Factor Space Model for Fuzzy Data

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  • ファジィデータの因子空間モデル
  • ファジィ データ ノ インシ クウカン モデル

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Abstract

A set of qualitative data obtained by rating a product usually has a large variance reflecting tastes and preferences of individuals. It is sensible to express such fluctuations by fuzzy numbers to treat vagueness and unvertainty of the feeling of individuals. This paper proposes a factor analysis technique for fuzzy data which are rating scores measured by words that are mainly adjective such as innovative, bright, elegant or cheerful. Fuzzy correlation coefficients are introduced and factor loadings are determined as fuzzy numbers through linear programming. Thus, words are identified as fuzzy objects in the factor space. After fuzzy distances between words in the factor space are defined, a covering problem is formulated as an integer programming problem to determine a set of representative words and an overlapped partition of words simultaneously. This provides a useful information to study the relation between words and design elements.

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