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Resume on “Reply of William E. Combs About the Article of Jerry M Resume on “Reply of William E. Combs about the article of Analogously we can divide the consequent in three single Jerry M. Mendel and Qilian Liang” by Wilmer Garzón A input/output fuzzy rules: IF Humidity is Low THEN the Fan Speed is Low. IF Humidity is Average THEN the Fan Speed is Index Terms – Combinatorial problem, Combs method, curse of dimensionality, intersection rule configuration (IRC) and union rule Moderate. configuration (URC). IF Humidity is High THEN the Fan Speed is High. As stated in [3], the Mamdani fuzzy reasoning method is I. INTRODUCTION comprised of two inference steps. This paper has how objective reply four points mentioned in the • “The IF … THEN fuzzy implication is defined as a paper or Mendel and Liang about Fuzzy Rule Configuration. conjunction (AND) of the antecedent and consequent; it is usually implemented as the MIN (∧) aggregating operator though other t-norms are possible.” • “The logical connective between the rules, ALSO, is II. DISCUSSION assumed to be a disjunction (OR). It is usually implemented as the MAX ( ) aggregating operator. We can also use other Reply to Point #1: Generalized Modus Ponens and . t-conorms.” With one example can be represented a system with two input and one output, they are talking about fan speed system, the inputs are Grouping the last six expressions as obtained: temperature and humidity and the output is fan speed; one intersection rule configuration is: IF temperature is cool THEN the fan speed is low OR IF Temperature is Hot and humidity is Low THEN IF humidity is low THEN the fan speed is low Fan Speed is Moderate (1) Applying the equivalence is obtained: IF temperature is warm THEN the fan speed is moderate OR IF humidity is average THEN the fan speed is moderate [(IF Temperature is Hot THEN Fan Speed is Hight) or (IF Humidity is Low THEN Fan Speed is Low)] (2) IF temperature is hot THEN the fan speed is high OR This result has two problems, the first is that convert one IRC IF humidity is high THEN the fan speed is high rules into twice as many URC rule clauses and secondly is possible think the expressions (1) and (2) are equal but is no true because in the conclusions the fan is different In order to obtain the actual fan speed, all we have to do now is insert the results of step two into centroid defuzzification; this The fan speed system in the URC’s propositional rule structural three expression can be separated in six with only input/output but is: united by six connectors or. [ ] (3) Therefore the structure of the URC is logically equivalent to the structure of IRC only when its implication relations [the rule [(Temperature Fan Speed) clauses] are coupled by union. (Humidity Fan Speed] (4) Reply to Point #2: Why the URC can be used as the basis for a In (3) y (4) the consequent is the same and this have two inputs, fuzzy logic system, even though its derivation uses De Morgan’s supposed the temperature has three states {cool, warm, hot}, the Law. set humidity {low, average, high} and fan speed contain {low, Thanks to the method of construction of truth tables for fuzzy moderate, high}. logic explained by the PhD. Rogelio Palomera it can be shown that the URC is equivalent to the IRC for Lukasiewicz implication The antecedent of (4) we can divide in three single input/output [ ] and also it can be shown that the URC is fuzzy rules: equivalent to the IRC for the Kleene-Dienes implication [ ]. IF Temperature is Cool THEN the Fan Speed is Low. Furthermore JE Andrews has made a propositional logic test to IF Temperature is Warm THEN the Fan Speed is demonstrate the equivalence between the URC and IRC without Moderate. the use of theorems of De Morgan, the demonstration will be made below: IF Temperature is Hot THEN the Fan Speed is High. [ ∧ ] ∧ Point #3: Multi-Antecedent URC’s The approach of Mendel and Liang about is completely correct; also make it easier to identify relationships between the antecedents and consequences, since it helpful for learning the system. Point #4: Can single-antecedent questions (clauses) rally replace multiple-antecedent questions? As a suggestion, for the possible case of the environment to ask questions that have only one input and one input, so the linguistic transformation to conjunctions math easy and so can perform the conjunctions between them. In cases other entry depends on the separation is not so easy to suggest how URC converter and assign a degree of influence of background elements in or consistent. .
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