A Similarity Classifier with Bonferroni Mean Operators

Abstract

A similarity classifier based on Bonferroni mean based operators is introduced. The new Bonferroni mean based variant of the similarity classifier is also extended to cover a new Bonferroni-OWA variant. The new Bonferroni-OWA based similarity classifier raises the question of how to accomplish the weighting needed and for this reason we also examine a number of linguistic quantifiers for weight generation. The new proposed similarity classifier variants are tested on four real world medical research related data sets. The results are compared with results from two previously presented similarity classifiers, one based on the generalized mean and another based on an arithmetic mean operator. The results show that comparatively better classification accuracy can be reached with the proposed new similarity classifier variants. Advances in Fuzzy SystemsMedical diagnosis of common diseases like breast cancer, lung cancer, hepatitis, thyroid, and many others requires high accuracy. However, in real world (medical) problems, it is most often not possible to achieve a 100% classification accuracy due to the complexity of the analyzed conditions and the complications caused by the available data [20]. The complications connected to the data can be the result of several different causes, for example, small (limited) amount of data samples that make accurate generalizations impossible, very large number of attributes and/or variables that creates complexity, and the difficulty in determining the relevance of the considered attribute. Often even small improvements in classification accuracy connected to medical diagnoses can be valuable, since even small improvements can help save human lives. Similarity based classifiers (see [21]) have been shown to have the ability to work well on medical diagnosis problems (see, e.g., [11,22]) and have advantages such as fast speed and high classification accuracy and have already been shown to work rather well with small sets of samples (see, e.g., [20]). For more information about fuzzy classification and clustering methods, see [23][24][25][26][27][28][29].The rest of the paper is organized as follows: in the second section we briefly go through the aggregation operators, the weight generation schemes for the new OWA based classifier variants, and the similarity measures applied in the paper, in the third section we introduce the new similarity classifiers and the new variants, and in the fourth section we first shortly introduce the used medical research data sets and then examine the achieved results. The paper is closed with discussion and conclusions.

A New Joint Strategy for Multi-Criteria Decision-Making: A Case Study for Prioritizing Solid-State Drive

“…Step 4 of the MARCOS method is achieved by employing objective weights, and three modes are utilized to compute weights, including the Entropy weights method [22], CRITIC [6] and MEREC method [20]. Finally, the three objective weights were combined using the Bonferroni operator [23], [46]. The essential steps of the MEREC method and computation concepts are discussed below:…”

“…Objective weights were computed employing the Entropy weights method [22], CRITIC [6] and MEREC method [20]. Finally, the three objective weights were combined using the Bonferroni operator [23], [46], as shown in Table 2.…”

A new fuzzy k-nearest neighbor classifier based on the Bonferroni mean

“…The Bonferroni mean is an aggregation operator that was originally introduced in [19] and further developments were discussed, e.g., in [20,21] . It can be defined as a function of means and it has been used as a very useful indicator in many applications [see 22,23 ]) due to its capability to perceive inter-relationships and to allow multiple comparisons between input arguments [24] .…”