Comparative Study of Fuzzy Logic Operators

Fuzzy logic is currently very relevant because it offers a new way to approach tuning and decision-making problems. In this paper, we discuss a comparative study between Zadeh fuzzy operators and probabilistic operators, which are used during the activation outputs of the rules, to see which of them maximize or minimize the result of the defuzzification, in a fuzzy inference system used to create the fuzzy command control model, in artificial intelligence.

The aim of this paper is to conduct a comparative study of rule output values by applying Zadeh's fuzzy operators and those of probability when activating rule outputs; and not to create other applications or to compare our solutions with previous results.

We point out that we have carried out this comparative study of Zadeh fuzzy operators and probabilistic ones by exploiting several numerical examples such as in [1, 2, 3, 4, 5].

But to lighten the writing of this article, knowing that the steps of fuzzy inference are manually tedious, we consider the control data of a house fan, with two inputs (temperature and humidity) and one output (fan speed) processed by Baali Sabeur & Mahmoudi Messaoud in 2022.

We have presented the cuts of the outputs from Zadeh's methods compared to those called probabilistic.

After Fuzzification, activation of the Rules outputs, Aggregation of the outputs and defuzzification, we identified the fuzzy operators which maximize and those which minimize the net outputs, among the two families.