The basic sets of logical connectives of fuzzy systems are analyzed. It is shown that triangular norms are the basis for constructing the operators for logical connectives. Two main classes are distinguished – conditional and algebraic. The known generators of operators of triangular norms are described. It is shown that they have limited functional characteristics. To expand them, a parameterized additive-multiplicative generator is proposed for constructing the logical operators of fuzzy systems. It is proved that this generator satisfies the requirements of the necessary axioms. Examples of construction of fuzzy system operators, which are generally known, are presented. The introduction of parameterized coefficient provides the obtaining of triangular norms of a new type.

1. Zadeh, L. A. Fuzzy sets. Information and Control. 1965; 8, 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X

2. Klement, E. P.; Mesiar, R.; Pap, E. Triangular norms. Kluwer Academic Publ.: Dordrecht-Boston-London, 2000; p 386.

3. Borisov, V.V.; Kruglov, V.V.; Fedulov, A.S. Fuzzy models and systems. Goriachaya liniya-Telecom: Moscow, 2007; p 284. (in russian)

4. Vorobel, R.A. Logarithmic image processing. Naukova Dumka: Kyiv, 2012; p 232. (in Ukrainian)

5. Klir, G. A.; Folger, T. A. Fuzzy sets, uncertainty and information. Ptentice-Hall, Englewood Cliffs: New York, 1988; p 368.

6. Gupta, M. M.; Qi, J. Theory of T-norms and fuzzy inference methods. Fuzzy sets and systems. 1991; 40, 431-450. https://doi.org/10.1016/0165-0114(91)90171-L

7. Schweizer, B.; Sklar, A. Associative functions and abstract semi groups. Publ. Mathematicae Debrecen, 1963; 40, 69-81.

8. Yager, R. R. On a general class of fuzzy connectives. Fuzzy sets and systems. 1980; 4, 235-242. https://doi.org/10.1016/0165-0114(80)90013-5

9. Dubois, D.; Prade, H. New results about properties and semantics of fuzzy set-theoretic operators. In Fuzzy sets. Wang P. P.; Chang S. K. Eds.; Plenum Press.: New York, 1980; pp 59-75. https://doi.org/10.1007/978-1-4684-3848-2_6

10. Roychowdhury, R.; Wang, B. H. Composite generalization of Dombi class and new family of T-operators using additive-product connective generator. Fuzzy sets and systems. 1994; 66, 329-346. https://doi.org/10.1016/0165-0114(94)90100-7

11. Aczel, J. Vorlesungen uber Funktionalgleichungen und ihre Anwendungen. Birkhauser Verlag: Basel, 1961; p 332. (in German) https://doi.org/10.1007/978-3-0348-6904-1

12. Vorobel, R. New Triangular operator generator for fuzzy systems. In Proc. XV Int. Conf. "Mathematical Support and Software for Artificial Intelligence-2017" (MPZIS-2017), November 22-24, 2017; Ukraine, Dnipro; 2017; pp 42-43.

13. Alsina, C.; Frank, M. J.; Schweizer, B. Associative functions: triangular norms and copulas. World Scientific: Hackensack; London; Singapore, 2006; p 238. https://doi.org/10.1142/9789812774200

14. Dombi, J. A general class of fuzzy operators, the De-Morgan class of fuzzy operators and fuzziness induced by fuzzy operators. Fuzzy sets and systems. 1982; 8, 149-163. https://doi.org/10.1016/0165-0114(82)90005-7