Calculus for interval-valued functions using generalized Hukuhara derivative and applications
Calculus for interval-valued functions using generalized Hukuhara derivative and applications
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DOI：
10.1016/j.fss.2012.12.004
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发表时间：
2013-05-16
影响因子：
3.9
通讯作者：
Jimenez-Gamero, M. D.
中科院分区：
文献类型：
--
作者：
Chalco-Cano, Y.;Rufian-Lizana, A.;Jimenez-Gamero, M. D.
利用区间值函数可微性的最一般概念--广义Hukuhara可微性，研究了区间值函数的微分学.给出了极限、连续、可积、可微的条件、例子和反例。特别强调的是类F（t）= C。g（t），其中C是区间，g是真实的变量的真实的函数。在这里，重点放在F和g不一定共享它们的属性的事实上，这是处理区间值函数时必须考虑的额外注意的基础。所得结果的两个应用。第一种方法确定了区间值随机元的Delta方法。在第二个应用程序中，一个新的程序，以获得解决方案的区间微分方程。我们的结果是相关的模糊集理论，因为通常的模糊运算，扩展功能和（数学）分析上的CC-割，这是区间。(C)2012爱思唯尔有限公司版权所有。
This paper is devoted to studying differential calculus for interval-valued functions by using the generalized Hukuhara differentiability, which is the most general concept of differentiability for interval-valued functions. Conditions, examples and counterexamples for limit, continuity, integrability and differentiability are given. Special emphasis is set to the class F(t) = C . g(t), where C is an interval and g is a real function of a real variable. Here, the emphasis is placed on the fact that F and g do not necessarily share their properties, underlying the extra care that must be taken into account when dealing with interval-valued functions. Two applications of the obtained results are presented. The first one determines a Delta method for interval valued random elements. In the second application a new procedure to obtain solutions to an interval differential equation is introduced. Our results are relevant to fuzzy set theory because the usual fuzzy arithmetic, extension functions and (mathematical) analysis are done on cc-cuts, which are intervals. (C) 2012 Elsevier B.V. All rights reserved.