Correlation coefficient of linguistic variables and its applications to quantifying relations in imprecise management data

We frequently use the standard correlation coefficient to quantify linear relation between two given variables of interest in crisp industrial data. On the other hand, in many real world applications involving the opinions of experts, the domain of a variable of interest, e.g. the rating of the innovativeness of a new product idea, is oftentimes composed of subjective linguistic concepts such as very poor, poor, average, good and excellent. In this article, we extend the standard correlation coefficient to the subjective, linguistic setting, so as to quantify relations in imprecise industrial and management data. Unlike the correlation measures for fuzzy variables proposed in the literature, the present approach allows one to develop a correlation coefficient for linguistic variables that can account for and reflect the conditional dependence assumptions underlying a given data set. We apply the proposed method to quantify the degree of correlation between technology and management achievements of 15 large-scale machinery firms in Taiwan. It is shown that the flexibility of the present framework in allowing for the incorporation of appropriate conditional dependence assumptions to derive a correlation measure for linguistic variables can be essential in approximate reasoning applications.