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Semiautoduality in a restricted family of aggregation operators


Bustince, H. y Montero, Javier y Pagola, M. (2007) Semiautoduality in a restricted family of aggregation operators. Fuzzy Sets and Systems, 158 (12). pp. 1360-1377. ISSN 0165-0114

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In this paper we consider aggregation operators satisfying non-decreasingness and some specific boundary conditions. We then analyze some properties of such a family of aggregation operators, introducing the semiautoduality condition, which is weaker than the standard autoduality condition (i.e., the standard self De Morgan identity). Particular families of aggregation operators will appear depending on the context.

Tipo de documento:Artículo
Palabras clave:Aggregation operations; Associative operators; Duality property; Idempotent operators
Materias:Ciencias > Informática > Inteligencia artificial
Código ID:16328

J. Aczél, On mean values, Bull. Amer. Math. Soc. 54 (1948) 392–400.

C. Alsina, G. Mayor, M.S. Tomas, J. Torrens,A haracterization of a class of aggregation functions, Fuzzy Sets and Systems 53 (1993) 33–88.

A. Amo, J. Montero, E. Molina, Representation of consistent recursive rules, European J. Oper. Res. 130 (2001) 29–53.

H. Bustince, V. Mohedano, E. Barrenechea, M. Pagola, Definition and construction of fuzzy DI-subsethood measures, Inform. Sci. 176 (2006)3190–3231.

T. Calvo, A. Kolesarova, M. Komornikova, R. Mesiar, Aggregation operators: properties, classes and construction methods, in: T. Calvo, G.Mayor, R. Mesiar (Eds.), Aggregation Operators, Springer, Berlin, 2002, pp. 3–104.

T. Calvo, R. Mesiar,Weighted triangular norms-based aggregation operators, Fuzzy Sets and Systems 137 (2003)3–10.

T. Calvo, R. Mesiar, R.R.Yager, Quantitative weights and aggregation, IEEE Trans. Fuzzy Systems 12 (2004) 62–69.

F. Chiclana, F. Herrera, E. Herrera-Viedma, L. Martínez, A note on the reciprocity in the aggregation of fuzzy preference relations using OWA operators, Fuzzy Sets and Systems 137 (2003) 71–83.

W. Cholewa, Aggregation for fuzzy opinions—an axiomatic approach, Fuzzy Sets and Systems 17 (1985) 249–258.

V. Cutello, J. Montero, Recursive connective rules,Internat. J. Intelligent Systems 14 (1999) 3–20.

J. Dombi,A general class of fuzzy operators, the De Morgan class of fuzzy operators and fuzziness measures induced by fuzzy operators, Fuzzy Sets and Systems 8 (1982) 149–163.

J. Dombi, Basic concept for a theory of evaluation: the aggregative operator, European J. Oper. Res. 10 (1982) 282–293.

D. Dubois, J.L. Koning, Social choice axioms for fuzzy set aggregation, Fuzzy Sets and Systems 58 (1991) 339–342.

D. Dubois, H. Prade, A class of fuzzy measures based on triangular norms, Internat. J. Gen. Systems 8 (1982) 43–61.

D. Dubois, H. Prade, Criteria aggregation and ranking of alternatives in the framework of fuzzy theory, in: H.J. Zimmermann, L.A. Zadeh, B.Gaines (Eds.), Fuzzy Sets and Decision Analysis, TIMS Studies in Management Science, Vol. 20, 1984, pp. 209–240.

D. Dubois, H. Prade, A review of fuzzy ser aggregation connectives, Inform. Sci. 36 (1985) 85–121.

J.J. Dujmovic,Weighted conjunctive and disjunctive means and their application in system evaluation, Univ. Beograd. Publ. Elektrotechn. Fak.(1974) 147–158.

F. Esteva, E. Trillas, X. Domingo,Weak and strong negation function for fuzzy set theory, in: Proc. 11th IEEE Internat. Symp. on Multivalued Logic, Norman, Oklahoma, 1981, pp. 23–27.

J. Fodor, M. Roubens, Fuzzy Preference Modelling and Multicriteria Decision Support, Kluwer Academic Publishers, Dordrecht, 1994.

M.J. Frank, On the simultaneous associativity of F(x, y) and x + y − F(x, y), Aequationes Math. 19 (1979) 194–226.

L.W. Fung, K.S. Fu, An axiomatic approach to rational decision making in a fuzzy environment, in: L.A. Zadeh, K.S. Fu, K. Tanaka, M. Simura (Eds.), Fuzzy Sets and their Applications to Cognitive and Decision Processes, Academic Press, NewYork, 1975, pp. 227–256.

J.A. Goguen, L-fuzzy sets, J. Math. Anal. Appl. 18 (1967) 145–174.

J.A. Goguen, The logic of inexact concepts, Synthese 19 (1969) 325–373.

D. Gómez, J. Montero, A discussion on aggregation operators, Kybernetika 40 (2004) 107–120.

G.H. Hardy, J.E. Littlewood, G. Polya, Inequalities, second ed., Cambridge Mathematical Library, 1988.

E.P. Klement, R. Mesiar, E. Pap, On the relationship of associative compensatory operators to triangular norms and conorms, Internat. J.Uncertainty, Fuzziness and Knowledge-Based Systems 4 (1996) 129–144.

E.P. Klement, R. Mesiar, E. Pap, Triangular Norms, Kluwer Academic Publishers, Dordrecht, 2000.

G. Klir, B.Yuan, Fuzzy Sets and Fuzzy Logic: Theory and Applications, Prentice-Hall, Englewood Cliffs, NJ, 1995.

G.J. Klir, T.A. Folger, Fuzzy Sets Uncertainty and Information, Prentice-Hall International, 1988.

A. Kolesárová, Limit properties of quasi-arithmetic means, Fuzzy Sets and Systems 124 (2001) 65–71.

A. Kolesárová, M. Komorníková, Triangular norm-based iterative compensatory operators, Fuzzy Sets and Systems 104 (1999) 109–120.

A.N. Kolmogoroff, Sur la notion de la moyenne, Accad. Naz. Lincei Mem. Cl. Sci. Fis. Mat. Natur. Sez. 12 (1930) 388–391.

R. Lowen, On fuzzy complements, Inform. Sci. 14 (1978) 107–113.

J.L. Marichal, Aggregation operators for multicriteria decision aid, Ph.D. Thesis, University of Liege, 1998.

G. Mayor, J. Torrens, On a class of binary operations: non-strict Archimedian aggregation functions, in: Proc. 18th ISMVL, Palma de Mallorca,1988, pp. 54–59.

G. Mayor, E. Trillas, On the representation of some aggregation functions, in: Proc. 16th ISMVL, Blacksburg, 1986, pp. 110–114.

R. Mesiar, M. Komornikova, Aggregation operators, in: D. Herceg, K. Surla (Eds.), Proc. PRIM Conf. on Applied Mathematics, Budva, 1996,pp. 193–211.

J. Montero, A note of Fung-Fu’s theorem, Fuzzy Sets and Systems 13 (1985) 259–269.

J. Montero, Rational aggregation rules, Fuzzy Sets and Systems 62 (1994) 267–276.

[40] M. Nagumo, Uber eine Klasse der Mittelwerte, Japanese J. Math. 6 (1930) 71–79.

S.V. Ovchinnikov, Structure of fuzzy binary relations, Fuzzy Sets and Systems 6 (2) (1981) 169–195.

S.V. Ovchinnikov, General negations in fuzzy set theory, J. Math. Anal. Appl. 92 (1983) 234–239.

S.V. Ovchinnikov, M. Roubens, On strict preference relations, Fuzzy Sets and Systems 43 (1991) 319–326.

R. Ramakrishnan, C.J.M. Rao, The fuzzy weighted additive rule, Fuzzy Sets and Systems 46 (1992) 177–187.

W. Silvert, Symmetric summation: a class of operations on fuzzy subsets, IEEE Trans. Systems Man Cybernet. 9 (1979) 659–667.

D. Sinha, E.R. Dougherty, Fuzzification of set inclusion: theory and applications, Fuzzy Sets and Systems 55 (1993) 15–42.

V. Torra, On some aggregation operators for numerical information, in: V. Torra (Ed.), Information Fusion in Data Mining, Springer, Berlin,2003.

E. Trillas, Sobre funciones de negación en la teoría de conjuntos difusos, Stochastica III-1 (1979) 47–59 (in Spanish) (Reprinted (English version), in: S. Barro, A. Sobrino, A. Bugarin (Eds.), Advances of Fuzzy Logic, Universidad de Santiago de Compostela, 1998, pp. 31-43).

E. Trillas, C. Alsina, J.M. Terricabras, Introducción a la lógica borrosa. Ariel Matemática (1995).

R.R.Yager, On the measure of fuzziness and negation. Part I : membership in the unit interval, Internat. J. Gen. Systems 5 (1979) 221–229.

R.R.Yager, On the measure of fuzziness and negation. Part II: lattices, Inform. Control 44 (1979) 236–260.

R.R.Yager, Families of OWA operators, Fuzzy Sets and Systems 59 (1993) 125–148.

R.R.Yager, Induced aggregation operators, Fuzzy Sets and Systems 137 (2003) 59–69.

V.R.Young, Fuzzy subsethood, Fuzzy Sets and Systems 77 (1996) 371–384.

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