A method for the detection of the most suitable fuzzy implication for data applications

Fuzzy implications are widely used in applications where propositional logic is applicable. In cases where a variety of fuzzy implications can be used for a specific application, it is important that the optimal candidate to be chosen in order valuable inference to be drawn for a given set of data. This study introduces a method for detecting the most suitable fuzzy implication among others under consideration by evaluating the metric distance between each implication and the ideal implication for a given data application. The ideal implication I is defined and used as a reference in order to measure the suitability of fuzzy implications. The method incorporates an algorithm which results in two extreme cases of fuzzy implications regarding their suitability for inference making; the most suitable and the least suitable implications. An example involving five fuzzy implications is included to illustrate the procedure of the method. The results obtained verify that the resulting implication is the optimal operator for inference making for the data.