Alcohol drinkers in Japan
This paper proposes a new technique for measuring consumer's attitudes which might have fuzzy characteristics. In most of the traditional market segmentation, multidimensional configurations are initially divided into several discrete clusters and then those clusters are predicted using socio-demographic and life-style variables. More specifically, scores obtained by factor analysis or correspondence analysis are usually analyzed by cluster analysis, and then analyzed by multiple discriminant analysis. However, the traditional approach might be inappropriate since the market structure consists of fuzzy sets which was proposed by Zadeh (1965). Therefore, the authors applied fuzzy discriminant analysis (FDA) to the survey data on alcohol drinking attitudes. In FDA, the likelihood of subjects belonging to each cluster is expressed by a membership function, which can describe the relationship between the respondents and the fuzzy groups uncrisply. Secondary, the fuzzy multivariate analysis can be used as a weighting adjuster for parameters to be estimated when the sample distribution is biased from population distribution. The elements of the criterion data matrix are dummy variables in the case of discriminant analysis, weight-back coefficients in the case of weight- back, and membership values in the case of FDA. Although these three analytical methods are mathematically equivalent, FDA is the most generalized model and the other two methods are its special cases. The authors illustrate that discriminant coefficients can be estimated accurately by weight-back, and some research implications of weighting coefficients are also discussed. Rationale and mathematical derivation of membership function and weighting on respondents are described in the appendixes.
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