A novel difference and derivative of linearly correlated fuzzy number-valued functions

In the present paper, the notion of the linearly correlated difference for linearly correlated fuzzy numbers is introduced. Especially, the linearly correlated difference and the generalized Hukuhara difference are coincident for interval numbers or even symmetric fuzzy numbers. Accordingly, an appropriate metric is induced by using the norm and the linearly correlated difference in the set of linearly correlated fuzzy numbers. Based on the symmetry of the basic fuzzy number, the linearly correlated derivative is proposed by the linearly correlated difference of linearly correlated fuzzy number-valued functions. In both non-symmetric and symmetric cases, the equivalent characterizations of the linearly correlated differentiability of a linearly correlated fuzzy number-valued function are established, respectively. Moreover, it is shown that the linearly correlated derivative is consistent with the generalized Hukuhara derivative for interval-valued functions.

Numerical Investigation of Fuzzy Predator-Prey Model with a Functional Response of the Form Arctan(ax)

In this paper we study a fuzzy predator-prey model with functional response arctan(ax). The fuzzy derivatives are approximated using the generalized Hukuhara derivative. To execute the numerical simulation, we use the fuzzy Runge-Kutta method. The results obtained over time for the evolution and the population are presented numerically and graphically with some conclusions.

Common α-Fuzzy Fixed Point Results for F-Contractions with Applications

F-contractions have inspired a branch of metric fixed point theory committed to the generalization of the classical Banach contraction principle. The study of these contractions and α-fuzzy mappings in b-metric spaces was attempted timidly and was not successful. In this article, the main objective is to obtain common α-fuzzy fixed point results for F-contractions in b-metric spaces. Some multivalued fixed point results in the literature are derived as consequences of our main results. We also provide a non-trivial example to show the validity of our results. As applications, we investigate the solution for fuzzy initial value problems in the context of a generalized Hukuhara derivative. Our results generalize, improve and complement several developments from the existing literature.

An optimization technique for national income determination model with stability analysis of differential equation in discrete and continuous process under the uncertain environment

The paper represents a variation of the national income determination model with discrete and continuous process in fuzzy environment, a significant implication in economics planning, by means of fuzzy assumptions. This model is re-recognized and deliberated with fuzzy numbers to estimate its uncertain parameters whose values are not precisely known. Exhibition of imprecise solutions of the concerned model is carried out by using the proposed two methods: generalized Hukuhara difference and generalized Hukuhara derivative (gH-derivative) approaches. Moreover, the stability analysis of the model in two different systems in fuzzy environment is illustrated. Additionally, different illustrative examples for optimization of national income determination model are undertaken with the constructive graph and table for convenience for clarity of the projected approaches.

Application of Contractive-like Mapping Principles to Fuzzy Functional Differential Equation

In this paper, we prove the existence and uniqueness of solution for the fuzzy functional differential equation under generalized Hukuhara derivative via contractive-like mapping principles.

Numerical Solution of First Order Linear Differential Equations in Fuzzy Environment by Modified Runge-Kutta- Method and Runga-Kutta-Merson-Method under generalized H-differentiability and its Application in Industry

The paper presents an adaptation of numerical solution of first order linear differential equation in fuzzy environment. The numerical method is re-established and studied with fuzzy concept to estimate its uncertain parameters whose values are not precisely known. Demonstrations of fuzzy solutions of the governing methods are carried out by the approaches, namely Modified Runge Kutta method and Runge Kutta Merson method. The results are compared with the exact solution which is found using generalized Hukuhara derivative (gH-derivative) concepts. Additionally, different illustrative examples and an application in industry of the methods are also undertaken with the useful table and graph to show the usefulness for attained to the proposed approaches.