A fuzzy linear basis algorithm for nonlinear separable programming problems

P. Z. Wang

doi:10.1016/S0165-0114(98)00335-2

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A fuzzy linear basis algorithm for nonlinear separable programming problems

2001-04-01

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DOI：10.1016/S0165-0114(98)00335-2

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Abstract

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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 epsilon. 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 subproblems at the prespecified accuracy epsilon. The principles of the Fuzzy Linear Basis Algorithm are illustrated in an example. (C) 2001 Elsevier Science B.V. All rights reserved.

Keywords:

fuzzy linear bases

fuzzy interpolation

maximal profile

nonlinear separable programming

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