Journal of Uncertain Systems, Volume (6), No (3), Year (2012-1) , Pages (214-222)

Title : ( Generalized Derivative of Fuzzy Nonsmooth Functions )

Authors: mohammad hadi noori skandari , Hamid Reza Erfanian , Ali Vahidian Kamyad ,

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In this paper, we consider fuzzy nonsmooth functions which can be appeared in a large number of systems and problems. To the best of the authors’ knowledge, there are not enough contributions about introducing suitable approximated derivatives for this class of fuzzy functions. For this purpose, we are going to define a generalized derivative (GD) for fuzzy nonsmooth functions. We first define a special functional optimization problem for crisp smooth functions which its optimal solution is the derivative of these functions. Then, we solve this problem for crisp nonsmooth functions and obtain the GD of these functions. Here, we apply the discretization method and introduce a linear programming problem for approximating the GD. In next step, we extend this definition of GD for intervalvalued nonsmooth functions. Moreover, using  alpha-levels of a fuzzy number, the GD of fuzzy nonsmooth functions is defined. In addition, we show that the result of our approach for fuzzy smooth functions is exactly similar to the generalized Hakuhara derivative defined by Bede. Finally, we obtain the GD of fuzzy nonsmooth functions in several illustrative examples.


, generalized derivative, smooth and nonsmooth functions, interval-valued function, fuzzy function, functional optimization
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author = {Noori Skandari, Mohammad Hadi and Erfanian, Hamid Reza and Vahidian Kamyad, Ali},
title = {Generalized Derivative of Fuzzy Nonsmooth Functions},
journal = {Journal of Uncertain Systems},
year = {2012},
volume = {6},
number = {3},
month = {January},
issn = {1752-8909},
pages = {214--222},
numpages = {8},
keywords = {generalized derivative; smooth and nonsmooth functions; interval-valued function; fuzzy function; functional optimization},


%0 Journal Article
%T Generalized Derivative of Fuzzy Nonsmooth Functions
%A Noori Skandari, Mohammad Hadi
%A Erfanian, Hamid Reza
%A Vahidian Kamyad, Ali
%J Journal of Uncertain Systems
%@ 1752-8909
%D 2012