An algorithm for generalized fuzzy binary linear programming problems

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.