Summary: The phenomena treated in this paper are classified into the following three cases:

(I)

Phenomena whose objective variable is quantitative, where such quantitative changes of the objective variable are referred to as quantitative extemal criterion.

(II)

Phenomena whose objective variable is qualitative, where the qualitative changes of the objective variable are referred to as qualitative external criterion.

(III)

Phenomena which are specified without any objective variables.

This paper has consisted of three parts corresponding to the above classification of phenomena. The methods for analyzing phenomena with quantitative external criterion are presented in Section 3 as fuzzy time-series analysis and in Section 4 as fuzzy regression qualitative analysis. The methods for analyzing phenomena with qualitative external criterion are described in Section 5 as fuzzy discriminant qualitative analysis and in Section 7 as fuzzy discriminant analysis. In Section 6 the fuzzy discriminant qualification analysis is successively applied to the analysis of purchasing factors in consumer’s behavior. The methods for analyzing phenomena without any external criteria are treated in Sections 8 to 11. In Section 8 the heuristic method is proposed in order to find a fuzzy transitive relation. This heuristic method is applied to the hierarchical clustering problem in Section 9 and to the identifying problem of preference ordering in Section 10. In Section 11 the evaluation of alternatives with multiple attributes is analytically discussed in view of the concept of fuzzy sets.
In Section 1 the survey of the fuzzy set theory and the into-introductory description of fuzzy multivariate analysis are given. Section 2 briefly describes concepts and definitions of fuzzy sets in preparation for the main parts of this paper. At the end Section 12 summarizes the results of this paper.