Complutense University Library

A class of aggregation functions encompassing two-dimensional OWA operators

Bustince, H. and Calvo, T. and De Baets, B. and Fodor, J. and Mesiar, R. and Montero de Juan, Francisco Javier and Paternain, D. and Pradera, A. (2010) A class of aggregation functions encompassing two-dimensional OWA operators. Information Sciences, 180 (10). pp. 1977-1989. ISSN 0020-0255

[img] PDF
Restricted to Repository staff only until 2020.

259kB

Official URL: http://www.sciencedirect.com/science/journal/00200255

View download statistics for this eprint

==>>> Export to other formats

Abstract

In this paper we prove that, under suitable conditions, Atanassov’s Ka operators, which act
on intervals, provide the same numerical results as OWA operators of dimension two. On
one hand, this allows us to recover OWA operators from Ka operators. On the other hand,
by analyzing the properties of Atanassov’s operators, we can generalize them. In this way,
we introduce a class of aggregation functions – the generalized Atanassov operators – that,in particular, include two-dimensional OWA operators. We investigate under which conditions these generalized Atanassov operators satisfy some properties usually required for aggregation functions, such as bisymmetry, strictness, monotonicity, etc. We also show that if we apply these aggregation functions to interval-valued fuzzy sets, we obtain an
ordered family of fuzzy sets.


Item Type:Article
Uncontrolled Keywords:OWA operators; interval-valued fuzzy sets; Ka operators;generalized Ka operators; dispersion
Subjects:Sciences > Computer science > Artificial intelligence
ID Code:16002
References:

J. Aczél, On mean values, Bulletin of the American Mathematical Society 54 (1948) 392–400.

K. Atanassov, Intuitionistic fuzzy sets, VIIth ITKR Session, Deposited in the Central Science and Technology Library of the Bulgarian Academy of Sciences, Sofia, Bulgaria, 1983, pp. 1684–1697.

K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20 (1986) 87–96.

P. Burillo, H. Bustince, Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets, Fuzzy Sets and Systems 78 (1996) 305–316.

H. Bustince, Construction of intuitionistic fuzzy relations with predetermined properties, Fuzzy Sets and Systems 109 (2000) 379–403.

H. Bustince, E. Barrenechea, M. Pagola, Generation of interval-valued fuzzy and Atanassov’s intuitionistic fuzzy connectives from fuzzy connectives and from K(alpha) operators. Laws for conjunctions and disjunctions. Amplitude, International Journal of Intelligent Systems 23 (2008) 680–714.

H. Bustince, J. Montero, E. Barrenechea, M. Pagola, Laws of conjunctions and disjunctions in interval type 2 fuzzy sets, in: Proceedings of the IEEE World Congress on Computational Intelligence, WCCI2008, Hong Kong, 2008, pp. 615–620.

H. Bustince, J. Montero, M. Pagola, E. Barrenechea, D. Gómez, A survey on interval-valued fuzzy sets, in: W. Pedrycz, A. Skowron, V. Kreinovich (Eds.),Handbook of Granular Computing, John Wiley and Sons, New York, 2008 (Chapter 22).

T. Calvo, B. De Baets, J. Fodor, The functional equations of Frank and Alsina for uninorms and nullnorms, Fuzzy Sets and Systems 120 (2001) 385–394.

T. Calvo, A. Kolesárová, M. Komornikova, R. Mesiar, Aggregation operators: properties classes and construction methods, in: T. Calvo, G. Mayor, R. Mesiar (Eds.), Aggregation Operators: New Trends and Applications, Physica-Verlag, Heidelberg, 2002, pp. 3–104.

C. Cornelis, G. Deschrijver, E.E. Kerre, Advances and challenges in interval-valued fuzzy logic, Fuzzy Sets and Systems 157 (2006) 622–627.

V. Cutello, J. Montero, Hierarchical aggregation of OWA operators: basic measures and related computational problems, Uncertainty, Fuzziness and Knowledge-Based Systems 3 (1995)17–26.

G. Deschrijver, C. Cornelis, E.E. Kerre, On the representation of intuitionistic fuzzy t-norms and t-conorms, IEEE Transactions on Fuzzy Systems 12 (2004) 45–61.

J. Fodor, J. Marichal, On nonstrict means, Aequationes Mathematicae 54 (1997) 308–327.

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

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

M.B. Gorzalczany, A method of inference in approximate reasoning based on interval-valued fuzzy sets, Fuzzy Sets and Systems 21 (1987) 1–17.

[18] E.P. Klement, R. Mesiar, E. Pap, Triangular Norms, Kluwer, Dordrecht, 2000.

[19] G.J. Klir, T.A. Folger, Fuzzy Sets, Uncertainty and Information, Prentice Hall, Englewood Cliffs, NJ, 1988.

[20] R. Sambuc, Fonctions U-Flous, Application a l’aide au Diagnostic en Pathologie Thyroidienne, Thèse de Doctorat en Médicine, University of Marseille, 1975.

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

R.R. Yager, On ordered weighted averaging aggregation operators in multicriteria decision-making, IEEE Transactions on Systems, Man and Cybernetics 18 (1988) 183–190.

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

L.A. Zadeh, Fuzzy sets, Information Control 8 (1965) 338–353.

L.A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning – I, Information Sciences 8 (1975) 199–249.

L.A. Zadeh, Is there a need for fuzzy logic? Information Sciences 178 (2008) 2751–2779.

L.A. Zadeh, Toward a generalized theory of uncertainty (GTU) - an outline, Information Sciences 172 (1–2) (2005) 1–40.

Deposited On:19 Jul 2012 09:17
Last Modified:06 Feb 2014 10:36

Repository Staff Only: item control page