Type-2 fuzzy fractional derivatives

Mazandarani, Mehran; Najariyan, Marzieh

doi:10.1016/j.cnsns.2013.11.003

Cited by 101 publications

(27 citation statements)

References 21 publications

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“…The A-IFS and its extensions could describe the fuzziness of an object more comprehensively than the FS and has a good performance in dealing with uncertain information. Up to now, plenty of research work has been done on A-IFSs and their extensions [8][9][10][11][12][13][14]. In 2004, Szmidt and Kacprzyk [8] proposed a similarity measure for A-IFSs and applied it in supporting medical diagnostic reasoning.…”

Section: Introductionmentioning

confidence: 98%

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Exponential operations of interval-valued intuitionistic fuzzy numbers

Gou

Zhang

Liao

2015

Int. J. Mach. Learn. & Cyber.

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The operational laws of intuitionistic fuzzy numbers are useful in dealing with the problems under intuitionistic fuzzy circumstances. As a supplementation, the exponential operational law of intuitionistic fuzzy numbers has been defined. Consider that we may utilize interval-valued intuitionistic fuzzy numbers (IVIFNs) to express uncertain weight information comprehensively in the complex multi-attribute decision making problems, in this paper, we discuss two exponential operational laws of IVIFNs, namely, the exponential operational law of IVIFNs with crisp parameter and the exponential operational law of IVIFNs with interval-valued parameter. Several properties and aggregation methods based on the exponential operational laws are discussed. Furthermore, we propose a new method to compare the novel dual interval-valued intuitionistic fuzzy numbers. Additionally, we give two information aggregation methods over these two exponential operational laws for dealing with some special problems in multi-attribute decision making, and finally, we apply the methods to a practical problem involving the choice of the optimal powered roof support for coal extraction with a high recovery rate.

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Section: Introductionmentioning

confidence: 98%

“…Yu [12] introduced a prioritized information fusion method for triangular A-IFSs and used it for teaching quality evaluation. Mazandarani and Najariyan [13,14] proposed a Type-2 fuzzy number, which can express uncertain information more comprehensive and accurate.…”

Section: Introductionmentioning

confidence: 99%

Exponential operations of interval-valued intuitionistic fuzzy numbers

Gou

Zhang

Liao

2015

Int. J. Mach. Learn. & Cyber.

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“…On the other hand, after the time that Agarwal et al [20] proposed the concept of solutions for fractional differential equations with uncertainty, a few researches have been done to find the fuzzy solution of FDEs by means of analytical and numerical methods [21][22][23][24][25][26][27][28][29][30][31]. The main motivation of this paper is to recommend a suitable way to approximate fuzzy fractional PKPD models using a shifted Legendre tau approach.…”

Section: Introductionmentioning

confidence: 99%

A Legendre Approximation for Solving a Fuzzy Fractional Drug Transduction Model into the Bloodstream

Ahmadian

Senu

Larki

et al. 2014

Advances in Intelligent Systems and Computing

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Abstract. While an increasing number of fractional order integrals and differential equations applications have been reported in the physics, signal processing, engineering and bioengineering literatures, little attention has been paid to this class of models in the pharmacokineticspharmacodynamic (PKPD) literature. In this research, we are confined with the application of Legendre operational matrix for solving fuzzy fractional differential equation arising in the drug delivery model into the bloodstream. The results illustrates the effectiveness of the method which can be in high agreement with the exact solution.

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“…In addition, the Riemann-Liouville derivative requires a quantity of the fractional derivative of unknown solution at the initial point, but it could not be measured and perhaps may not exist. In order to overcome these drawbacks, there have appeared some papers integrated the Caputo derivatives with generalized Hukuhara differentiability (gH-differentiability), called Caputo gH-differentiability, such as Allahviranloo et al [3,4], Hoa [9], Long et al [14], and Mazandarani [18,19].…”

Section: Introductionmentioning

confidence: 99%

Ulam Stability for Fractional Partial Integro-Differential Equation with Uncertainty

Long¹,

Son

Tam

et al. 2017

Acta Math Vietnam

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In this paper, the solvability of Darboux problems for nonlinear fractional partial integro-differential equations with uncertainty under Caputo gH-fractional differentiability is studied in the infinity domain J ∞ = [0, ∞) × [0, ∞). New concepts of Hyers-Ulam stability and Hyers-Ulam-Rassias stability for these problems are also investigated through the equivalent integral forms. A computational example is presented to demonstrate our main results.

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Type-2 fuzzy fractional derivatives

Cited by 101 publications

References 21 publications

Exponential operations of interval-valued intuitionistic fuzzy numbers

Exponential operations of interval-valued intuitionistic fuzzy numbers

A Legendre Approximation for Solving a Fuzzy Fractional Drug Transduction Model into the Bloodstream

Ulam Stability for Fractional Partial Integro-Differential Equation with Uncertainty

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