Logical Comparison Measures in Classification of Data—Nonmetric Measures

  • Kalle SaastamoinenEmail author
Conference paper
Part of the Contributions to Statistics book series (CONTRIB.STAT.)


In this chapter, we will create and use generalized combined comparison measures from t-norms (T) and t-conorms (S) for comparison of data. Norms are combined by the use of generalized mean, where t-norms give minimum and t-conorms give maximum compensation. From this intuitively thinking follows that when these norms are aggregated together, these new comparison measures should be able to find the best possible classification result in between minimum and maximum. We will use classification as our test bench for the suitability of these new comparison measures created. In these classification tasks, we have tested five different types of combined comparison measures (CCM), with t-norms and t-conorms. That were Dombi family, Frank family, Schweizer-Sklar family, Yager family, and Yu family. In classification, we used the following datasets: ionosphere, iris, and wine. We will compare the results achieved with CCM to the ones achieved with pseudo equivalences and show that these new measures tend to give better results.


Ionos Iris Wine Similarity Comparison measure Logical Classification Data 


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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of Military TechnologyNational Defence UniversityHelsinkiFinland

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