A rule-based method to calculate exactly the widest solution sets of a max-min fuzzy relational inequality

In this paper, we propose a rule-based method to calculate exactly all the widest solution sets of a fuzzy relational inequality. Viewed as an extension of fuzzy relational equations, fuzzy relational inequalities can be applied to many fields of fuzzy logic. Yet, they provide with more flexibility, as they enable to get rid of the sensitivity of fuzzy relational equations to numerical values. Up to now however, fuzzy relational inequalities have received few attention from researchers, and few methods have been proposed to solve these inequalities. The proposed analytical methods, furthermore, do not calculate exactly all the widest solutions sets of a fuzzy relational inequality, and often lead to redundant solution sets. The rule-based method we propose in this paper determines easily exactly all the widest solution sets of a fuzzy relational inequality.