Fuzzy Optimization and Decision Making

, Volume 6, Issue 3, pp 199–219 | Cite as

Aggregation of ordinal information

Article

Abstract

Our interest is with the fusion of information which has an ordinal structure. Information fusion in this environment requires the availability of ordinal aggregation operations. Basic ordinal operations are first introduced. Next we investigate conjunctive and disjunction aggregations of ordinal information. The idea of a pseudo-log in the ordinal environment is presented. We discuss the introduction of a zero like point on an ordinal scale along with the related ideas of bipolarity (positive and negative values) and uni-norm aggregation operators. We introduce mean like aggregation operators as well weighted averages on a ordinal scale. The problem of selecting between ordinal models is considered.

Keywords

Aggregation operations information fusion ordinal operators linguistic values uni-norm ordinal weighted average 

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References

  1. Alsina C., Trillas E., Valverde L. (1983). On some logical connectives for fuzzy set theory. Journal of Mathematical Analysis and Applications 93, 15–26MATHCrossRefMathSciNetGoogle Scholar
  2. De Baets B. (1998). Uninorms: The known classes. In: Ruan D., Abderrahim H.A., D’hondt P., Kerre E. (eds) Fuzzy logic and intelligent technologies for nuclear science and industry. Singapore, World Scientific, pp.21–28Google Scholar
  3. De Baets, B., & Fodor, J. (1997). On the structure of uninorms and their residual implicators. Proc. Eighteenth Linz Seminaron Fuzzy Set Theory: Linz, Austria, pp. 81–87.Google Scholar
  4. Dubois D., Fargier H., Prade H. (1996). Refinements of the maximin approach to fuzzy decision making. Fuzzy Sets and Systems 81: 103–122MATHCrossRefMathSciNetGoogle Scholar
  5. Dubois, D., Kaci, S., & Prade, H. (2004). Bipolarity in reasoning and decision—an introduction. The case of the possibility framework. In Proc. of the 10th International Conf. on Information processing and the management of uncertainty in knowledge-based systems (IPMU) (pp. 959–966). Perugia, Italy.Google Scholar
  6. Fodor J.C., Yager R.R., Rybalov A. (1997). Structure of uni-norms. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 5, 411–427CrossRefMathSciNetGoogle Scholar
  7. Grabisch M., Labreuche C. (2005). Bi-capacities—parts I and II. Fuzzy Sets and Systems 151: 211–260MATHCrossRefMathSciNetGoogle Scholar
  8. Janssens S., De Baets B., De Meyer H. (2004). Bell-type inequalities for quasi-copulas. Fuzzy Sets and Systems 148: 263–278MATHCrossRefMathSciNetGoogle Scholar
  9. Klement E.P., Mesiar R., Pap E. (2000). Triangular norms. Dordrecht, Kluwer Academic PublishersMATHGoogle Scholar
  10. Murofushi, T., & Sugeno, M. (2000). Fuzzy measures and fuzzy integrals. In Grabisch, M., Murofushi, T., & Sugeno, M. (Eds.) Fuzzy measures and integrals. Heidelberg, Physica-Verlag, pp. 3–41Google Scholar
  11. Yager R.R. (1980). Extending Nash’s bargaining model to include importance for multiple objective decision making. IEEE Transactions on Systems, Man and Cybernetics 10, 405–407MathSciNetCrossRefGoogle Scholar
  12. Yager R.R. (1981). A new methodology for ordinal multiple aspect decisions based on fuzzy sets. Decision Sciences 12, 589–600CrossRefMathSciNetGoogle Scholar
  13. Yager R.R. (1992). Applications and extensions of OWA aggregations. International Journal of Man–Machine Studies 37, 103–132CrossRefGoogle Scholar
  14. Yager R.R. (1996). Structures generated from weighted fuzzy intersection and union. Journal of the Chinese Fuzzy Systems Association 2, 37–58Google Scholar
  15. Yager R.R. (2002). Ordinal decision making with a notion of acceptable: Denoted ordinal scales. In Lin T.Y., Yao Y.Y. & Zadeh L.A. (eds). Data mining, rough sets and granular computing. Heidelberg, Physica-Verlag, pp. 98–413Google Scholar
  16. Yager R.R. (2003). Generalized triangular norm and conorm aggregation operators on ordinal spaces. International Journal of General Systems 32, 475–490MATHCrossRefMathSciNetGoogle Scholar
  17. Yager R.R. (2004). Weighted triangular norms using generating functions. International Journal of Intelligent Systems 19, 217–231MATHCrossRefGoogle Scholar
  18. Yager R.R. (2006). Modeling holistic fuzzy implication operators using co-copulas. Fuzzy Optimization and Decision Making 5, 207–226CrossRefMathSciNetMATHGoogle Scholar
  19. Yager R.R., Rybalov A. (1996). Uninorm aggregation operators. Fuzzy Sets and Systems 80, 111–120MATHCrossRefMathSciNetGoogle Scholar
  20. Yager R.R., Walker C.L., Walker E.A. (2005). Generalizing leximin to t-norms and t-conorms: The LexiT and LexiS orderings. Fuzzy Sets and Systems 151, 327–340MATHCrossRefMathSciNetGoogle Scholar
  21. Zadeh L.A. (2000). Toward a logic of perceptions based on fuzzylogic. In: Novak W., Perfilieva I. (eds). Discovering the world with fuzzy logic. Heidelberg, Physica-Verlag, pp. 4–28Google Scholar
  22. Zadeh L.A. (2002). Toward a perception-based theory of probabilistic reasoning with imprecise probabilities. Journal of Statistical Planning and Inference 105, 233–264MATHCrossRefMathSciNetGoogle Scholar
  23. Zadeh L.A. (2005). Toward a generalized theory of uncertainty (GTU)—an outline. Information Sciences 172: 1–40MATHCrossRefMathSciNetGoogle Scholar
  24. Zaruda J.M. (1992). Introduction to artificial neural systems. St Paul, MN, West Publishing Co.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Machine Intelligence InstituteIona CollegeNew RochelleUSA

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