The Journal of the Indian Mathematical Society

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Existence of Hukuhara Differentiability of Fuzzy-Valued Functions


Affiliations
1 School of Science and Engineering, Navrachana University of Vadodara-391410, India
2 Department of Applied Mathematics, M. S. University of Baroda, Vadodara-390001, India
     

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In this paper, we discuss existence of Hukuhara differentiability of fuzzy-valued functions. Several examples are worked out to check that fuzzy-valued functions are one time, two times and n-times H-differentiable. We study the effects of fuzzy modelling on existence of Hukuhara differentiability of fuzzy-valued functions. We discuss existence of gH-differentiability and its comparison with H-differentiability.

Keywords

Fuzzy-valued Functions, Hukuhara Differentiability, Fuzzy Modelling.
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  • Bede B. and Gal S. G., Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations, Fuzzy Sets and Systems, 151 (2005) 581-599.

  • Bede B. and Stefanini L., Generalized differentiability of fuzzy-valued functions, Fuzzy Sets and Systems, 230 (2013) 119-141.

  • Diamond P., Kloeden P., Metric spaces of fuzzy sets: Theory and Applications, World Scientific (1994).

  • George A. A., Fuzzy Ostrowski Type Inequalities, Computational and Applied mathematics. 22 (2003) 279-292.

  • George, A. A., Fuzzy Taylor Formulae, CUBO, A Mathematical Journal, 7 (2005) 1-13.

  • Hukuhara M., Integration des applications mesurables dont la valeur est un compact convexe, Funkc. Ekvac., 10 (1967) 205-223.

  • Hsien-Chung Wu, Duality Theory in Fuzzy Optimization Problems, Fuzzy Optimization and Decision Making, 3 (2004) 345-365.

  • Hsien-Chung Wu, An (α, β)-Optimal Solution Concept in Fuzzy Optimization Problems, Optimization, 53 (2004) 203-221.

  • Kaleva O., Fuzzy Differential Equations, Fuzzy Sets and Systems, 24 (1987) 301-317.

  • Pathak V.D and Pirzada U.M., Ncessary and Sufficient Optimality Conditions for Nonlinear Unconstrained Fuzzy Optimization Problem, Journal of the Indian Math. Soc., 80 (2013) 141-155.

  • Pirzada U. M. and Pathak V. D., Newton Method for Solving Multi-variable Fuzzy Optimization Problem, Journal of Optimization Theory and Applications; Springer, 156 (2013) 867-881.

  • Puri M. L. and Ralescu D. A., Differentials of fuzzy functions, J. of Math. Analysis and App., 91 (1983) 552-558.

  • Saito, S. and Ishii H., L-Fuzzy Optimization Problems by Parametric Representation, IEEE, (2001) 1173-1177.

  • Song S., Wu C., Existence and uniqueness of solutions to Cauchy problem of fuzzy differential equations, Fuzzy Sets and Systems, 110 (2000) 55-67.

  • Stefanini L., A generalization of Hukuhara difference and division for interval and fuzzy arithmetic, Fuzzy Sets Syst. 161 (2010) 1564-1584.

  • Stefanini L. and Bede B., Generalized Hukuhara differentiability of interval-valued functions and interval differential equations, Nonlinear Anal. 71 (2009) 1311-1328.


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  • Existence of Hukuhara Differentiability of Fuzzy-Valued Functions

Abstract Views: 400  |  PDF Views: 2

Authors

U. M. Pirzada
School of Science and Engineering, Navrachana University of Vadodara-391410, India
D. C. Vakaskar
Department of Applied Mathematics, M. S. University of Baroda, Vadodara-390001, India

Abstract


In this paper, we discuss existence of Hukuhara differentiability of fuzzy-valued functions. Several examples are worked out to check that fuzzy-valued functions are one time, two times and n-times H-differentiable. We study the effects of fuzzy modelling on existence of Hukuhara differentiability of fuzzy-valued functions. We discuss existence of gH-differentiability and its comparison with H-differentiability.

Keywords


Fuzzy-valued Functions, Hukuhara Differentiability, Fuzzy Modelling.

References