A New Perspective on Reasoning with Fuzzy Rules

Fuzzy inference based on fuzzy concept lattice

“…The subsethood degree S(X 1 ,X 2 ) expresses the truth value of the statement "X 1 isX 2 " by a implication (with a negative emphasis), and fuzzy relation T (X 1 ,X 2 ) expresses the truth value of the statement "X 1 isX c 2 " by a conjunction (with a positive emphasis) (see [7,23] for more information about inference rules with negative or positive emphasis). We will define the lower approximate fuzzy inference by S(X 1 ,X 2 ) and the upper approximate fuzzy inference by T (X 1 ,X 2 ).…”

A multi-objective genetic optimization of interpretability-oriented fuzzy rule-based classifiers

“…[71], [72], [23]) that two different interpretations of fuzzy rules IF A THEN B are distinguished: a) the conjunction-based approach (fuzzy rule interpreted as "A coupled with B") and b) the implicationbased or logical approach (fuzzy rule interpreted as "A entails B"). The first one uses t-norms (usually, the minimum or product operators) to combine A and B and t-conorms (usually, the maximum operator) to aggregate multiple rules.…”

Practical Inference With Systems of Gradual Implicative Rules

“…A crisp rule "If X is A then Z is O" relates two universes of discourse U and W that form the domains of variables X and Z, respectively, locally restricting the domains of X and Z to subsets A of U and O of W . Such a rule can be interpreted in two ways according to whether one focuses on its examples or its counterexamples [11]. The examples of the rule precisely form the set of pairs (u, w) ∈ A × O.…”