Derivative and Differential Operations of Intuitionistic Fuzzy Numbers

Lei, Qian; Zhang, Xu

doi:10.1002/int.21696

Cited by 66 publications

(43 citation statements)

References 37 publications

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“…Since the q‐ ROFN is a generalization of the IFN, then on the basis of the relationship between the IFN and the q‐ ROFN, we introduce some necessary prior knowledge regarding the continuity and derivative, infinitesimal of IFFs.…”

Section: Preliminariesmentioning

confidence: 99%

Single variable differential calculus under q ‐rung orthopair fuzzy environment: Limit, derivative, chain rules, and its application

Zhang

2019

Int J Intell Syst

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The q‐rung orthopair fuzzy set ( q‐ROFS) that the sum of the qth power of the membership degree and the qth power of the nonmembership degree is restricted to one is a generalization of fuzzy set (FS). Recently, many researchers have given a series of aggregation operators to fuse q‐rung orthopair fuzzy discrete information. Subsequently, although some scholars have also focused on studying q‐rung orthopair fuzzy continuous information and give its continuity, derivative, differential, and integral, those studies are only considered from the perspective of multivariable fuzzy functions. Thus, the main aim of the paper is to study the q‐rung orthopair fuzzy continuous single variable information. In this paper, we first define the concept of q‐rung orthopair single variable fuzzy function ( q‐ROSVFF) to describe the fuzzy continuous information, and give its domain to make sure that this kind of function is meaningful. Afterward, we propose the limits, continuities, and infinitesimal of q‐ROSVFFs, and offer the relationship between the limit of q‐ROSVFF and that of q‐ROSVFF infinitesimal. On the basis of the definition of derivative in mathematical analysis, we define the subtraction and division derivatives and basic operational rules, and offer the simpler proofs for the derivatives of q‐ROSVFFs. What is more, we propose the subtraction and division differential invariances, and give the approximate calculation formulas of q‐ROSVFFs when the value of independent variable is changed small enough. In the real situation, fundamental functions cannot be used to express more complicated functions, thus we define the compound q‐ROSVFFs and give their chain rules of subtraction and division derivatives. Finally, we use numerical examples by simulation to verify the feasibility and veracity of the approximate calculation on q‐ROSVFFs.

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Section: Preliminariesmentioning

confidence: 99%

Single variable differential calculus under q ‐rung orthopair fuzzy environment: Limit, derivative, chain rules, and its application

Zhang

2019

Int J Intell Syst

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“…After defining the subtraction and division operations of IFNs, Lei and Xu [13] analyzed the In the following, we introduce the concepts of Archimedean t-conorm and t-norm and some corresponding aggregation operations of IFNs:…”

Section: Preliminariesmentioning

confidence: 99%

Intuitionistic fuzzy integrals based on Archimedean t-conorms and t-norms

Lei

Zhang

Bustince

et al. 2016

Information Sciences

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“…In the course of the most recent decades, the operational laws are one of the hotly debated issues to the hypothesis and the use of IFSs and IFNs. Toward that path, Atanassov and De et al characterized the essential operations, for example, “union,” “intersection,” “power.” Furthermore, Xu and Yager and Xu characterized some essential operational laws for IFNs, for example, “addition,” “subtraction,” “scalar multiplication.” Lei and Xu characterized the subtraction and division administrators (operators) for IFNs. By utilizing these operational laws for IFNs, heaps of work has been executed by the researchers, such as aggregation techniques, information measures, multiple criteria decision‐making .…”

Section: Introductionmentioning

confidence: 99%

New logarithmic operational laws and their aggregation operators for Pythagorean fuzzy set and their applications

Garg

2018

Int J Intell Syst

165

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The aim of this paper is to develop some new logarithm operational laws (LOL) with real number base λ for the Pythagorean fuzzy sets. Some properties of LOL have been studied and based on these, various weighted averaging and geometric operators have been developed. Then, we utilized it to solve the decision‐making problems. The validity of the proposed method is demonstrated with a numerical example and compared the results with the several existing approaches result. Finally, the influences of logarithmic operation and the selection of the logarithmic base λ in practice are discussed.

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Derivative and Differential Operations of Intuitionistic Fuzzy Numbers

Cited by 66 publications

References 37 publications

Single variable differential calculus under q ‐rung orthopair fuzzy environment: Limit, derivative, chain rules, and its application

Single variable differential calculus under q ‐rung orthopair fuzzy environment: Limit, derivative, chain rules, and its application

Intuitionistic fuzzy integrals based on Archimedean t-conorms and t-norms

New logarithmic operational laws and their aggregation operators for Pythagorean fuzzy set and their applications

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