Construction of General Types of Fuzzy Implications Produced by Comparing Different T-Conorms: An Application Case Using Meteorological Data

This research work is an extension of a previous work in which the authors created an innovative family of fuzzy implication using as t-conorm probor, as fuzzy negation the 1-x and the type of Newton's binomial. The purpose of this paper is to compare the type of fuzzy implication probor with three other constructed fuzzy implications produced by max, Einstein and Lukasiewicz t-conorms maintaining in each case the same negation. T-conorms perform the fuzzy logical operation "or" of the corresponding fuzzy sets. The main methods used for the comparisons are the basic axioms of fuzzy logic. The authors performed six combinations of t-conorm comparisons, in order to find the rank order of the five fuzzy implications. Although the general type of fuzzy implication probor came out smaller than Hamacher, Einstein and Lukasiewicz and the type of Einstein smaller than Lukasiewicz authors make extensive tests using four different membership functions and different values to the parameter m so as to examine which out of the four fuzzy implications receive the best results. The application of isosceles trapezium to the fuzzy implications probor and Einstein give the best values (most values greater than or equal to 0.9 and equal to 1).