The paper presents non-adjustable T-norm operators. They are a special type of function used in multi-valued logic, specifically in fuzzy logic. T-norms are a generalization of the standard logical product operator known from Boolean logic. For input sigmoidal functions, fuzzy membership functions of non-adjustable T-norm operators have been determined.The calculation results are presented in graphical form. In classical set theory, the product operation is a relatively simple and unambiguously defined mathematical operation. However, in the case of fuzzy sets, this issue is more complex. This is due to the fact that fuzzy sets consist of elements that belong to them fully or only partially.
The product of fuzzy sets A and B defined in a certain universe of discourse X can be defined using the minimum operator in relation to the membership functions that describe the input sets. The use of the minimum operator means that the value of the membership function of the product of fuzzy sets depends solely on the smaller value, in a given interval, of the input function. Conversely, the value of the larger membership function, in a given interval, does not affect the final result, which constitutes a certain drawback of the minimum operator. Therefore, many other definitions of the product of fuzzy sets have been created. (…)
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Source: Logistyka Magazine
Determining the product of fuzzy sets using non-adjustable t-norm operators – PDF file for download