Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/21586
Title: Ordinal fuzzy sets
Authors: Lee, JWT
Yeung, DS
Tsang, ECC
Keywords: Ordinal fuzzy set
Ordinal intersection
Ordinal union
Issue Date: 2002
Publisher: Institute of Electrical and Electronics Engineers
Source: IEEE transactions on fuzzy systems, 2002, v. 10, no. 6, p. 767-778 How to cite?
Journal: IEEE transactions on fuzzy systems 
Abstract: Fuzzy set theory has been used as a framework for interpreting imprecise linguistic expressions. In general, a linguistic term is described by the compatibility ordering induced in some universe of discourse (UoD). A membership function in fuzzy set theory serves to reflect this ordering by assignment of values in [0, 1] for objects in UoD. When we compute the meaning of a linguistic expression such as "young and tall" using fuzzy membership functions, two implicit assumptions are made. First, we assume the membership values have quantitative meaning so that they can be quantitatively manipulated, for example, by adding or subtracting (the extensive scale assumption). Second, we assume that the scales of the membership values used in describing the different linguistic terms are comparable and the same (the common scale assumption). In many cases, these assumptions cannot be justified. Some proposals have been made to address the first issue by using ordinal scale in defining fuzzy membership functions. However, the second issue has not been properly investigated. In this paper, we propose a framework that does not depend on both of these assumptions. Such framework will facilitate our understanding and investigation of qualitative reasoning without the extensive scale and common scale assumptions.
URI: http://hdl.handle.net/10397/21586
ISSN: 1063-6706
EISSN: 1941-0034
DOI: 10.1109/TFUZZ.2002.805888
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