On interactive fuzzy solutions for mechanical vibration problems
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Elsevier B.V.
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Article
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Abstract
Fuzzy initial value problems describing classical mechanical vibrations are the focus of this paper. In particular, this work considers systems described by nth-order linear ordinary differential equations whose initial conditions are uncertain and given by interactive fuzzy numbers. The concept of interactivity arises from the concept of joint possibility distribu-tion ( J). An approach based on the sup -J extension principle, which is a generalization of Zadeh & rsquo;s extension principle, is presented. This theory is applied to two major examples of oscillatory systems: the forced vibration of an uncoupled mass-spring-damper system and the free vibration of a coupled undamped mass-spring system. In both cases, we have that the solution via sup -J extension, where the fuzzy initial conditions are given by linearly correlated fuzzy numbers, is contained in the solution via Zadeh & rsquo;s extension. (c) 2021 Elsevier Inc. All rights reserved.
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Keywords
Fuzzy initial value problems, Interactive fuzzy numbers, Sup-J extension principle, Mechanical vibration
Language
English
Citation
Applied Mathematical Modelling. New York: Elsevier Science Inc, v. 96, p. 304-314, 2021.
