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In this paper, new fuzzy numerical methods based on the fuzzy transform (F-transform or FT) for solving the Cauchy problem are introduced and discussed. In accordance with existing methods such as trapezoidal rule, Adams Moulton methods are improved using FT. We propose three new fuzzy methods where the technique of FT is combined with one-step, two-step, and three-step numerical methods. Moreover, the FT with respect to generalized uniform fuzzy partition is able to reduce error. Thus, new representations formulas for generalized uniform fuzzy partition of FT are introduced. As an application, all these schemes are used to solve Cauchy problems. Further, the error analysis of the new fuzzy methods is discussed. Finally, numerical examples are presented to illustrate these methods and compared with the existing methods. It is observed that the new fuzzy numerical methods yield more accurate results than the existing methods.

Multicriteria decision making (MCDM) is one of the methods that popularly has been used in solving personnel selection problem. Alternatives, criteria, and weights are some of the fundamental aspects in MCDM that need to be defined clearly in order to achieve a good result. Apart from these aspects, fuzzy data has to take into consideration that it may arise from unobtainable and incomplete information. In this paper, we propose a new approach for personnel selection problem. The proposed approach is based on Hamming distance method with subjective and objective weights (HDMSOW's). In case of vagueness situation, fuzzy set theory is then incorporated onto the HDMSOW's. To determine the objective weight for each attribute, the fuzzy Shannon's entropy is considered. While for the subjective weight, it is aggregated into a comparable scale. A numerical example is presented to illustrate the HDMSOW's.

We study a fuzzy fractional differential equation (FFDE) and present its solution using Zadeh's extension principle. The proposed study extends the case of fuzzy differential equations of integer order. We also propose a numerical method to approximate the solution of FFDEs. To solve nonlinear problems, the proposed numerical method is then incorporated into an unconstrained optimisation technique. Several numerical examples are provided.

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This paper explores the application of fuzzy differential equations in modeling of prey and predator populations. A new model, referred to as fuzzy predator-prey model is introduced. This model is then solved numerically by means of a fuzzy Euler method. Some numerical results are presented in order to show the evolution of the prey and predator populations over time. Finally, the stability of the new fuzzy model is studied and shown graphically in the fuzzy phase plane.

Abstract:In this paper, we study the classical Sumudu transform in fuzzy environment, referred to as the fuzzy Sumudu transform (FST). We also propose some results on the properties of the FST, such as linearity, preserving, fuzzy derivative, shifting and convolution theorem. In order to show the capability of the FST, we provide a detailed procedure to solve fuzzy differential equations (FDEs). A numerical example is provided to illustrate the usage of the FST.

In this paper, new approximation methods for solving systems of ordinary differential equations (SODEs) by fuzzy transform (FzT) are introduced and discussed. In particular, we propose two modified numerical schemes to solve SODEs where the technique of FzT is combined with one-stage and two-stage numerical methods. Moreover, the error analysis of the new approximation methods is discussed. Finally, numerical examples of the proposed approach are confirmed, and applications are presented.