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Chalco-Cano, Y.; Maqui-Huamán, Gino G.; Silva, G. N.; Jiménez-Gamero, M. D.

Algebra of generalized Hukuhara differentiable interval-valued functions: review and new properties. (English) Zbl 1423.26055

Fuzzy Sets Syst. 375, 53-69 (2019).
Summary: This article deals with the algebra of \(gH\)-differentiable interval-valued functions. Specifically, we give conditions for the \(gH\)-differentiability of the sum and the \(gH\)-difference of two \(gH\)-differentiable interval-valued functions; we also consider the product and the composition of a differentiable real function and a \(gH\)-differentiable interval-valued function. We briefly review existing results on the topic and show that some of them are not correct. New properties are also presented. Therefore, this article corrects, complements and generalizes previously obtained results. Some examples and counterexamples illustrate the theory.

Cited in 15 Documents

MSC:

26E50 Fuzzy real analysis
26A24 Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems

Keywords:

fuzzy-valued functions; interval-valued functions; generalized Hukuhara differentiability; algebra of interval-valued functions
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References:

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