Abstract
In this paper, we present a new Fuzzy Implication Generator via Fuzzy Negations which was generated via conical sections, in combination with the well-known Fuzzy Conjunction. The new Fuzzy Implication Generator takes its final forms after being configured by the fuzzy strong negations and combined with the most well-known fuzzy conjunctions TM, TP, TLK, TD, and TnM. The final implications that emerge, given that they are configured with the appropriate code, select the best value of the parameter and the best combination of the fuzzy conjunctions. This choice is made after comparing them with the Empiristic implication, which was created with the help of real temperature and humidity data from the Hellenic Meteorological Service. The use of the Empiristic implication is based on real data, and it also reduces the volume of the data without canceling them. Finally, the MATLAB code, which was used in the programming part of the paper, uses the new Fuzzy Implication Generator and approaches the Empiristic implication satisfactorily which is our final goal.
Highlights
The Theory of Fuzzy Implications and Fuzzy Negations plays an important role in many applications of fuzzy logic, such as approximate reasoning, formal methods of proof, inference systems, and decision support systems
In Souliotis G.’s and Papadopoulos B.’s paper [8], p. 5 proves a new family of strong fuzzy negations, which is produced by conical sections and is given from Equation (1), which will play a key role in building the algorithmic procedure we propose in the section “Main Results”
It is evident that the type of the strong fuzzy negations that are generated via conical sections, combined with the fuzzy conjunctions from the Table Basic t-norms
Summary
The motivation for writing this paper was the construction of flexible fuzzy implications via strong negations and their application to real data collected from the thirteen regions of Greece in the last five years 2015–2019 by the Hellenic Meteorological Service (see Reference [1]). Reference [2,3,4]) use mostly fuzzy systems or Generalized Fuzzy Rules without the use of fuzzy negations (for Fuzzy Negations, see Reference [5,6,7]). It was, a research challenge to study whether negations and especially fuzzy negations with a parameter, such as Sugeno class, and Yager class (see Example 2 and Reference [8]) can be used in fuzzy implications by lending their parameter to fuzzy rules ). The configuration of fuzzy rules creates flexible fuzzy implications since, by changing the parameter, the implication changes, as well. The best implication is found through the square error of the empiristic implication (see Section 4.1)
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