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Propositional Belief Merging with T-conorms

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Multi-Agent Systems and Agreement Technologies (EUMAS 2016, AT 2016)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10207))

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Abstract

We analyze in this paper the impact of introducing fuzzy T-conorm operators in the area of belief merging. There are mainly two subclasses of merging operators: the utilitarian and the egalitarian ones. We prove that a T-conorm merging operator can be included in the subtype of egalitarian operators. We also study how the different T-conorm operators behave with respect to their logical properties and how this affects their rationality.

This research is supported by CNPq and CAPES.

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References

  1. Alcantud, J.: Liberal approaches to ranking infinite utility streams: When can we avoid interferences? Mpra paper, University Library of Munich, Germany (2011). http://EconPapers.repec.org/RePEc:pra:mprapa:32198

  2. Alcantud, J.C.R.: Non-interference and continuity: impossibility results for the evaluation of infinite utility streams. Technical report, p. 13 (2011)

    Google Scholar 

  3. Butnariu, D., Klement, E.P.: Triangular norm-based measures and games with fuzzy coalitions, vol. 10. Springer Science & Business Media, New York (1993)

    MATH  Google Scholar 

  4. Cappelen, A.W., Tungodden, B.: A liberal egalitarian paradox. Econ. Philos. 22, 393–408 (2006)

    Article  Google Scholar 

  5. Dalal, M.: Investigations into a theory of knowledge base revision. In: Proceedings of the Seventh American National Conference on Artificial Intelligence (AAAI88). pp. 475–479 (1988)

    Google Scholar 

  6. Dalton, H.: The measurement of the inequality of incomes. Econ. J. 30, 348–361 (1920)

    Article  Google Scholar 

  7. Detyniecki, M., Yager, R.R., Bouchon-Meunier, B.: Reducing t-norms and augmenting t-conorms. Int. J. Gen. Syst. 31(3), 265–276 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  8. Everaere, P., Konieczny, S., Marquis, P.: On egalitarian belief merging. In: AAAI (2014)

    Google Scholar 

  9. Hammond, P.J.: Equity, arrow’s conditions, and rawls’ difference principle. Econ.: J. Econom. Soc. 793–804 (1976)

    Google Scholar 

  10. Klement, E.P., Mesiar, R.: Logical, Algebraic, Analytic and Probabilistic Aspects of Triangular Norms. Elsevier Science B.V., Amsterdam (2005)

    MATH  Google Scholar 

  11. Klement, E.P., Mesiar, R., Pap, E.: On the order of triangular norms: comments on “a triangular norm hierarchy” by e. cretu. Fuzzy Sets Syst. 131(3), 409–413 (2002)

    Article  MATH  Google Scholar 

  12. Klement, E.P., Pap, E., Mesiar, R.: Triangular Norms. Trends in logic, Kluwer Academic Publ. cop., Dordrecht (2000). http://opac.inria.fr/record=b1104736

    Book  MATH  Google Scholar 

  13. Konieczny, S., Lang, J., Marquis, P.: DA\(^2\) merging operators. Artif. Intell. 157(1–2), 49–79 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  14. Konieczny, S., Pino-Pérez, R.: Merging with integrity constraints. In: Fifth European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 1999). pp. 233–244 (1999)

    Google Scholar 

  15. Konieczny, S., Pino-Pérez, R.: Merging information under constraints: a logical framework. J. Log. Comput. 12(5), 773–808 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  16. Lin, J., Mendelzon, A.O.: Merging databases under constraints. Int. J. Coop. Inf. Syst. 7, 55–76 (1996)

    Article  Google Scholar 

  17. Lombardi, M., Miyagishima, K., Veneziani, R.: Liberal Egalitarianism and the Harm Principle. Mpra Paper. University Library of Munich, Germany (2013)

    Google Scholar 

  18. Mariotti, M., Veneziani, R.: ‘Non-interference’ implies equality. Soc. Choice Welf. 32(1) (2008). http://dx.doi.org/10.1007/s00355-008-0316-x

  19. Moulin, H.: Axioms of Cooperative Decision Making, Econometric Society monographs, vol. 15. Cambridge University Press, Cambridge (1988)

    Book  MATH  Google Scholar 

  20. Revesz, P.Z.: On the semantics of theory change: arbitration between old and new information. In: Proceedings of the 12th ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems. pp. 71–82. ACM (1993)

    Google Scholar 

  21. Savage, L.: The Foundations of Statistics. Wiley, New York (1954)

    MATH  Google Scholar 

  22. Schweizer, B., Sklar, A.: Associative functions and statistical triangle inequalities. Publ. Math. Debrecen. 8, 169–186 (1961)

    MathSciNet  MATH  Google Scholar 

  23. Sen, A.K.: Choice, Welfare and Measurement. Harvard University Press, Cambridge (1997)

    MATH  Google Scholar 

  24. Tungodden, B.: Egalitarianism: is leximin the only option? Working papers, Norwegian School of Economics and Business Administration (1999). http://EconPapers.repec.org/RePEc:fth:norgee:4/99

  25. Viana, H., Alcântara, J.: Propositional Belief Merging with T-conorms (proofs) https://db.tt/OZWSR0EO

  26. Weber, S.: A general concept of fuzzy connectives, negations and implications based on t-norms and t-conorms. Fuzzy Sets Syst. 11(1–3), 103–113 (1983)

    MathSciNet  MATH  Google Scholar 

  27. Yager, R.R.: On a general class of fuzzy connectives. Fuzzy Sets Syst. 4(3), 235–242 (1980)

    Article  MathSciNet  MATH  Google Scholar 

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Correspondence to Henrique Viana .

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Viana, H., Alcântara, J. (2017). Propositional Belief Merging with T-conorms. In: Criado Pacheco, N., Carrascosa, C., Osman, N., Julián Inglada, V. (eds) Multi-Agent Systems and Agreement Technologies. EUMAS AT 2016 2016. Lecture Notes in Computer Science(), vol 10207. Springer, Cham. https://doi.org/10.1007/978-3-319-59294-7_34

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  • DOI: https://doi.org/10.1007/978-3-319-59294-7_34

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