On optimizing a linear objective function subjected to fuzzy relation inequalities

摘要

In this paper, we extend Guo and Xia’s necessary condition which has been presented by Guo and Xia (Fuzzy optimizat Decis Mak 5: 33–47, 2006) in order to study the finitely many constraints of fuzzy relation inequalities and optimize a linear objective function on this region which is defined by the fuzzy max–min operator. The new condition provides a means for removing the unnecessary paths resulting from Guo and Xia’s paths. Also, an algorithm and two numerical examples are offered to abbreviate and illustrate the steps of the resolution process of the problem.