SIMILARITY CLASSIFIER WITH WEIGHTED ORDERED WEIGHTED AVERAGING OPERATOR

Abstract

(ProQuest: ... denotes formulae omitted.)1.INTRODUCTIONVast amount of data produced by computers and the internet of things and the increased ability to create automated systems have led to a growing need for effective ways to monitor performance and to detect problems, monitoring and problem detection are often linked to classification as states of performance can be understood as classes. Classification has been used in connection with variety of problems that range from medical diagnostics to fault detection and are embedded in many common appliances such as air conditioners, vacuum cleaners, and industrial equipment, e.g., see (Bagby and Cormier, 1989; Haberl and Claridge, 1987). The use of classifiers is also making its' way into business enterprises, where classifiers are, e.g., used to guide decision making (Dubois and Prade, 1985; Torra and Narukawa, 2007; Yager and Kacprzyk, 1997; Yager, et al., 2011). The main point that separates good and bad classifiers is classification accuracy, because incorrect classification may lead to many unwanted consequences such as the administration of inappropriate drugs, false positive or negative diagnoses, unnecessary actions of control in a management setting, and to bad decisions. One of the key questions in classification is typically the partitioning of the feature space as accurately as possible (Duda and Hart, 1973) to enable as correct as possible decisions based on the classification.Studies have shown that classification accuracy is affected by the kind of aggregation operator that is used in the classifier. In addition to the classical averaging operators there are also more advanced aggregation operators available, such as the Ordered Weighted Averaging (OWA) operator presented in (Yager, 1988) and further extensions of the OWA like the Weighted Ordered Weighted Averaging (WOWA) operator, introduced by Torra (Torra, 1996; 1997; 1998). The WOWA operator was applied to the purpose of interpolation in (Torra, 2000) and in fusing information in (Torra, 2003; Torra and Narukawa, 2007). In addition to the re-ordering step that emphasizes the relative importance of data values, the WOWA operator can also be understood to incorporate the consideration of importance of the data sources used. Two different kinds of aggregations are performed in the WOWA process and it is a combinations and a generalization of the weighted arithmetic mean and the OWA operators, see (Ogryczak and Sliwinski, 2007; Torra and Narukawa, 2007).Several different kinds of classification techniques can be found in literature, in this paper we focus on classifiers that use fuzzy set theoretical methods and that belong to the family of similarity based classifiers, for more information on similarity-based fuzzy classifiers we suggest the interested reader to see, e.g., (Luukka, 2007; Luukka and Kurama, 2013; Luukka and Leppalampi, 2006; Luukka, et al., 2001). Classification accuracy of similarity-based classifiers is also affected by the choice of the aggregation operator used, this is visible from the results presented in (Luukka and Kurama, 2013), where a similarity-based classifier using OWA-based aggregation over-performed the accuracy gained with a previously presented generalized mean-based similarity classifier, see (Luukka and Leppalampi, 2006). In this paper we continue in the same vein with the previous research on the topic of similarity-based classifiers and propose a new similarity-based classifier that uses WOWA in the aggregation of information. We present the construct of the new classifier, study the classification accuracy and compare results with previously presented methods.The rest of this paper is arranged as follows: Section two goes through the preliminaries and introduces the notation and the common definitions used.Section three describes the design of the proposed new classifier and section four is used to present the data sets used and the empirical results obtained. …