Factor analysis for fuzzy data

This paper proposes a factor analysis technique for fuzzy data which are rating scores measured by adjectives. Fuzzy correlation coefficients are introduced and factor loadings are determined as fuzzy numbers. Thus, adjectives are identified as fuzzy objects in the factor space. After fuzzy distances between adjectives in the factor space are defined, a covering problem is formulated as an integer programming problem to determine a set of representative adjectives and an overlapped partition of adjectives simultaneously. This provides a useful information to study the relation between adjectives and designs