On the Analysis of Fuzzy Life Times and Quality of Life Data

Reinhard Viertl

Vienna University of Technology, 1040 Wien, Austria [email protected]

Summary. Life times, health data, and general quality of life data are often not adequately represented by precise numbers or classes. Such data are called non-precise or fuzzy, because their quantitative characterization is possible by so-called non-precise numbers. To analyze such data a more general concept than fuzzy numbers from the theory of fuzzy sets is necessary. A suitable concept are so-called non-precise numbers. Generalized methods to analyze such data are available, and basic methods for that are described in the paper.

1 Introduction

Life times of systems are frequently not adequately characterized by precise time values. Therefore precise numbers are not always suitable to describe life times. Generally all results of measurements of continuous quantities are not precise numbers. For details compare [Vie02]. Even more uncertainty is connected with recovering times from illness.

Quality of life is a complex task and several approaches to measure it are possible. There are different methodological difficulties, for example the necessity of aggregating variables. But at the beginning of the analysis process, data quality considerations are indispensable in order to avoid unrealistic results of analyses.

There are different kinds of uncertainty in life time data: Variability, errors, and imprecision. It is important to note that imprecision is the kind of uncertainty inherent in single measurement results. Imprecision should not be confused with errors. Errors can be modeled with probability distributions, but imprecision cannot be modeled adequately in this way, because imprecision is another kind of uncertainty.

The best up-to-date description of imprecision is - in case of one-dimensional quantities - by so-called non-precise numbers which are special fuzzy subsets of the set R of real numbers. Therefore such data are also called fuzzy data.

In the paper generalized methods for the description and analysis of fuzzy data are explained.

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