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This paper describes a new method for ranking of z-numbers according to the radii of gyration in the circulating dynamics of objects. We improve the center of mass technique that was used for ranking of fuzzy data, and by using moments of inertia or second moments, we present the new method for ranking z-numbers by the Radii of Gyration (ROG). In this paper, seven principles are stated to make any ranking method of z-numbers well defined. Eventually, three different types of examples are given, first comparing two z-numbers with each other and also a comparison of the proposed approach with the existing methods is conducted. [ABSTRACT FROM AUTHOR]

In this work, a new solution for the bipolar-fuzzy initial value problem is proposed. This method is obtained by approximating the solution by piece-wise polynomial of order three. The existence and uniqueness of the solution and convergence of the method are discussed in detail. Finally, for more explanation, several numerical examples are solved. [ABSTRACT FROM AUTHOR]

This article presents the exact solution of a bipolar fuzzy heat equation based on bipolar fuzzy Fourier transform under generalized Hukuhara partial (gH-p) differentiability. A bipolar fuzzy Fourier transform is defined, and the related key propositions and fundamental characteristics are discussed. Further, a bipolar fuzzy heat equation model is constructed using gH-differentiability, and the analytical solution of a bipolar fuzzy heat equation with bipolar fuzzy Fourier transform approach is examined. Some illustrative examples are provided to check the suggested methodology’s liability and efficiency. The type of differentiability and the solution of the bipolar fuzzy heat equation are shown graphically, demonstrating the versatility of the proposed methodology and elucidating the impact of differentiability types on the solution behavior of the bipolar fuzzy heat equation. Additionally, the impact of different parameters on the solution behavior is analyzed, revealing insights into the underlying dynamics. [ABSTRACT FROM AUTHOR]

Generally exploring the exact solution of linear programming problems in which all variables and parameters are Z-numbers, is either not possible or difficult. Therefore, a few numerical methods to find the numerical solutions do act an important role in these problems. In this paper, we concentrate on introducing a new numerical method to solve such problems based on the ranking function. After proving the necessary theories, for more illustrations and the correctness of the topic, some theoretical and practical examples are also provided. Finally, the results obtained from the proposed method have been compared with some existing methods. [ABSTRACT FROM AUTHOR]

Our aim in this paper is to study the fuzzy stability of a fractional Lorenz system in the sense of the Caputo-Fabrizio derivative and a fractional financial crisis in the sense of ♄−Hilfer derivative. Defining a new type of fuzzy control function that has a dynamic situation helps us to investigate new stability results for these mathematical models. [ABSTRACT FROM AUTHOR]