Solving a fuzzy set-covering problem

K e y w o r d s S e t c o v e r i n g problems, Fuzzy sets, Fuzzy set-covering problem, Algebraic sum operator. 1. I N T R O D U C T I O N A classical set-covering problem considers the subsets I = {1, 2 , . . . , m} and J = {1, 2 , . . . , n} of integers. A collection p of subset Pj of I is a cover of I, if the union of the members of go is I, i.e., let Pj C I, go = {Pj : j C J0}, J0 C J, go is a cover of I, if U{Pj : j E J0} = I. For each Pj, there is a positive number cj associated with it. The classical set-covering problem finds an optimal cover go* = {Pj : j C J~}, J~ C J, such that, for any cover go = {Pj : j • J0}, J0 C J , we have ~-~J~ep* cj < ~P~e~ cj. The following is the classical set-covering model, Min E cjxj j=l n s.t. E a~jxJ > 1, j = l xj c {0,1}, i = 1 , 2 , . . . , m , j = 1 , 2 , . . . , n , This paper is based primarily on research supported by the National Science Council under Contract NSC-912416-H-364-001. 0895-7177/04/$ see front matter (~) 2004 Elsevier Ltd. All rights reserved. Typeset by JtA~-TEX doi:10.1016/j.mcm.2004.10.015 862 M.J. HWANG et al.