Dealing with uncertainty and imprecision by means of fuzzy numbers

Abstract The problem of the combination of imprecision and uncertainty combination from the approximate reasoning point of view is addressed. An imprecise and uncertain information can be represented as a fuzzy quantity together with a certainty value. In order to simplify the use of such information, it is necessary to combine the imprecision and uncertainty of the fuzzy number. In this paper we propose a method for combining them based on the use of information measures. The first step consists in truncating the fuzzy number by the certainty value. Since non-normalized fuzzy numbers are difficult to use, we transform the truncated fuzzy number into a normalized fuzzy number which contains the same amount of information. To formalize this process, we develop a theoretical context for the information measures on fuzzy values. We study the fuzzy numbers transformation and its properties, and give an approximate reasoning interpretation to the approach.