Constructing Fuzzy Implications and Determining Their Ranking Order Through Comparative Analysis of Fuzzy Negations

The aim of this paper is the construction and comparison of fuzzy implications derived from four different fuzzy negations, namely Zadeh, Yager, Sugeno, and Power. A comparative framework is developed by examining all pairwise combinations of these negations to determine how the corresponding fuzzy implications are ranked. The proposed methodology incorporates the fuzzification of real meteorological data, using four membership functions. The resulting membership degrees are used as inputs for the fuzzy implication operators. The results after extensive tests indicate that the fuzzy implication constructed using Sugeno negation, with parameter λ = −0.9, provides the highest percentages of values greater than or equal to 0.9 and equal to 1. For the winter dataset, the scalene triangle achieves optimal performance for m = 470 and strong performance for m = 40. For the summer dataset, the isosceles trapezium yields optimal performance for m = 83 and strong performance for m = 7. In conclusion, when the parameter λ = −0.9, the Sugeno fuzzy implication is ranked among the first or the second ranking category depending on the fuzzified values of parameter x demonstrating its effectiveness for real-data applications.