De Miguel, L.; Paternain, D.; Lizasoain, I.; Ochoa, G.; Bustince, H. Orness measurements for lattice \(m\)-dimensional interval-valued OWA operators. (English) Zbl 1429.91100 Appl. Math. Comput. 339, 63-80 (2018). Summary: Ordered weighted average (OWA) operators are commonly used to aggregate information in multiple situations, such as decision making problems or image processing tasks. The great variety of weights that can be chosen to determinate an OWA operator provides a broad family of aggregating functions, which obviously give different results in the aggregation of the same set of data. In this paper, some possible classifications of OWA operators are suggested when they are defined on \(m\)-dimensional intervals taking values on a complete lattice satisfying certain local conditions. A first classification is obtained by means of a quantitative orness measure that gives the proximity of each OWA to the OR operator. In the case in which the lattice is finite, another classification is obtained by means of a qualitative orness measure. In the present paper, several theoretical results are obtained in order to perform this qualitative value for each OWA operator. Cited in 1 Document MSC: 91B06 Decision theory 03E72 Theory of fuzzy sets, etc. Keywords:OWA operator; lattice-valued fuzzy sets; interval-valued fuzzy sets; orness; t-norm; t-conorm PDFBibTeX XMLCite \textit{L. De Miguel} et al., Appl. Math. Comput. 339, 63--80 (2018; Zbl 1429.91100) Full Text: DOI References: [1] Bedregal, B.; Beliakov, G.; Bustince, H.; Calvo, T.; Mesiar, R.; Paternain, D., A class of fuzzy multisets with a fixed number of memberships, Inf. Sci., 189, 1-17 (2012) · Zbl 1247.03113 [2] 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 [3] De Baets, B.; Mesiar, R., Triangular norms on product lattices, Fuzzy Sets Syst., 104, 61-75 (1999) · Zbl 0935.03060 [4] De Cooman, G.; Kerre, E. E., Order norms on bounded partially ordered sets, J. Fuzzy Math., 2, 281-310 (1993) · Zbl 0814.04005 [5] Dubois, D.; Prade, H., On the use of aggregation operations in information fusion processes, Fuzzy Sets Syst., 142, 143-161 (2004) · Zbl 1091.68107 [6] Komorníková, M.; Mesiar, R., Aggregation functions on bounded partially ordered sets and their classification, Fuzzy Sets Syst., 175, 48-56 (2011) · Zbl 1253.06004 [7] Lizasoain, I.; Moreno, C., OWA operators defined on complete lattices, Fuzzy Sets Syst., 224, 36-52 (2013) · Zbl 1284.03246 [8] Lizasoain, I.; Ochoa, G., Generalized Atanassov’s operators defined on lattice multisets, Inf. Sci., 278, 408-422 (2014) · Zbl 1354.03079 [9] Ochoa, G.; Lizasoain, I.; Paternain, D.; Bustince, H.; Pal, N. R., From quantitative to qualitative orness for lattice OWA operators, Int. J. Gen. Syst., 46, 640-669 (2017) [10] Paternain, D.; Ochoa, G.; Lizasoain, I.; Bustince, H.; Mesiar, R., Quantitative orness for OWA operators, Inf. Fusion, 30, 27-35 (2016) [11] Yager, R. R., On ordered weighting averaging aggregation operators in multicriteria decision-making, IEEE Trans. Syst. Man Cybern., 18, 183-190 (1988) · Zbl 0637.90057 [12] Yager, R. R., Families of OWA operators, Fuzzy Sets Syst., 59, 125-148 (1993) · Zbl 0790.94004 [13] Yager, R. R.; Gumrah, G.; Reformat, M., Using a web personal evaluation tool-PET for lexicographic multi-criteria service selection, Knowl.-Based Syst., 24, 929-942 (2011) [14] Zhou, S. M.; Chiclana, F.; John, R. I.; Garibaldi, J. M., Type-1 OWA operators for aggregating uncertain information with uncertain weights induced by type-2 linguistic quantifiers, Fuzzy Sets Syst., 159, 3281-3296 (2008) · Zbl 1187.68619 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.