Abstract
The choice of suitable robots in manufacturing, to improve product quality and to increase productivity, is a complicated decision due to the increase in robot manufacturers and configurations. In this article, a novel approach is proposed to choose among alternatives, differently assessed by decision makers on different criteria, to make the final evaluation for decision-making. The approach is based on the ellipsoid algorithm for systems of linear inequalities. Most of the ranking methods depend on integration that becomes complicated for nonlinear membership functions, which is the case in robot selection. The method simply uses the membership function or its derivative. It takes the decision maker’s attitude in ranking. It effectively ranks fuzzy numbers and their images, preserving symmetry. It is a simple recursive algebraic formula that can be easily programmed. The performance of the algorithm is compared with the performance of some existing methods through several numerical examples to illustrate its advantages in ranking, and a robot selection problem is solved.
Highlights
The wide use of robot automation in the industry creates new challenges in the development of robot control and in the preferred choice among robots performing the same task
The area enclosed by the fuzzy number will be dealt with as the solution set of a system of linear inequalities, where the membership functions represent the constraints
It is not affected by the centroid like the distance method and the area method that fail in ranking fuzzy numbers having the same centroid (Deng et al 2006)
Summary
The wide use of robot automation in the industry creates new challenges in the development of robot control and in the preferred choice among robots performing the same task. The area enclosed by the fuzzy number will be dealt with as the solution set of a system of linear inequalities, where the membership functions represent the constraints. The membership function y 1⁄4 fA~ðxÞ is used to represent the area enclosed by the fuzzy number by a system of linear inequalities with the non-negativity condition as follows: Suppose A~i; i 1⁄4 1; 2; . Applying the proposed method for ranking after replacing the nonlinear membership functions by their tangent planes at are obtained: 1⁄2 0:5312 0:4917 thCeaÀnpS~do1ÁinC1⁄4tsÀS~1⁄21⁄2x30Á0::551⁄4;5021⁄2:550:,55t0h4:e488f8o2l0lo:,4w8i5n3CgÀr.S~e2sTÁuhl1⁄4tiss makes the third robot R3 the most suitable selection for the loading task. This result agrees with the result of Liang and. Wang (1993) while it differs from the result of Chu and Lin (2003) TOPSIS that ranked R1 as the best selection
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