Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Capacities, Survival Functions and Universal Integrals Read chapter Read first chapter

2018 | OriginalPaper | Chapter

On Some Classes of RU-Implications Satisfying U-Modus Ponens

Authors : Margarita Mas, Daniel Ruiz-Aguilera, Joan Torrens

Published in: Aggregation Functions in Theory and in Practice

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

The Modus Ponens property for fuzzy implication functions is essential in the inference process in approximate reasoning. It is usually considered with respect to a continuous t-norm T but it can be generalized to any conjunctor and, in particular, to a conjunctive uninorm U. In this paper, it is investigated when RU-implications derived from uninorms satisfy the Modus Ponens with respect to a conjunctive uninorm U. The new property, called here U-Modus Ponens, is studied in detail for RU-implications derived from uninorms lying in the classes of representable uninorms and uninorms continuous in the open unit square.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter k-maxitivity of Order-Preserving Homomorphisms of Lattices
next chapter CMin-Integral: A Choquet-Like Aggregation Function Based on the Minimum t-Norm for Applications to Fuzzy Rule-Based Classification Systems
Literature
1.
Aguiló, I., Suñer, J., Torrens, J.: A characterization of residual implications derived from left-continuous uninorms. Inf. Sci. 180, 3992–4005 (2010)MathSciNetCrossRefMATH
2.
Alsina, C., Trillas, E.: When \((S, N)\)-implications are \((T, T_1)\)-conditional functions? Fuzzy Sets Syst. 134, 305–310 (2003)MathSciNetCrossRefMATH
3.
Baczyński, M., Jayaram, B.: Fuzzy Implications. Studies in Fuzziness and Soft Computing, vol. 231. Springer, Heidelberg (2008)MATH
4.
5.
6.
7.
Drygaś, P.: On properties of uninorms with underlying t-norm and t-conorm given as ordinal sums. Fuzzy Sets Syst. 161, 149–157 (2010)MathSciNetCrossRefMATH
8.
Drygaś, P., Ruiz-Aguilera, D., Torrens, J.: A characterization of a class of uninorms with continuous underlying operators. Fuzzy Sets Syst. 287, 137–153 (2016)MathSciNetCrossRef
9.
10.
Hu, S.K., Li, Z.F.: The structure of continuous uninorms. Fuzzy Sets Syst. 124, 43–52 (2001)CrossRef
11.
Klement, E.P., Mesiar, R., Pap, E.: Triangular norms. Kluwer Academic Publishers, Dordrecht (2000)CrossRefMATH
12.
Martín, J., Mayor, G., Torrens, J.: On locally internal monotonic operators. Fuzzy Sets Syst. 137, 27–42 (2003)CrossRefMATH
13.
Mas, M., Massanet, S., Ruiz-Aguilera, D., Torrens, J.: A survey on the existing classes of uninorms. J. Intell. Fuzzy Syst. 29, 1021–1037 (2015)MathSciNetCrossRef
14.
Mas, M., Monserrat, M., Ruiz-Aguilera, D., Torrens, J.: Residual implications derived from uninorms satisfying the Modus Ponens. In: IFSA-EUSFLAT-2015, pp. 233–240. Atlantis Press, Gijón (2015)
15.
Mas, M., Monserrat, M., Ruiz-Aguilera, D., Torrens, J.: \(RU\) and \((U, N)\)-implications satisfying Modus Ponens. Int. J. Approx. Reason. 73, 123–137 (2016)MathSciNetCrossRefMATH
16.
Mas, M., Monserrat, M., Ruiz-Aguilera, D., Torrens, J.: On a generalization of the Modus Ponens: \(U\)-conditionality. In: Carvalho, J.P., et al. (eds.) Information Processing and Management of Uncertainty in Knowledge-Based Systems in the series Communications in Computer and Information Science, vol. 610, pp. 387–398. Springer, Cham (2016)
17.
18.
Mas, M., Monserrat, M., Torrens, J.: Modus Ponens and Modus Tollens in discrete implications. Int. J. Approx. Reason. 49, 422–435 (2008)MathSciNetCrossRefMATH
19.
Mas, M., Monserrat, M., Torrens, J.: A characterization of \((U, N), RU, QL\) and \(D\)-implications derived from uninorms satisfying the law of importation. Fuzzy Sets Syst. 161, 1369–1387 (2010)MathSciNetCrossRefMATH
20.
Mas, M., Monserrat, M., Torrens, J., Trillas, E.: A survey on fuzzy implication functions. IEEE Trans. Fuzzy Syst. 15(6), 1107–1121 (2007)CrossRef
21.
Massanet, S., Torrens, J.: On a new class of fuzzy implications: h-implications and generalizations. Inf. Sci. 181, 2111–2127 (2011)MathSciNetCrossRefMATH
22.
Massanet, S., Torrens, J.: An overview of construction methods of fuzzy implications. In: Baczyński, M., Beliakov, G., Bustince Sola, H., Pradera, A. (eds.) Advances in Fuzzy Implication Functions. Studies in Fuzziness and Soft Computing, vol. 300, pp. 1–30. Springer, Berlin (2013)CrossRef
23.
Ruiz, D., Torrens, J.: Residual implications and co-implications from idempotent uninorms. Kybernetika 40, 21–38 (2004)MathSciNetMATH
24.
Ruiz-Aguilera, D., Torrens, J.: Distributivity of residual implications over conjunctive and disjunctive uninorms. Fuzzy Sets Syst. 158, 23–37 (2007)MathSciNetCrossRefMATH
25.
Ruiz-Aguilera, D., Torrens, J.: S- and R-implications from uninorms continuous in \(]0,1[^2\) and their distributivity over uninorms. Fuzzy Sets Syst. 160, 832–852 (2009)MathSciNetCrossRefMATH
26.
Ruiz-Aguilera, D., Torrens, J., Baets, B., Fodor, J.: Some remarks on the characterization of idempotent uninorms. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds.) IPMU 2010. LNCS, vol. 6178, pp. 425–434. Springer, Heidelberg (2010). doi:10.​1007/​978-3-642-14049-5_​44 CrossRef
27.
Trillas, E., Alsina, C., Pradera, A.: On MPT-implication functions for fuzzy logic. Revista de la Real Academia de Ciencias Serie A. Matemáticas (RACSAM) 98(1), 259–271 (2004)MathSciNetMATH
28.
Trillas, E., Alsina, C., Renedo, E., Pradera, A.: On contra-symmetry and MPT-conditionality in fuzzy logic. Int. J. Intell. Syst. 20, 313–326 (2005)CrossRefMATH
29.
Trillas, E., Campo, C., Cubillo, S.: When QM-operators are implication functions and conditional fuzzy relations. Int. J. Intell. Syst. 15, 647–655 (2000)CrossRefMATH
30.
Trillas, E., Valverde, L.: On Modus Ponens in fuzzy logic. In: 15th International Symposium on Multiple-Valued Logic, pp. 294–301. Kingston, Canada (1985)
Metadata
Title
On Some Classes of RU-Implications Satisfying U-Modus Ponens
Authors
Margarita Mas
Daniel Ruiz-Aguilera
Joan Torrens
Copyright Year
2018
Book
Aggregation Functions in Theory and in Practice

Print ISBN: 978-3-319-59305-0

Electronic ISBN: 978-3-319-59306-7

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-59306-7_8

Premium Partner

    Image Credits