Method for generating of Archimedian triangular connective operators

  • Roman Vorobel Department of Computer Science, Faculty of Physics and Applied Informatics, University of Lodz and Karpenko Physico-Mechanical Institute, National Academy of Sciences of Ukraine
Keywords: T-norms, S-norms, T-operators, connective generators


Archimedean triangular operators form the basis of the tools for development, analysis and designing of fuzzy systems. They are generated by simple, monotone, single-valued and continuous functions. The basic sets of logical connectives of fuzzy systems are analyzed. It is shown that they are divided into conditional and algebraic ones. The well-known methods for generating of Archimedean triangular operators are described. Limitation of the functional characteristics of such generated operators is shown. To expand them, a method for generating has been created, which makes it possible to build new parameterized operators. Examples of constructing both new operators and those that generalize the already known ones are given. The tendency of the change of the characteristic hyper surface, which is build by new operator, is revealed.


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