Geodesic
Additive generators of discrete semi-uninorms
Kybernetika, Tome 60 (2024) no. 6, pp. 740-753
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This work explores commutative semi-uninorms on finite chains by means of strictly increasing unary functions and the usual addition. In this paper, there are three families of additively generated commutative semi-uninorms. We not only study the structures and properties of semi-uninorms in each family but also show the relationship among these three families. In addition, this work provides the characterizations of uninorms in $\mathcal{U}_{\min}$ and $\mathcal{U}_{\max}$ that are generated by additive generators.
This work explores commutative semi-uninorms on finite chains by means of strictly increasing unary functions and the usual addition. In this paper, there are three families of additively generated commutative semi-uninorms. We not only study the structures and properties of semi-uninorms in each family but also show the relationship among these three families. In addition, this work provides the characterizations of uninorms in $\mathcal{U}_{\min}$ and $\mathcal{U}_{\max}$ that are generated by additive generators.
DOI : 10.14736/kyb-2024-6-0740
Classification : 46F10, 62E86
Keywords: aggregation operations; semi-uninorms; additive generators; semi-t-norms; semi-t-conorms; finite chains 
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Wang, Ya-Ming; Zhan, Hang; Zhao, Yuan-Yuan. Additive generators of discrete semi-uninorms. Kybernetika, Tome 60 (2024) no. 6, pp. 740-753. doi: 10.14736/kyb-2024-6-0740

[1] Beliakov, G., Pradera, A., Calvo, T.: Aggregation functions: A guide for practitioners. Stud. Fuzziness Soft Comput. 221 (2007), Springer, Berlin, Heidelberg.

[2] Calvo, T., Mayor, G., Mesiar, R.: Aggregation operators: New trends and applications. Stud. Fuzziness Soft Comput. 97 (2002), Springer, Berlin, Heidelberg. | DOI | MR

[3] Baets, B. De, Mesiar, R.: Triangular norms on product lattices. Fuzzy Sets Syst. 104 (1999), 61-75. | DOI | MR | Zbl

[4] Baets, B. De, Mesiar, R.: Discrete Triangular Norms, in Topological and Algebraic Structures in Fuzzy Sets. Trends in Logic (S. Rodabaugh and E.-P. Klement, eds.), 20 (2003), pp. 389-400. | DOI | MR

[5] Baets, B. De, Fodor, J., Ruiz-Aguilera, D., Torrens, J.: Idempotent uninorms on finite ordinal scales. Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 17 (2009), 1-14. | DOI | MR | Zbl

[6] Durante, F., Klement, E. P., Mesiar, R., Sempi, C.: Conjunctors and their residual implicators: characterizations and construct methods. Mediterr. J. Math. 4 (2007), 343-356. | DOI | MR

[7] Fodor, J.: Smooth associative operations on finite ordinal scales. IEEE Trans. Fuzzy Syst. 8 (2000), 791-795. | DOI

[8] Fodor, J., Keresztfalvi, T.: Nonstandard conjunctions and implications in fuzzy logic. Int. J. Approx. Reason. 12 (1995), 69-84. | DOI | MR

[9] Fodor, J., Yager, R. R., Rybalov, A.: Structure of uninorms. Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 5 (1997), 411-427. | DOI | MR | Zbl

[10] Han, L., Liu, H. W.: On the distributivity of logical operators on a finite chain. School Math., Shandong University 2014, pp. 42-47. | MR

[11] Kolesarova, A., Mesiar, R., Mordelova, J., Sempi, C.: Discrete copulas. IEEE Trans. Fuzzy Syst. 14 (2006), 698-705. | DOI

[12] Li, G., Liu, H. W., Fodor, J.: On weakly smooth uninorms on finite chain. Int. J. Intell. Syst. 30 (2015), 421-440. | DOI

[13] Liu, H. W.: Semi-uninorms and implications on a complete lattice. Fuzzy Sets Syst. 191 (2012), 72-82. | DOI | MR

[14] Munar, M., Massanet, S., Ruiz-Aguilera, D.: A review on logical connectives defined on finite chains. Fuzzy Sets Syst. 462 (2023), 108469. | DOI | MR

[15] Mas, M., Mayor, G., Torrens, J.: T-operators and uninorms on a finite totally ordered set. Int. J. Intell. Syst. 14 (1999), 909-922. | DOI | MR

[16] Mas, M., Monserrat, M., Torrens, J.: On bisymmetric operators on a finite chain. IEEE Trans. Fuzzy Syst. 11 (2003), 647-651. | DOI

[17] Mas, M., Monserrat, M., Torrens, J.: On left and right uninorms on a finite chain. Fuzzy Sets Syst. 146 (2004), 3-17. | DOI | MR | Zbl

[18] Mas, M., Monserrat, M., Torrens, J.: Smooth t-subnorms on finite scales. Fuzzy Sets Syst. 167 (2011), 82-91. | DOI | MR

[19] Mayor, G., Monreal, J.: Additive generators of discrete conjunctive aggregation operations. IEEE Trans. Fuzzy Syst. 15 (2007), 1046-1052. | DOI

[20] Mayor, G., Monreal, J.: On some classes of discrete additive generators. Fuzzy Sets Syst. 264 (2015), 110-120. | DOI | MR

[21] Mayor, G., Torrens, J.: Triangular Norms on Discrete Settings, in Logical, Algebraic, Analytic, and Probabilistic Aspects of Triangular Norms. Elsevier, Amsterdam. 2005, pp. 189-230. | MR

[22] Mayor, G., Suñer, J., Torrens, J.: Copula-like operations on finite settings. IEEE Trans. Fuzzy Syst. 13 (2005), 468-477. | DOI

[23] Pradera, A., Beliakov, G., Bustince, H.: A review of the relationships between implication, negation and aggregation functions from the point of view of material implication. Inform. Sci. 329 (2016), 357-380. | DOI

[24] Ruiz-Aguilera, D., Torrens, J.: A characterization of discrete uninorms having smooth underlying operators. Fuzzy Sets Syst. 268 (2015), 44-58. | DOI | MR

[25] Sander, W.: Associative aggregation operators. In: Aggregation Operators (T. Calvo, G. Mayor, R. Mesiar, eds.), Physica-Verlag, Heidelberg 2002, pp. 124-158. | DOI | MR

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