Abstract
In this chapter we review several properties of Atanassov’s intuitionistic fuzzy relations, recalling the main concepts related to Atanassov’s intuitionistic fuzzy relations and the main properties that can be demanded to such conepts. We also consider the use of Atanassov’s operators over such relations.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
K. Atanassov, Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20, 87–96 (1986)
K. Atanassov, Review and new results on intuitionistic fuzzy sets. IM-MFAIS 1 (1988)
K. Atanassov, Two operators on intuitionistic fuzzy sets. Comptes rendus de l’Academie bulgare des Sciences, Tome 41 (1988)
K. Atanassov, Intuitionistic Fuzzy Sets. Theory and Applications (Physica-Verlag, Heidelberg, 1999)
K. Atanassov, Intuitionistic fuzzy sets, VII ITKR’s Session, Deposed in Central Science and Technology. Library of the Bulgarian academy of sciences, Sofia, 1983, pp. 1684–1697
K.T. Atanassov, More on intuitionistic fuzzy sets. Fuzzy Sets Syst. 33, 37–45 (1989)
G. Beliakov, H. Bustince, S. James, T. Calvo, J. Fernandez, Aggregation for Atanassovs intuitionistic and interval valued fuzzy sets: the median operator. IEEE Trans. Fuzzy Syst. 20(3), 487–498 (2012)
U. Bentkowska, H. Bustince, A. Jurio, M. Pagola, B. Pekala, Decision making with an interval-valued fuzzy preference relation and admissible orders. Appl. Soft Comput. 35, 792–801 (2015)
T. Buhaescu, Some observations on intuitionistic fuzzy relations. Itimerat Seminar on Functional Equations, 1989, 111–118
P. Burillo, H. Bustince, Estructuras algebraicas en conjuntos IFS, II Congreso Nacional ESTYLF, Boadilla del Monte, Madrid, Spain, 1992, pp. 135–147
P. Burillo, H. Bustince, Structures on intuitionistic fuzzy relations. Fuzzy Sets Syst. 78, 293–303 (1996)
P. Burillo, H. Bustince, Construction theorems for intuitionistic fuzzy sets. Fuzzy Sets Syst. 84, 271–281 (1996)
P. Burillo, H. Bustince, Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets. Fuzzy Sets Syst. 78, 305–316 (1996)
P. Burillo, H. Bustince, Intuitionistic fuzzy relations (Part I). Mathware Soft Comput. 2, 5–38 (1995)
P. Burillo, H. Bustince, Orderings in the referential set induced by an intuitionistic fuzzy relation. Notes IFS I, 93–103 (1995)
H. Bustince, Conjuntos Intuicionistas e Intervalo valorados Difusos: Propiedades y Construcción, Relaciones Intuicionistas Fuzzy, Thesis, Universidad Pública de Navarra (1994)
H. Bustince, Construction of intuitionistic fuzzy relations with predetermined properties. Fuzzy Sets Syst. 109, 379–403 (2000)
H. Bustince, P. Burillo, Intuitionistic fuzzy relations (Part II). Mathware Soft Comput. 2, 117–148 (1995)
H. Bustince, P. Burillo, Perturbation of intuitionistic fuzzy relations. Int. J. Uncertain. Fuzziness Knowl. Based Syst. 9(1), 81–103 (2001)
L. De Miguel, H. Bustince, J. Fernandez, E. Induráin, A. Kolesárová, R. Mesiar, Construction of admissible linear orders for interval-valued Atanassov intuitionistic fuzzy sets with an application to decision making. Inf. Fusion 27, 189–197 (2016)
G. Deschrijver, E.E. Kerre, On the composition of intuitionistic fuzzy relations. Fuzzy Sets Syst. 136, 333–361 (2003)
J. Drewniak, U. Dudziak, Aggregations preserving classes of fuzzy relations. Kybernetika 41(3), 265–284 (2005)
J. Drewniak, U. Dudziak, Preservation of properties of fuzzy relations during aggregation processes. Kybernetika 43(2), 115–132 (2007)
U. Dudziak, B. Pekala, Equivalent bipolar fuzzy relations. Fuzzy Sets Syst. 161, 234–253 (2010)
U. Dudziak, Weak and graded properties of fuzzy relations in the context of aggregation process. Fuzzy Sets Syst. 161, 216–233 (2010)
A. Kaufmann, Introduction a la Théorie des Sous-Ensembles Flous, vols. I–IV (Masson. Paris, 1977)
P. Melo-Pinto, P. Couto, H. Bustince, E. Barrenechea, M. Pagola, J. Fernandez, mage segmentation using Atanassovs intuitionistic fuzzy sets. Expert Syst. Appl. 40(1), 15–26 (2013)
N.R. Pal, H. Bustince, M. Pagola, U.K. Mukherjee, D.P. Goswami, G. Beliakov, Uncertainties with Atanassovs intuitionistic fuzzy sets: fuzziness and lack of knowledge. Inf. Sci. 228, 61–74 (2013)
B. Pekala, Properties of Atanassov’s intuitionistic fuzzy relations and Atanassov’s operators. Inf. Sci. 213, 84–93 (2012)
E. Szmidt, I. Kacprzyk, Intuitionistic fuzzy sets in group decision making. Notes IFS 2, 15–32 (1996)
L.A. Zadeh, Similarity relations and fuzzy orderings. Inf. Sci. 3, 177–200 (1971)
X. Zeshui, Intuitionistic preference relations and their application in group decision making. Inf. Sci. 177, 2363–2379 (2007)
Acknowledgments
This work has been supported by projects TIN2013-40765-P and TIN2012-32482 of the Spanish Ministry of Science.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Bustince, H., Barrenechea, E., Pagola, M., Fernandez, J., Orduna, R., Montero, J. (2016). A Survey of Atanassov’s Intuitionistic Fuzzy Relations. In: Calvo Sánchez, T., Torrens Sastre, J. (eds) Fuzzy Logic and Information Fusion. Studies in Fuzziness and Soft Computing, vol 339. Springer, Cham. https://doi.org/10.1007/978-3-319-30421-2_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-30421-2_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-30419-9
Online ISBN: 978-3-319-30421-2
eBook Packages: EngineeringEngineering (R0)