Measures of Location for Imprecise Data

Abstract

Abstract
Statistical analysis is usually done on data sets that contain precise information. However, data obtained may not be precise always. This may be due to vagueness in the process of measurement itself or due to the values being expressed in linguistic terms. Data that are not precise are referred to as imprecise data or fuzzy data. Developing statistical measures for imprecise data has been pursued by researchers during the past decade. However, the methodologies adopted involve operations on fuzzy numbers through α-cut approach, thereby making the process difficult. Liu (2007) developed a mathematical theory for studying the behavior of fuzzy phenomena known as “Credibility Theory”. This theory provides operations on fuzzy numbers that do not depend on the α-cut approach. In this paper, a methodology for obtaining measures of location for imprecise data is developed by using the concepts available in “Credibility Theory”. Numerical Illustration for calculating the proposed measures is also provided.

Keywords: Credibility theory, credibility distribution, fuzzy number, expectation, variance, percentiles