Next Article in Journal
On Characterizations of Directional Derivatives and Subdifferentials of Fuzzy Functions
Next Article in Special Issue
Sandor Type Fuzzy Inequality Based on the (s,m)-Convex Function in the Second Sense
Previous Article in Journal
Chiral Buckybowl Molecules
Previous Article in Special Issue
On Extended Representable Uninorms and Their Extended Fuzzy Implications (Coimplications)
Article Menu
Issue 9 (September) cover image

Export Article

Open AccessArticle
Symmetry 2017, 9(9), 175; https://doi.org/10.3390/sym9090175

The Orthogonality between Complex Fuzzy Sets and Its Application to Signal Detection

1
School of Mechanical and Electrical Engineering, Guizhou Normal University, Guiyang 550025, China
2
School of Electronics and Communication Engineering, Yulin Normal University, Yulin 537000, China
3
School of Information Science and Engineering, Xiamen University, Xiamen 361005, China
*
Author to whom correspondence should be addressed.
Academic Editor: Hsien-Chung Wu
Received: 25 July 2017 / Revised: 19 August 2017 / Accepted: 25 August 2017 / Published: 31 August 2017
(This article belongs to the Special Issue Fuzzy Sets Theory and Its Applications)
  |  
PDF [949 KB, uploaded 31 August 2017]
  |  

Abstract

A complex fuzzy set is a set whose membership values are vectors in the unit circle in the complex plane. This paper establishes the orthogonality relation of complex fuzzy sets. Two complex fuzzy sets are said to be orthogonal if their membership vectors are perpendicular. We present the basic properties of orthogonality of complex fuzzy sets and various results on orthogonality with respect to complex fuzzy complement, complex fuzzy union, complex fuzzy intersection, and complex fuzzy inference methods. Finally, an example application of signal detection demonstrates the utility of the orthogonality of complex fuzzy sets. View Full-Text
Keywords: orthogonality; complex fuzzy sets; complex fuzzy operations; complex fuzzy inference orthogonality; complex fuzzy sets; complex fuzzy operations; complex fuzzy inference
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
SciFeed

Share & Cite This Article

MDPI and ACS Style

Hu, B.; Bi, L.; Dai, S. The Orthogonality between Complex Fuzzy Sets and Its Application to Signal Detection. Symmetry 2017, 9, 175.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Symmetry EISSN 2073-8994 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top