control 7 (1976) 703-710.
12. M. Sakawa, H. Yano, Feasibility and pareto optimality for multiobjective linear and linear fractional programming problems with fuzzy parameters, in: Verdegacy, M. Delgado (Eds.), The Interface between Artificial Intelligence and Operations Research in Fuzzy Environment, Verlag TUV, Rheinland, 1990, pp. 213-232.
13. L.A. Zadeh, The concept of linguistic variable and its application to approximate reasoning I, II and III, Inform. Sci. 8 (1975) 199-249; 8 (1975) 301-357; 9 (1975) 43-80.
14. L.A. Zadeh, The concept of linguistic variable and its application to approximate reasoning I, II and III, Inform. Sci. 8 (1975) 199-249; 8 (1975) 301-357; 9 (1975) 43-80.
15. L.A. Zadeh, The concept of linguistic variable and its application to approximate reasoning I, II and III, Inform. Sci. 8 (1975) 199-249; 8 (1975) 301-357; 9 (1975) 43-80.
16. C.V. Negoita, D.A. Ralescu, Applications of Fuzzy Sets to Systems Analysis, Wiley, New York, 1975.
17. H.L. Royden, Real Analysis, 2nd ed., Macmillan, New York, 1968.
18. H.T. Nguyen, A note on extension principle for fuzzy sets, J. Math. Anal. Appl. 64 (1978) 369-380.