Solution of Fuzzy Growth and Decay Model

TL;DR

This paper develops a fuzzy differential equation model for population growth and decay, accounting for uncertainty in initial population measurements, and analyzes solutions using fuzzy calculus techniques.

Contribution

It introduces a fuzzy growth and decay model and provides its solution using Seikkala differentiability, addressing measurement ambiguity in population models.

Findings

Solution of fuzzy growth and decay model derived

Analysis using Seikkala differentiability conducted

Addresses measurement uncertainty in population modeling

Abstract

Mathematical modelling for population growth leads to a differential equation. In population growth model, we assume that rate increase of population is proportional to current population. That is, dx / dt = kx, x is a current population, k is proportionality constant represents growth rate. But in real situation, it is often ambiguous to determine exact amount of current population. It can be measured approximately. For instance, initially number of bacteria is approximately 20 and this approximate number can be represented using fuzzy number. Therefore, the appropriate growth or decay model is described using fuzzy concept. With this motivation, this paper presents solution of fuzzy growth and decay model. The solution is analysed using Seikkala differentiability of fuzzy-valued function.