Bustince, H.; Fernandez, J.; Kolesárová, A.; Mesiar, R. Generation of linear orders for intervals by means of aggregation functions. (English) Zbl 1284.03242 Fuzzy Sets Syst. 220, 69-77 (2013). Summary: The problem of choosing an appropriate total order is crucial for many applications that make use of extensions of fuzzy sets. In this work we introduce the concept of an admissible order as a total order that extends the usual partial order between intervals. We propose a method to build these admissible orders in terms of two aggregation functions and we prove that some of the most used examples of total orders that appear in the literature are specific cases of our construction. Cited in 63 Documents MSC: 03E72 Theory of fuzzy sets, etc. 06A05 Total orders Keywords:Atanassov’s intuitionistic fuzzy set; linear order; aggregation function PDFBibTeX XMLCite \textit{H. Bustince} et al., Fuzzy Sets Syst. 220, 69--77 (2013; Zbl 1284.03242) Full Text: DOI References: [1] Beliakov, G.; Bustince, H.; Goswami, D. P.; Mukherjee, U. K.; Pal, N. R., On averaging operators for Atanassov’s intuitionistic fuzzy sets, Inform. Sci., 181, 1116-1124 (2010) · Zbl 1215.03064 [2] Brouwer, L. E.J., Über Abbildung von Mannigfaltigkeiten, Mathematische Annalen, 71, 1, 97-115 (1911) · JFM 42.0417.01 [4] Bustince, H.; Barrenechea, E.; Pagola, M.; Fernandez, J., Interval-valued fuzzy sets constructed from matrices: application to edge detection, Fuzzy Sets Syst., 160, 1819-1840 (2009) · Zbl 1182.68191 [5] Bustince, H.; Calvo, T.; De Baets, B.; Fodor, J.; Mesiar, R.; Montero, J.; Paternain, D.; Pradera, A., A class of aggregation functions encompassing two-dimensional OWA operators, Inform. Sci., 180, 1977-1989 (2010) · Zbl 1205.68419 [6] Fodor, J.; Roubens, M., Fuzzy Preference Modelling and Multicriteria Decision Support. Theory and Decision Library (1994), Kluwer Academic Publishers · Zbl 0827.90002 [7] Galar, M.; Fernandez, J.; Beliakov, G.; Bustince, H., Interval-valued fuzzy sets applied to stereo matching of color images, IEEE Trans. Image Process., 20, 1949-1961 (2011) · Zbl 1372.94085 [8] Grabisch, M.; Marichal, J.-L.; Mesiar, R.; Pap, E., Aggregation Functions (2009), Cambridge University Press: Cambridge University Press Cambridge [9] Komorníková, M.; Mesiar, R., Aggregation functions on bounded partially ordered sets and their classification, Fuzzy Sets and Systems, 175, 48-56 (2011) · Zbl 1253.06004 [10] Sanz, J.; Fernandez, A.; Bustince, H.; Herrera, F., A genetic tuning to improve the performance of fuzzy rule-based classification systems with interval-valued fuzzy sets: degree of ignorance and lateral position, Int. J. Approx. Reas., 52, 6, 751-766 (2011) [11] Xu, Z. S., Choquet integrals of weighted intuitionistic fuzzy information, Inform. Sci., 180, 726-736 (2010) · Zbl 1186.68469 [12] Xu, Z. S.; Da, Q. L., The uncertain OWA operator, Int. J. Intel. Syst., 17, 569-575 (2002) · Zbl 1016.68025 [13] Xu, Z. S.; Yager, R. R., Some geometric aggregation operators based on intuitionistic fuzzy sets, Int. J. Gen. Syst., 35, 417-433 (2006) · Zbl 1113.54003 [14] Zadeh, L. A., The concept of a linguistic variable and its applications to approximate reasoning, Inform. Sci., 8 (1975), Part I, pp. 199-251, Part II, pp. 301-357, Inform. Sci. 9, Part III, pp. 43-80 · Zbl 0397.68071 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.