Application of the Horizontal Membership Function to the Uncertain Displacement Calculation of a Composite Massless Rod Under a Tensile Load

Abstract

Fuzzy arithmetic, based on Zadeh's extension principle, is a common method applied to solve problems with uncertain parameters. The paper presents the fuzzy arithmetic operations on fuzzy numbers in a new way, using the horizontal membership functions (HMFs). The horizontal membership functions enable to introduce uncertain, interval, or fuzzy variable values together with crisp values in arithmetic operations without using Zadeh's extension principle. Thus, a relatively easy aggregation of crisp and uncertain knowledge is possible. The numerical example of one-dimensional static problem consisting of a two-component massless rod under tensile load is considered.