"A conditional of the form IF X IS A, THEN Y IS B where A and B are fuzzy sets. In mathematical terms a rule is a relation between fuzzy sets. Each rule defines a fuzzy patch (the product A x B) in the system 'state space'. The wider the fuzzy sets A and B, the wider and more uncertain the fuzzy patch. Fuzzy rules are the knowledge-building blocks in a fuzzy system. In mathematical terms each fuzzy rule acts as an associative memory that associates the fuzzy response B with the fuzzy stimulus A." (Guido Deboeck & Teuvo Kohonen (Eds), "Visual Explorations in Finance with Self-Organizing Maps" 2nd Ed., 2000)
"In general, in rule-based systems, rules look something like: If A1 and A2 and … An then C1 and C2 and … Cm; where the Ai are the antecedents (conditions) on the left hand side (LHS) of the rule and the Cj are the consequents (conclusions) on the right hand side (RHS) of the rule. In this format, if all of the antecedents on the LHS of the rule are true then the rule will fire and the consequents will be asserted / executed. With Fuzzy rules both antecedents and conclusions can be of fuzzy nature." (Juan R González et al, Nature-Inspired Cooperative Strategies for Optimization, 2008)
"Fuzzy If-Then or fuzzy conditional statements are expressions of the form 'If A Then B', where A and B are labels of fuzzy sets characterised by appropriate membership functions. Due to their concise form, fuzzy If-Then rules are often employed to capture the imprecise modes of reasoning that play an essential role in the human ability to make decision in an environment of uncertainty and imprecision. The set of If-Then rules relate to a fuzzy logic system that are stored together is called a Fuzzy Rule Base." (Masoud Mohammadian, Supervised Learning of Fuzzy Logic Systems, 2009)
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