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What is T-norm

Handbook of Research on Modern Educational Technologies, Applications, and Management
A function of two fuzzy sets which is equivalent to the intersection of sets in classical logic.
Published in Chapter:
Estimating Levels of Learning Outcomes Acquirement Based on Fuzzy Sets, Relations, and Their Compositions
Aleksandra Mreła (Kazimierz Wielki University in Bydgoszcz, Poland) and Oleksandr Sokolov (Nicolaus Copernicus University in Torun, Poland)
DOI: 10.4018/978-1-7998-3476-2.ch006
Abstract
New curriculum designers should prepare the set of learning outcomes that will be studied by students, and their acquirement will be verified by teachers. It is not easy to estimate whether students achieved the required learning outcomes even in the range of knowledge and skills, but when the competencies are considered, it becomes harder. Because of the convenience of using the linguistic terms (excellent, poor, good, and so on), it is better to apply fuzzy relations (type 1 if the numbers are chosen or type 2 if the sets are used), which can handle with the linguistic terms better than classical relations. The estimation of the learning outcome's acquirement can be conducted on the bases of a test or tests. For calculating the levels of learning outcome's acquirement, two fuzzy input relations are designed. Experts build one based on their knowledge, and the second one is based on the test results. The output relation, showing levels of learning outcome/outcomes' acquirement, is built with the application of the S-T composition of the first and second relations.
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More Results
Introduction and Trends to Fuzzy Logic and Fuzzy Databases
Function t establishing a generic model for the operation of intersection with fuzzy sets. These functions must comply with certain basic properties: commutative, associative, monotonicity, and border conditions (x t 0 = 0, and x t 1 = x). The most typical is the minimum function, but there exists other t-norms widely accepted (Table 1).
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Computational Intelligence Using Type-2 Fuzzy Logic Framework
In the field of mathematics, is respected as an operation in the interval [0, 1], which is always utilized in fuzzy logic. A T-norm can be extended to be a conjunction in fuzzy logic and an intersection in fuzzy set theory, such as a Minimum T-norm and a Product T-norm, both of which are involved in the operations on type-2 fuzzy sets.
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