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India; Russia Guwahati; Moscow
Year
2021
Volume
31
Issue
4
Pages
578-596
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Section Mathematics
Title Soft rational line integral
Author(-s) Acharjee S.a, Molodtsov D.A.b
Affiliations Gauhati Universitya, Dorodnitsyn Computing Centre, Russian Academy of Sciencesb
Abstract Soft set theory is a new area of mathematics that deals with uncertainties. Applications of soft set theory are widely spread in various areas of science and social science viz. decision making, computer science, pattern recognition, artificial intelligence, etc. The importance of soft set-theoretical versions of mathematical analysis has been felt in several areas of computer science. This paper suggests some concepts of a soft gradient of a function and a soft integral, an analogue of a line integral in classical analysis. The fundamental properties of soft gradients are established. A necessary and sufficient condition is found so that a set can be a subset of the soft gradient of some function. The inclusion of a soft gradient in a soft integral is proved. Semi-additivity and positive uniformity of a soft integral are established. Estimates are obtained for a soft integral and the size of its segment. Semi-additivity with respect to the upper limit of integration is proved. Moreover, this paper enriches the theoretical development of a soft rational line integral and associated areas for better functionality in terms of computing systems.
Keywords soft rational analysis, soft gradient, soft integral, soft set
UDC 517.977
MSC 03E99, 91F99
DOI 10.35634/vm210404
Received 30 October 2020
Language English
Citation Acharjee S., Molodtsov D.A. Soft rational line integral, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2021, vol. 31, issue 4, pp. 578-596.
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