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| Content Provider | IEEE Xplore Digital Library |
|---|---|
| Author | Ramot, D. Milo, R. Friedman, M. Kandel, A. |
| Copyright Year | 1993 |
| Abstract | The objective of this paper is to investigate the innovative concept of complex fuzzy sets. The novelty of the complex fuzzy set lies in the range of values its membership function may attain. In contrast to a traditional fuzzy membership function, this range is not limited to [0, 1], but extended to the unit circle in the complex plane. Thus, the complex fuzzy set provides a mathematical framework for describing membership in a set in terms of a complex number. The inherent difficulty in acquiring intuition for the concept of complex-valued membership presents a significant obstacle to the realization of its full potential. Consequently, a major part of this work is dedicated to a discussion of the intuitive interpretation of complex-valued grades of membership. Examples of possible applications, which demonstrate the new concept, include a complex fuzzy representation of solar activity (via measurements of the sunspot number), and a signal processing application. A comprehensive study of the mathematical properties of the complex fuzzy set is presented. Basic set theoretic operations on complex fuzzy sets, such as complex fuzzy complement, union, and intersection, are discussed at length. Two novel operations, namely set rotation and set reflection, are introduced. Complex fuzzy relations are also considered. Index Terms-Complex fuzzy intersection, complex fuzzy relations, complex fuzzy sets, complex fuzzy union, complex-valued grades of membership, fuzzy complex numbers. |
| Sponsorship | IEEE Computational Intelligence Society |
| Starting Page | 171 |
| Ending Page | 186 |
| Page Count | 16 |
| File Size | 769312 |
| File Format | |
| ISSN | 10636706 |
| Volume Number | 10 |
| Issue Number | 2 |
| Language | English |
| Publisher | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Publisher Date | 2002-04-01 |
| Publisher Place | U.S.A. |
| Access Restriction | One Nation One Subscription (ONOS) |
| Rights Holder | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Subject Keyword | Fuzzy sets Uncertainty Fuzzy set theory Fuzzy logic Humans Signal processing Reflection Instruments System testing Physics |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Artificial Intelligence Control and Systems Engineering Computational Theory and Mathematics |
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