TY - JOUR

T1 - An algorithm for generalized fuzzy binary linear programming problems

AU - Yu, Chian Son

AU - Li, Han-Lin

PY - 2001/9/16

Y1 - 2001/9/16

N2 - Fuzzy binary linear programming (FBLP) problems are very essential in many fields such as assignment and assembly line balancing problems in operational research, multiple projects, locations, and candidates selection cases in management science, as well as representing and reasoning with prepositional knowledge in artificial intelligence. Although FBLP problems play a significant role in human decision environment, not very much research has focused on FBLP problems. This work first proposes a simple means of expressing a triangular fuzzy number as a linear function with an absolute term. A method of linearizing absolute terms is also presented. The developed goal programming (GP) model weighted by decision-makers' (DMs) preference aims to optimize the expected objective function and minimize the sum of possible membership functions' deviations. After presented a novel way of linearizing product terms, the solution algorithm is proposed to generate a crisp trade-off promising solution that is also an optimal solution in a certain sense. Three examples, equipment purchasing choice, investment project selection, and assigning clients to project leaders, illustrate that the proposed algorithm can effectively solve generalized FBLP problems.

AB - Fuzzy binary linear programming (FBLP) problems are very essential in many fields such as assignment and assembly line balancing problems in operational research, multiple projects, locations, and candidates selection cases in management science, as well as representing and reasoning with prepositional knowledge in artificial intelligence. Although FBLP problems play a significant role in human decision environment, not very much research has focused on FBLP problems. This work first proposes a simple means of expressing a triangular fuzzy number as a linear function with an absolute term. A method of linearizing absolute terms is also presented. The developed goal programming (GP) model weighted by decision-makers' (DMs) preference aims to optimize the expected objective function and minimize the sum of possible membership functions' deviations. After presented a novel way of linearizing product terms, the solution algorithm is proposed to generate a crisp trade-off promising solution that is also an optimal solution in a certain sense. Three examples, equipment purchasing choice, investment project selection, and assigning clients to project leaders, illustrate that the proposed algorithm can effectively solve generalized FBLP problems.

KW - Binary linear programming

KW - Fuzzy mathematical programming

UR - http://www.scopus.com/inward/record.url?scp=0035899773&partnerID=8YFLogxK

U2 - 10.1016/S0377-2217(00)00193-4

DO - 10.1016/S0377-2217(00)00193-4

M3 - Article

AN - SCOPUS:0035899773

SN - 0377-2217

VL - 133

SP - 496

EP - 511

JO - European Journal of Operational Research

JF - European Journal of Operational Research

IS - 3

ER -