A Multiobjective Genetic Fuzzy Systemwith ImpreciseProbability Fitness forVague Data
CousoiswithStatistics De · 2006
Whenquestionnaires aredesigned, eachfactor un- derstudy canbeassigned asetofdifferent items. Theanswers tothesequestions mustbemergedinordertoobtain thelevel ofthatinput. Therefore, itistypical fordataacquired from questionnaires thateachoftheinputs andoutputs arenot numbers, butsetsofvalues. Inthis paper, werepresent theinformation contained insucha setofvalues bymeansofafuzzy number. A fuzzy statistics-based interpretation ofthesemantic ofafuzzy setwill beusedforthis purpose, aswewill consider thatthis fuzzy numberisanested family ofconfidence intervals forthevalueofthevariable. The accuracy ofthemodelwill beexpressed bymeansofaninterval- valued function, derived fromarecent definition ofthevariance ofafuzzy randomvariable. A multicriteria genetic learning algorithm, abletooptimize this interval-valued function, isproposed. Asanexample ofthe application ofthis algorithm, apractical problem ofmodeling in marketing issolved.