Comparison of fuzzy values on a continuous domain

Abstract

A comparison measure called the satisfaction function (SF) is extended in this paper. The SF estimates the degree to which arithmetic comparisons between two fuzzy values are satisfied. The previously proposed SF was defined on a discrete domain (SFD). So, in order to compare continuous fuzzy values by the SFD, the fuzzy values should be converted into discrete ones. In order to directly compare continuous fuzzy values, the SF is extended to a continuous domain (SFC). The SFC is defined based on the SFD and its properties are also developed. Since the SFC is extended from the SFD, its properties includes those of the SFD, and it has the same interpretation as the SFD. Thus it can be used in any applications instead of the SFD. The SFC requires less computing time than the SFD under some conditions. For comparisons between a fuzzy and a crisp value, and between two crisp values, the SFC are also extended. (C) 2001 Elsevier Science B.V. All rights reserved.