Sankar Prasad Mondal

Discussion on fuzzy quota harvesting model in fuzzy environment: fuzzy differential equation approach

In the recent years much importance has been laid on the role of uncertainty (fuzzy, interval etc.) in mathematical biology. In this paper we tried to study on the quota harvesting model in fuzzy environment. This model is considered in three different ways viz. (1) Initial condition (population density) is a fuzzy number, (2) coefficients of quota harvesting model (intrinsic growth rate and quota harvesting rate) are fuzzy number and (3) both initial condition and coefficients are fuzzy number. We discuss all these fuzzy cases individually. The solution procedure is done by using the concept of fuzzy differential equation approach. We have discussed the equilibrium points and their feasibility in all the three cases. This paper explores the stability analysis of the quota harvesting model at the equilibrium points in fuzzy environment. In order to examine the stability systematically in different fuzzy cases, we have used numerical simulations and discussed them briefly.

Differential equation with interval valued fuzzy number and its applications

The paper presents an adaptation of solution of first order differential equation with initial value as interval valued triangular fuzzy number. The arithmetic operation of interval-valued triangular fuzzy number is re-established and studied with the help of fuzzy extension principle method. Demonstration of fuzzy solutions of the governing differential equation is carried out using the approaches namely, generalized Hukuhara derivative. Additionally, different illustratively examples and applications are also undertaken with the useful table and graph for usefulness for attained to the proposed approaches.

Developing a Decision-Making Model Using Interval-Valued Intuitionistic Fuzzy Number

A multi-criteria decision-making model is developed that considers the nondeterministic nature of decision-maker along with the vagueness in the decision. The main objective of this model is to minimize the risk associated with each alternative. For this reason, the ratings of alternatives versus criteria are assessed in Parametric Interval-Valued Intuitionistic Fuzzy Number (PIVIFN). A defuzzification method is developed using the Riemann integral method. In addition, different properties, theorems, and operators are redefined for PIVIFN. Finally, the model is applied to solve a decision-making problem.

Different Forms of Triangular Neutrosophic Numbers, De-Neutrosophication Techniques, and their Applications

In this paper, we introduce the concept of neutrosophic number from different viewpoints. We define different types of linear and non-linear generalized triangular neutrosophic numbers which are very important for uncertainty theory. We introduced the de-neutrosophication concept for neutrosophic number for triangular neutrosophic numbers. This concept helps us to convert a neutrosophic number into a crisp number. The concepts are followed by two application, namely in imprecise project evaluation review technique and route selection problem.

Existence and Stability of Difference Equation in Imprecise Environment

Abstract In this paper, first order linear homogeneous difference equation is evaluated in fuzzy environment. Difference equations become more notable when it is studied in conjunction with fuzzy theory. Hence, here amelioration of these equations is demonstrated by three different tactics of incorporating fuzzy numbers.Subsequently, the existence and stability analysis of the attained solutions of fuzzy difference equations (FDEs) are then discussed under different cases of impreciseness. In addition, considering triangular and generalized triangular fuzzy numbers, numerical experiments are illustrated and efficient solutions are depicted, graphically and in tabular form.

Solution of first order system of differential equation in fuzzy environment and its application

In this paper, we solve a system of differential equation of first order in fuzzy environment using generalised Hukuhara derivative approach. Four different cases are discussed for the said differential equation: 1) coefficient is positive crisp number and initial condition is fuzzy number; 2) coefficient is negative crisp number and initial condition is fuzzy number; 3) coefficient is fuzzy number and initial condition is fuzzy number; 4) coefficient is interval number and initial condition is fuzzy number. Finally, we apply the results in Lanchaster combat model. The solution that comes in the application are defuzzified by removal area method.

Some Comparison of Solutions by Different Numerical Techniques on Mathematical Biology Problem

We try to compare the solutions by some numerical techniques when we apply the methods on some mathematical biology problems. The Runge-Kutta-Fehlberg (RKF) method is a promising method to give an approximate solution of nonlinear ordinary differential equation systems, such as a model for insect population, one-species Lotka-Volterra model. The technique is described and illustrated by numerical examples. We modify the population models by taking the Holling type III functional response and intraspecific competition term and hence we solve it by this numerical technique and show that RKF method gives good results. We try to compare this method with the Laplace Adomian Decomposition Method (LADM) and with the exact solutions.