UsingOrdersofMagnitude andNominalVariables toConstruct FuzzyPartitions
Francesc Prats · 2007
The application of Qualitative Reasoning to Learning Algorithms canprovide thesemodelswiththeca- pability ofautomatecommon-sense and expertreasoning. Learning algorithms aimatautomatically gathering therelevant information froma setofpatterns andturnitintouseful knowledge. Thatinformation usually comesfromdifferent sources anddisplays subjectivity andambiguity, especially as farasqualitative dataisconcerned. Thispaperanalyses the unsupervised learning capability oftheLAMDA (Learning Algorithm forMultivariate DataAnalysis) algorithm. The LAMDA algorithm relies onthegeneralising capability offuzzy connectives obtained astheinterpolation ofat-normandits dualt-conormandpermits theuseofqualitative variables. Qualitative variables defined on ordersofmagnitude scales oron nominalscales areusedtoreducethesearchspace. A mathematical property ofthehybridconnectives usedis imposed toguarantee coherence intheobtained classification. Theresults obtained areapplied tosupport decision makingin amarketing problem: identifying customer behaviour. I.INTRODUCTION Whenemploying unsupervised learning methods toau- tomatically generate segmentations fromtheavailable data, alotofalternative segmentations areoften produced. This problem canbepartially reduced byusing qualitative varia- bles, bothdescribed onanordinal aswellasonanominal scale. Moreover, theuseoforders ofmagnitude variables induces reduction ofthesearch spaceandleads tomore explicative results. Theabsolute orders ofmagnitude variables involved inthe process canbedescribed indifferent levels ofprecision; this allows ahighdegree offlexibility intheinterpretation ofthe clusters obtained. Themethodology forclustering proposed inthis work consists ofthestrict useofqualitative descriptors, including those defined bynominal andordinal scales, andtheuseof fuzzy logic aggregation functions tosynthesise thisquali- tative information. Inorder totakeadvantage ofbothquali- tative reasoning andfuzzy logic techniques, theunsupervised learning capability oftheLAMDA (Learning Algorithm for Multivariate DataAnalysis) algorithm hasbeenused(6), (7). TheLAMDA algorithm canbeconsidered afuzzy qualitative