Geodesic
About a new family of fuzzy operations
Nečetkie sistemy i mâgkie vyčisleniâ, Tome 16 (2021) no. 2, pp. 123-138

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This article presents the results of the study of additive generators in the form of fractional linear functions. Restrictions on the coefficients of increasing and decreasing generators are determined. It is shown that inverse functions under certain conditions are also additive generators. For each case, the corresponding triangular norms or conorms are found. It is established that triangular norms and conorms obtained on the basis of fractional linear functions, as well as dual ones, have the same structure. The values of the parameters at which the known families are obtained are determined. In fact, a new family of dual triangular norms and conorms is proposed, which generalizes the known families.
Keywords: triangular norms and conorms, additive generators, fractional linear functions. 
@article{FSSC_2021_16_2_a3,
     author = {T. M. Ledeneva},
     title = {About a new family of fuzzy operations},
     journal = {Ne\v{c}etkie sistemy i m\^agkie vy\v{c}isleni\^a},
     pages = {123--138},
     publisher = {mathdoc},
     volume = {16},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FSSC_2021_16_2_a3/}
}
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T. M. Ledeneva. About a new family of fuzzy operations. Nečetkie sistemy i mâgkie vyčisleniâ, Tome 16 (2021) no. 2, pp. 123-138. http://geodesic.mathdoc.fr/item/FSSC_2021_16_2_a3/