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Generalized differentiability and integrability for fuzzy set-valued functions on time scales

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Abstract

This paper deals with the fuzzy set-valued functions of real variables on time scale whose values are normal, convex, upper semicontinuous and compactly supported fuzzy sets in \(\mathbb {R}^{n}\). We introduce and study the fundamental properties of new class of derivative called generalized delta derivative (\(\Delta _{g}\)-derivative) and generalized delta integral (\(\Delta _{g}\)-integral) for such fuzzy functions.

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Authors and Affiliations

  1. Department of Mathematics, Koneru Lakshmaiah University, Vaddeswaram, Guntur dt., A.P., India

    Ch. Vasavi & G. Suresh Kumar

  2. Sainivas, D. No. 21-47, Opp. State Bank of India, Bank Street, Nuzvid, Krishna dt., A.P., India

    M. S. N. Murty

Authors
  1. Ch. Vasavi
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  2. G. Suresh Kumar
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  3. M. S. N. Murty
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Corresponding author

Correspondence to G. Suresh Kumar.

Additional information

Communicated by V. Loia.

The third author, M.S.N. Murty, is a retired professor from the Department of Mathematics, Acharya Nagarjuna University.

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Vasavi, C., Suresh Kumar, G. & Murty, M.S.N. Generalized differentiability and integrability for fuzzy set-valued functions on time scales. Soft Comput 20, 1093–1104 (2016). https://doi.org/10.1007/s00500-014-1569-1

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  • DOI: https://doi.org/10.1007/s00500-014-1569-1

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