Dealing with uncertainty and imprecision by means of fuzzy numbers

✍ Scribed by A. Gonzalez; O. Pons; M.A. Vila

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 440 KB
• Volume: 21
• Category: Article
• ISSN: 0888-613X
• DOI: 10.1016/s0888-613x(99)00024-9

✦ Synopsis

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 ®rst step consists in truncating the fuzzy number by the certainty value. Since non-normalized fuzzy numbers are dicult 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.