@article{loetamonphong_fang_young_2002, title={Multi-objective optimization problems with fuzzy relation equation constraints}, volume={127}, ISSN={["1872-6801"]}, DOI={10.1016/S0165-0114(01)00052-5}, abstractNote={This paper studies a new class of optimization problems which have multiple objective functions subject to a set of fuzzy relation equations. Since the feasible domain of such a problem is in general non-convex and the objective functions are not necessarily linear, traditional optimization methods may become ineffective and inefficient. Taking advantage of the special structure of the solution set, a reduction procedure is developed to simplify a given problem. Moreover, a genetic-based algorithm is proposed to find the “Pareto optimal solutions”. The major components of the proposed algorithm together with some encouraging test results are reported.}, number={2}, journal={FUZZY SETS AND SYSTEMS}, author={Loetamonphong, H and Fang, SC and Young, RE}, year={2002}, month={Apr}, pages={141–164} }
@article{loetamonphong_fang_2001, title={Optimization of fuzzy relation equations with max-product composition}, volume={118}, ISSN={["0165-0114"]}, DOI={10.1016/S0165-0114(98)00417-5}, abstractNote={An optimization problem with a linear objective function subject to a system of fuzzy relation equations using max-product composition is considered. Since the feasible domain is non-convex, traditional linear programming methods cannot be applied. We study this problem and capture some special characteristics of its feasible domain and the optimal solutions. Some procedures for reducing the original problem are presented. The problem is transformed into a 0–1 integer program which is then solved by the branch-and-bound method. For illustration purpose, an example of the procedures is provided.}, number={3}, journal={FUZZY SETS AND SYSTEMS}, author={Loetamonphong, J and Fang, SC}, year={2001}, month={Mar}, pages={509–517} }
@article{loetamonphong_fang_1999, title={An efficient solution procedure for fuzzy relation equations with max-product composition}, volume={7}, ISSN={["1063-6706"]}, DOI={10.1109/91.784204}, abstractNote={We study a system of fuzzy relation equations with max-product composition and present an efficient solution procedure to characterize the whole solution set by finding the maximum solution as well as the complete set of minimal solutions. Instead of solving the problem combinatorially, the procedure identifies the "nonminimal" solutions and eliminates them from the set of minimal solutions.}, number={4}, journal={IEEE TRANSACTIONS ON FUZZY SYSTEMS}, author={Loetamonphong, J and Fang, SC}, year={1999}, month={Aug}, pages={441–445} }