On a fuzzy logistic difference equation
type: Item
instance of: scholarly article
title: On a fuzzy logistic difference equation
zbMATH Open document ID: 0873.39002
author: Elias Y. Deeba
author: E. L. Koh
author: André de Korvin
published in: Differential Equations and Dynamical Systems
publication date: 1997-03-13T00:00:00Z
review text: The paper deals with the difference equation \[ u_{k+1}-u_k= a(b- cu_k)u_{k+1} \] with fuzzy coefficients fulfilling the conditions: \[ \text{A}1)\quad a<1/b; \qquad \text{A}2)\quad u_k<b/c; \qquad \text{A}3)\quad u_k,\;a,\;b\text{ and \(c\) are positive}. \] The problem is reduced to the system of interval recurrences. Unfortunately the final result (Lemma 4.6) is false because of the following mistakes: 1) Wrong interpretation of the inequality A2) for fuzzy numbers. 2) The next term of the recurrence may not belong to its domain. (E.g. let \(a=[1/4,1/3]\), \(b=[2.5,3]\), \(c=[0.5,1.5]\), \(b/c=[5/3,6]\). If \(u_k=[L_k,R_k]= [0.5,1.5]\), then \(u_k<5/3\leq b/c\), \(u_{k+1}= [8/15,18]\) and \(u_{k+1}\) does not fulfil the condition A2). 3) Bad approximation of the final recurrence which gives a system of two simultaneous recurrences of the form \(L_{k+1}= f(L_k,R_k)\), \(R_{k+1}= g(L_k,R_k)\).
Mathematics Subject Classification ID: 39A10
Mathematics Subject Classification ID: 03B52
Mathematics Subject Classification ID: 26E50
Mathematics Subject Classification ID: 65G30
zbMATH DE Number: 990868
zbMATH Keywords: fuzzy logistic difference equation
zbMATH Keywords: fuzzy recurrence
zbMATH Keywords: interval arithmetic
reviewed by: Józef Drewniak
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 990868