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doi:10.1016/S0165-0114(98)00335-2 
Copyright © 2001 Elsevier Science B.V. All rights reserved.
A fuzzy linear basis algorithm for nonlinear separable programming problems
Abo Akademi University, Department of Business Administration, Henriksgatan 7, FIN-20500, ÅBO, Finland c Department of Mathematics, West Texas A&M University, Canyon TX 79016, USA d Center for Information Science, Peking University, Beijing 100871, People's Republic of China Received 1 March 1998;
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Abstract
In the paper we develop a theory of fuzzy linear bases. The theory is useful for transforming nonlinear separable programming problems (NLSP) into a finite sequence of fuzzy linear programming relaxations at a given level of accuracy 
. The key concepts of the theory are fuzzy linear interpolation and the maximal profile of the polyhedron generated from a set of break points for each variable dimension. The maximal profile is divided into adjacent convex sub-intervals, in which the nonlinear problem is transformed into a sequence of fuzzy linear sub-problems. All discontinuities are equipped with a break point, whereby the Fuzzy Linear Basis (FLB) Algorithm is applicable to separable NLPs with a finite number of discontinuities. We prove that the solution to the original nonlinear problem is included in the sequence of fuzzy linear sub-problems at the prespecified accuracy . The principles of the Fuzzy Linear Basis Algorithm are illustrated in an example.
Author Keywords: Fuzzy linear bases; Fuzzy interpolation; Maximal profile; Nonlinear separable programming
