Minimal solution of fuzzy linear system of differential equations

Neural Computing and Applications

Volumn 21, Issue SUPPL. 1, 2012, Pages 329-336

  Mosleh, Maryam ^a   Otadi, Mahmood ^a  

^a ISLAMIC AZAD UNIVERSITY   (Iran)

Author keywords

Fuzzy number; Fuzzy system; Linear fuzzy differential equations; Minimal solution

Indexed keywords

ARBITRARY INPUTS; FUZZY DERIVATIVES; FUZZY LINEAR SYSTEM; FUZZY NUMBERS; FUZZY VECTORS; INITIAL CONDITIONS; LINEAR FUZZY DIFFERENTIAL EQUATIONS; MINIMAL SOLUTIONS; PSEUDO-INVERSES; SUFFICIENT CONDITIONS;

FUZZY RULES; FUZZY SYSTEMS; LINEAR SYSTEMS; VECTORS;

DIFFERENTIAL EQUATIONS;

EID: 84865766956     PISSN: 09410643     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00521-012-0913-6     Document Type: Article

References (39)

1. Abbasbandy S, Jafarian A, Ezzati R (2005) Conjugate gradient method for fuzzy symmetric positive definite system of linear equations. Appl Math Comput 171: 1184-1191.
2. Abbasbandy S, Nieto JJ, Alavi M (2005) Tuning of reachable set in one dimensional fuzzy differential inclusions. Chaos Solitons Fractals 26: 1337-1341.
3. Abbasbandy S, Ezzati R, Jafarian A (2006) LU decomposition method for solving fuzzy system of linear equations. Appl Math Comput 172: 633-643.
4. Abbasbandy S, Otadi M, Mosleh M (2008) Minimal solution of general dual fuzzy linear systems. Chaos Solitons Fractals 37: 1113-1124.
5. Allahviranloo T, Ahmadi N, Ahmadi E (2007) Numerical solution of fuzzy differential equations by predictor-corrector method. Sciences 177: 1633-1647.
6. Allahviranloo T, Ahmadi E, Ahmadi N (2008) Nth-order fuzzy linear differential equations. Inf Sci 178: 1309-1324.
7. Allahviranloo T, Kiani NA, Motamedi N (2009) Solving fuzzy differential equations by differential transformation. Inf Sci 179: 956-966.
8. Allahviranloo T, Barkhordari Ahmadi M (2010) Fuzzy Laplace transforms. Soft Comput 14: 235-243.
9. Asady B, Abbasbandy S, Alavi M (2005) Fuzzy general linear systems. Appl Math Comput 169: 34-40.
10. Barnet S (1990) Matrix methods and applications. Clarendon Press, Oxford.
11. Buckley JJ, Feuring T (2000) Fuzzy differential equations. Fuzzy Sets Syst 110: 69-77.
12. Caldas M, Jafari S (2005) θ-Compact fuzzy topological spaces. Chaos Solitons Fractals 25: 229-232.
13. Chang SL, Zadeh SL (1972) On fuzzy mapping and control. IEEE Trans Syst Man Cybem 2: 30-34.
14. Dubois D, Prade H (1978) Operations on fuzzy numbers. J Syst Sci 9: 613-626.
15. Dubois D, Prade H (1982) Towards fuzzy differential calculus: part3, differentiation. Fuzzy Sets Syst 8: 225-233.
16. Elnaschie MS (2004) A review of E-infinity theory and the mass spectrum of high energy particle physics. Chaos Solitons Fractals 19: 209-236.
17. Elnaschie MS (2004) The concepts of E infinity: an elementary introduction to the Cantorian-fractal theory of quantum physics. Chaos Solitons Fractals 22: 495-511.
18. Elnaschie MS (2005) On a fuzzy Kãhler manifold which is consistent with the two slit experiment. Int J Nonlinear Sci Numer Simul 6: 95-98.
19. Elnaschie MS (2006) Elementary number theory in superstrings, loop quantum mechanics, twistors and E-infinity high energy physics. Chaos Solitons Fractals 27: 297-330.
20. Elnaschie MS (2006) Superstrings, entropy and the elementary particles content of the standard model. Chaos Solitons Fractals 29: 48-54.
21. Feng G, Chen G (2005) Adaptive control of discrete-time chaotic systems: a fuzzy control approach. Chaos Solitons Fractals 23: 459-467.
22. Friedman M, Ming M, Kandel A (1998) Fuzzy linear systems. Fuzzy Sets Syst 96: 201-209.
23. Friedman M, Ming M, Kandel A (2000) Duality in fuzzy linear systems. Fuzzy Sets Syst 109: 55-58.
24. Goetschel R, Voxman W (1986) Elementary fuzzy calculus. Fuzzy Sets Syst 18: 31-43.
25. ∞ variable universe adaptive fuzzy control for chaotic system. Chaos Solitons Fractals 24: 1075-1086.
26. Kaleva O (1987) Fuzzy differential equations. Fuzzy Sets Syst 24: 301-317.
27. Kaufmann A, Gupta MM (1985) Introduction fuzzy arithmetic. van Nostrand Reinhold, New York.
28. Kincaid D, Cheney W (1996) Numerical analysis, mathematics of scientific computing, 2nd edn. Brooks/Cole Publishing Co., Pacific Grove.
29. Ming M, Friedman M, Kandel A (1999) A new fuzzy arithmetic. Fuzzy Sets Syst 108: 83-90.
30. Ming M, Friedman M, Kandel A (1999) Numerical solutions of fuzzy differential equations. Fuzzy Sets Syst 105: 133-138.
31. Nozari K, Fazlpour B (2007) Some consequences of spacetime fuzziness. Chaos Solitons Fractals 34: 224-234.
32. Otadi M, Mosleh M (2011) Simulation and evaluation of dual fully fuzzy linear systems by fuzzy neural network. Appl Math Model 35: 5026-5039.
33. Otadi M, Mosleh M, Abbasbandy S (2011) Numerical solution of fully fuzzy linear systems by fuzzy neural network. Soft Comput 15: 1513-1522.
34. Park JH (2004) Intuitionistic fuzzy metric spaces. Chaos Solitons Fractals 22: 1039-1046.
35. Pearson DW (1997) A property of linear fuzzy differential equations. Appl Math Lett 10: 99-103.
36. Puri ML, Ralescu DA (1983) Differentials of fuzzy functions. J Math Anal Appl 91: 552-558.
37. Seikkala S (1987) On the fuzzy initial value problem. Fuzzy Sets Syst 24: 319-330.
38. Tanaka Y, Mizuno Y, Kado T (2005) Chaotic dynamics in the Friedman equation. Chaos Solitons Fractals 24: 407-422.
39. Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning. Inf Sci 8: 199-249.