Soft Computing and Human-Centered Machines pp 163-187 | Cite as

# Aggregation Operations for Fusing Fuzzy Information

## Abstract

Fuzzy sets can play an important role in the construction of human centered systems. They provide a mechanism for representing information in way that is compatible with human cognition. Particularly notable here is the idea of a linguistic variable [1]. In many of these applications we are faced with the problem of fusing or combining fuzzy subsets. For example, in multi-criteria decision making we need to combine the criteria to form an overall decision function. Since each criteria can be very naturally expressed as a fuzzy subset we are faced with the problem of combining fuzzy subsets. Fuzzy querying of data bases, information retrieval and pattern recognition also require us to face the problem of combining requirements expressed as fuzzy subsets. The construction of fuzzy systems models [2], which have been particularly successful in intelligent controllers, often require the aggregation of fuzzy subsets in the antecedents of the rules. Another class of problems which involves the fusion of fuzzy subsets arises in domains in which we obtain information from multiple sources and we desire to forge this information into one unified value. For example, if we search the Internet for information about the future exchange rate between the dollar and the yen we would get many estimates. Often these estimates are expressed in linguistic terms requiring the use of fuzzy subsets to translate them. Data mining [3] is another area where the fusion of fuzzy information is required.

## Keywords

Fuzzy Subset Aggregation Operator Fuzzy Measure Aggregation Operation Fuzzy Information## Preview

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## References

- [1]L.A. Zadeh, “Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic,”
*Fuzzy Sets and Systems*, Vol. 90, pp.111–127, 1997.MathSciNetMATHCrossRefGoogle Scholar - [2]R.R. Yager and D.P. Filev,
*Essentials of Fuzzy Modeling and Control*, John Wiley: New York, 1994.Google Scholar - [3]R.R. Yager, “On linguistic summaries of data,” in
*Knowledge Discovery in Databases*, Piatetsky-Shapiro, G. and Frawley, B. (eds.), Cambridge, MA: MIT Press, pp.347–363, 1991.Google Scholar - [4]R.R. Yager, “A general approach to the fusion of imprecise information,”
*International Journal of Intelligent Systems*Vol.12, pp.1–29, 1997.MATHCrossRefGoogle Scholar - [5]R.R. Yager and A. Kelman, “Fusion of fuzzy information with considerations for compatibility, partial aggregation and reinforcement,”
*International Journal of Approximate Reasoning*Vol.15, pp.93–122, 1996.MathSciNetMATHCrossRefGoogle Scholar - [6]D. Dubois, H. Prade, and R.R. Yager, “Merging fuzzy information,” Technical Report# MII-1910 Machine Intelligence Institute, Iona College, New Rochelle, NY, 1999.Google Scholar
- [7]Zadeh, L. A., “Fuzzy sets,”
*Information and Control*Vol.8, pp.338–353, 1965.MathSciNetMATHCrossRefGoogle Scholar - [8]U. Hohle, “Probabilistic uniformization of fuzzy topologies,”
*Fuzzy Sets and Systems*vol.1, 1978.Google Scholar - [9]E.P. Klement, “Characterization of fuzzy measures constructed by means of triangular norms,”
*J. of Math. Anal. and Appl.*Vol. 86, pp.345–358, 1982.MathSciNetMATHCrossRefGoogle Scholar - [10]C. Alsina, E. Trillas, and L. Valverde, “On some logical connectives for fuzzy set theory,”
*J. Math Anal. and Appl.*Vol.93, pp.15–26, 1983.MathSciNetMATHCrossRefGoogle Scholar - [11]D. Dubois and H. Prade, “A review of fuzzy sets aggregation connectives,”
*Information Sciences*Vol.36, pp.85–121, 1985.MathSciNetMATHCrossRefGoogle Scholar - [12]R.R. Yager, “On a general class of fuzzy connectives,”
*Fuzzy Sets and Systems*Vol.4, pp.235–242, 1980.MathSciNetMATHCrossRefGoogle Scholar - [13]M.J. Frank, “On the simultaneous associativity of
*F(x,y)*and*x + y F(x,y)*,”*Aequat. Math*. Vol.19, pp.194–226, 1979.MATHCrossRefGoogle Scholar - [14]R.R. Yager, “Fuzzy decision making using unequal objectives,”
*Fuzzy Sets and Systems*Vol.1, pp.87–95, 1978.MATHCrossRefGoogle Scholar - [15]R.R. Yager, “A note on weighted queries in information retrieval systems,”
*J. of the American Society of Information Sciences*Vol. 38, pp.23–24, 1987.CrossRefGoogle Scholar - [16]D. Dubois and H. Prade, “Weighted minimum and maximum operations in fuzzy sets theory,”
*Information Sciences*Vol.39, pp.205–210, 1986.MathSciNetMATHCrossRefGoogle Scholar - [17]E. Sanchez, “Importance in knowledge systems,”
*Information Systems*Vol.14, pp.455–464, 1989.CrossRefGoogle Scholar - [18]R.R. Yager and A. Rybalov, “Uninorm aggregation operators,”
*Fuzzy Sets and Systems*Vol.80, pp.111–120, 1996.MathSciNetMATHCrossRefGoogle Scholar - [19]J.C. Fodor, R.R. Yager, and A. Rybalov, “Structure of un i-norms,”
*International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems*Vol.5, pp.411–427, 1997.MathSciNetCrossRefGoogle Scholar - [20]B. De Baets, and J. Fodor, “On the structure of uninorms and their residual implicators,”
*Proc. Eighteenth Linz Seminar on Fuzzy Set Theory*, Linz, Austria, pp.81–87, 1997.Google Scholar - [21]B. De Baets, “Uninorms: The known classes,”
*in Fuzzy Logic and Intelligent Technologies for Nuclear Science and Industry*J.D. Ruan, H.A. Abderrahim, P. D’hondt, and E.E. Kerre (Eds.), World Scientific: Singapore, Vol. 21–28, 1998.Google Scholar - [22]R.R. Yager, “MAM and MOM operators for aggregation,”
*Information Sciences*Vol.69, pp.259–273, 1993.MATHCrossRefGoogle Scholar - [23]R.R. Yager, “Toward a unified approach to aggregation in fuzzy and neural systems,”
*Proceedings World Conference on Neural Networks*, Portland, Vol.II, pp.619–622, 1993.Google Scholar - [24]R.R. Yager, “A unified approach to aggregation based upon MOM and MAM operators,”
*International Journal of Intelligent Systems*Vol.10, pp.809–855, 1995.CrossRefGoogle Scholar - [25]Dyckhoff, H. and Pedrycz, W, “Generalized means as model of compensative connectives,”
*Fuzzy Sets and Systems*Vol. 14, pp.143–154, 1984.MathSciNetMATHCrossRefGoogle Scholar - [26]R.R. Yager, “On ordered weighted averaging aggregation operators in multi-criteria decision making,”
*IEEE Transactions on Systems, Man and Cybernetics*Vol.18, pp.183–190, 1988.MathSciNetMATHCrossRefGoogle Scholar - [27]R.R. Yager and J. Kacprzyk,
*The Ordered Weighted Averaging Operators: Theory and Applications*, Kluwer: Norwell, MA, 1997.CrossRefGoogle Scholar - [28]M. O’Hagan, “A fuzzy neuron based upon maximum entropy-ordered weighted averaging,” in
*Uncertainty in Knowledge Bases*, B. Bouchon Meunier, R.R. Yager, and L.A. Zadeh, (Eds.), Springer-Verlag: Berlin, pp.598–609, 1990.Google Scholar - [29]M. O’Hagan, “Using maximum entropy-ordered weighted averaging to construct a fuzzy neuron,”
*Proceedings 24th Annual IEEE Asilomar Conf. on Signals, Systems and Comp uters*, Pacific Grove, Ca, pp.618–623, 1990.Google Scholar - [30]D.P. Filev and R.R. Yager, “Learning OWA operator weights from data,”
*Proceedings of the Third IEEE International Conference on Fuzzy Systems*, Orlando, pp.468–473, 1994.Google Scholar - [31]D.P. Filev and R.R. Yager, “On the issue of obtaining OWA operator weights,”
*Fuzzy Sets and Systems*Vol.94, pp.157–169, 1998.MathSciNetCrossRefGoogle Scholar - [32]L.A. Zadeh, “A computational approach to fuzzy quantifiers in naturallanguages,”
*Computing and Mathematics with Applications*Vol.9, pp.149–184, 1983.MathSciNetMATHCrossRefGoogle Scholar - [33]M. Sugeno,
*Theory of fuzzy integrals and its applications*, Doctoral Thesis, Tokyo Institute of Technology, 1974.Google Scholar - [34]M. Sugeno, “Fuzzy measures and fuzzy integrals: a survey,” in
*Fuzzy Automata and Decision Process*, Gupta, M.M., Saridis, G.N. and Gaines, B.R. (Eds.), Amsterdam: North-Holland Pub, pp.89–102, 1977.Google Scholar - [35]D. Dubois and H. Prade, “A class of fuzzy measures based on triangular norms,”
*International Journal of General Systems*Vol.8, pp.43–61, 1982.MathSciNetMATHCrossRefGoogle Scholar - [36]T. Murofushi and M. Sugeno, “An interpretation of fuzzy measures and the Choquet integral as an integral with respect to fuzzy measure,”
*Fuzzy Sets and Systems*Vol.29, pp.201–227, 1989.MathSciNetMATHCrossRefGoogle Scholar - [37]T. Murofushi and M. Sugeno, “Theory of fuzzy measures: representations, the Choquet integral and null sets,”
*J. Math Anal. Appl*Vol.159, pp.532–549, 1991.MathSciNetMATHCrossRefGoogle Scholar - [38]D. Denneberg,
*Non-Additive Measure and Integral*, Kluwer Academic: Norwell, MA, 1994.MATHGoogle Scholar - [39]F. Modave, and M. Grabisch, “Preference representation by Choquet integral: the commensurability hypothesis,”
*Proceedings of the Seventh International Conference on Information Processing and Management of Uncertainty in Knowledge-based Systems*, Paris, pp.164–171, 1998.Google Scholar - [40]H.T. Nguyen and M. Sugeno,
*Fuzzy Systems: Modeling and Control*, Kluwer Academic Press: Norwell, Ma, 1998.MATHGoogle Scholar