Derivatives and indefinite integrals of single valued neutrosophic functions

Ning Liu; Zengtai Gong; Ning Liu; Zengtai Gong

doi:10.3934/math.2024022

AIMS Mathematics

2024, Volume 9, Issue 1: 391-411. doi: 10.3934/math.2024022

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Derivatives and indefinite integrals of single valued neutrosophic functions

Ning Liu ,
Zengtai Gong ^,

College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, P.R. China

Received: 21 August 2023 Revised: 07 November 2023 Accepted: 16 November 2023 Published: 29 November 2023
MSC : 03E72, 08A72, 26E50

With the continuous development of the fuzzy set theory, neutrosophic set theory can better solve uncertain, incomplete and inconsistent information. As a special subset of the neutrosophic set, the single-valued neutrosophic set has a significant advantage when the value expressing the degree of membership is a set of finite discrete numbers. Therefore, in this paper, we first discuss the change values of single-valued neutrosophic numbers when treating them as variables and classifying these change values with the help of basic operations. Second, the convergence of sequences of single-valued neutrosophic numbers are proposed based on subtraction and division operations. Further, we depict the concept of single-valued neutrosophic functions (SVNF) and study in detail their derivatives and differentials. Finally, we develop the two kinds of indefinite integrals of SVNF and give the relevant examples.
- single-valued neutrosophic set,
- single-valued neutrosophic function,
- continuities,
- derivatives,
- differentials,
- indefinite integrals
Citation: Ning Liu, Zengtai Gong. Derivatives and indefinite integrals of single valued neutrosophic functions[J]. AIMS Mathematics, 2024, 9(1): 391-411. doi: 10.3934/math.2024022

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Abstract

With the continuous development of the fuzzy set theory, neutrosophic set theory can better solve uncertain, incomplete and inconsistent information. As a special subset of the neutrosophic set, the single-valued neutrosophic set has a significant advantage when the value expressing the degree of membership is a set of finite discrete numbers. Therefore, in this paper, we first discuss the change values of single-valued neutrosophic numbers when treating them as variables and classifying these change values with the help of basic operations. Second, the convergence of sequences of single-valued neutrosophic numbers are proposed based on subtraction and division operations. Further, we depict the concept of single-valued neutrosophic functions (SVNF) and study in detail their derivatives and differentials. Finally, we develop the two kinds of indefinite integrals of SVNF and give the relevant examples.

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