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This paper considers the linear objective function optimization with respectto a novel system of fuzzy relation equations, where the fuzzy compositions aredefined by the minimum t-norm. It is proved that the feasible solution set isformed as a union of the finite number of closed convex cells. Some necessaryand sufficient conditions are presented to conceptualize the feasibility of theproblem. Moreover, seven rules are introduced with the aim of simplifying theoriginal problem, and then an algorithm is accordingly presented to find aglobal optimum. It is shown that the original problem in a special case isreduced to the well-known minimum vertex cover problem. Finally, an example isdescribed to illustrate the proposed algorithm.

Solving linear objective optimization problem subjected to novel max-min fuzzy relational equalities as a generalization of the vertex cover problem