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ISSN 0474-8662. Information Extraction and Processing. 2019. Issue 47 (123)
Parameterized operator for construction of Archimedian triangular norms
Vorobel R.A.
Karpenko Physico-Mechanical Institute of the NAS of Ukraine, Lviv
https://doi.org/10.15407/vidbir2019.47.034
Keywords: triangular norms, triangular conorms, T-norm, S-norm, logical connectives generators, fuzzy logic, associative functions
Cite as: Vorobel R.A. Parameterized operator for construction of Archimedian triangular norms. Information Extraction and Processing. 2019, 47(123), 34-39. DOI:https://doi.org/10.15407/vidbir2019.47.034
Abstract
Triangular norms and associative functions are the basis for building connectives in fuzzy logic and fuzzy systems. In this paper the possibility of constructing strict Archimedian triangular norms is considered. Their main feature is the ability to control the characteristics of such trian-gular norms. This is achieved by introducing a parameterizing coefficient. Change of its values leads to a change in the characteristics of the triangular norm. New triangular operator, that was built, can generate different classes of fuzzy connectives. It is proved that the proposed operator satisfies the requirements of such axioms, as commutativity, associativity, monotonicity and boundary conditions. It is parameterized and therefore gives the opportunity to build new trian-gular norms. Examples of the obtained triangular norms are given.
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