On Fuzzy Random Vectors with Stepwise Membership Levels and Their Application to Questionnaire Survey

Abstract

In this paper, the authors investigate a class of fuzzy random vectors, where they are considered as vague perceptions of random phenomena.First, based on the result previously proposed by the author[1, 2, 3], fuzzy random vectors are defined from the viewpoint of the multivalued logic, where for the convenience of numerical feasibility, the set representation of fuzzy sets is approximated by the stepwise membership levels. Secondly, the expectation and the variance of fuzzy random vectors obtained by the multivalued logic are reviewed, and the variance by Aréchef approach is introduced. The estimates of the expectation and two types of variances are also considered. Finally, the proposed fuzzy random vectors are tried to apply the analysis of statistical properties of the data obtained from the questionnaire concerned with bowling ball design.