A time variant multi-objective particle swarm optimization algorithm for solving fuzzy number linear programming problems using modified Kerre's method

Recently, Ghanbari et al. (IEEE Transactions on Fuzzy Systems 27:1286-1294, 2019) have proposed modified Kerre's method for comparison of LR fuzzy numbers. Here, we make use of the modified Kerre's method to solve fuzzy linear programming problems with LR coefficients. In an approach to solve a fuzzy linear program with fuzzy LR coefficients, a bi-objective optimization problem is formulated. For the associated bi-objective optimization problem, we present a time variant multi-objective particle swarm optimization (TV-MOPSO) algorithm to compute the Pareto front, a set containing a large number of solutions. Contrary to methods that change the fuzzy optimization problem to a crisp problem by use of a ranking function, using modified Kerre's method, the fuzzy optimization problem is solved directly, with no need for changing it to a crisp program. A comparative investigation using illustrative examples with triangular fuzzy coefficients show the effectiveness of the proposed algorithm.

Automated summary

The study introduces a modified Kerre's method for comparing LR fuzzy numbers and applies it to solving fuzzy linear programming problems with LR coefficients. By presenting a TV-MOPSO algorithm for computing the Pareto front, the effectiveness of the proposed algorithm is demonstrated through illustrative examples with triangular fuzzy coefficients.