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

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.

[1]  L X Wang,et al.  Fuzzy basis functions, universal approximation, and orthogonal least-squares learning , 1992, IEEE Trans. Neural Networks.

[2]  Annett Baier.  Programming Language Pragmatics , 2016 .

[3]  Abraham Kandel,et al.  On complex fuzzy sets , 2001, 10th IEEE International Conference on Fuzzy Systems. (Cat. No.01CH37297).

[4]  Chong-Won Lee,et al.  Fuzzy Control Algorithm for Multi-Objective Problems by Using Orthogonal Array and its Application to an AMB System , 2002, Intell. Autom. Soft Comput..

[5]  Chunshien Li,et al.  Function Approximation with Complex Neuro-Fuzzy System Using Complex Fuzzy Sets – A New Approach , 2011, New Generation Computing.

[6]  Abraham Kandel,et al.  Complex fuzzy logic , 2003, IEEE Trans. Fuzzy Syst..

[7]  Abd Ulazeez M. Alkouri,et al.  Linguistic variable, hedges and several distances on complex fuzzy sets , 2014, J. Intell. Fuzzy Syst..

[8]  Chunshien Li,et al.  Complex Neurofuzzy ARIMA Forecasting—A New Approach Using Complex Fuzzy Sets , 2013, IEEE Transactions on Fuzzy Systems.

[9]  Chunshien Li,et al.  Complex Fuzzy Computing to Time Series Prediction A Multi-Swarm PSO Learning Approach , 2011, ACIIDS.

[10]  Reza Langari,et al.  Building Sugeno-type models using fuzzy discretization and orthogonal parameter estimation techniques , 1995, IEEE Trans. Fuzzy Syst..

[11]  Chunshien Li,et al.  Complex Neuro-Fuzzy Self-learning Approach to Function Approximation , 2010, ACIIDS.

[12]  Scott Dick,et al.  Toward complex fuzzy logic , 2005, IEEE Transactions on Fuzzy Systems.

[13]  A. Kandel,et al.  Discrete complex fuzzy logic , 2012, 2012 Annual Meeting of the North American Fuzzy Information Processing Society (NAFIPS).

[14]  Chunshien Li,et al.  Complex-Fuzzy Adaptive Image Restoration - An Artificial-Bee-Colony-Based Learning Approach , 2011, ACIIDS.

[15]  Scott Dick,et al.  ANCFIS: A Neurofuzzy Architecture Employing Complex Fuzzy Sets , 2011, IEEE Transactions on Fuzzy Systems.

[16]  Chunshien Li,et al.  Self-learning complex neuro-fuzzy system with complex fuzzy sets and its application to adaptive image noise canceling , 2012, Neurocomputing.

[17]  Jie Lu,et al.  A Method for Multiple Periodic Factor Prediction Problems Using Complex Fuzzy Sets , 2012, IEEE Transactions on Fuzzy Systems.

[18]  J. Yen,et al.  Simplification of fuzzy rule based systems using orthogonal transformation , 1997, Proceedings of 6th International Fuzzy Systems Conference.

[19]  Kai-Yuan Cai,et al.  Operation Properties and δ-Equalities of Complex Fuzzy Sets , 2011 .

[20]  Omolbanin Yazdanbakhsh,et al.  On Pythagorean and Complex Fuzzy Set Operations , 2016, IEEE Transactions on Fuzzy Systems.

[21]  Chunshien Li,et al.  Intelligent financial time series forecasting: A complex neuro-fuzzy approach with multi-swarm intelligence , 2012, Int. J. Appl. Math. Comput. Sci..

[22]  Abraham Kandel,et al.  A new interpretation of complex membership grade , 2011, Int. J. Intell. Syst..

[23]  Chunshien Li,et al.  Complex fuzzy model with PSO-RLSE hybrid learning approach to function approximation , 2011, Int. J. Intell. Inf. Database Syst..

[24]  Omolbanin Yazdanbakhsh,et al.  Predicting solar power output using complex fuzzy logic , 2013, 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS).

[25]  Abraham Kandel,et al.  Axiomatic Theory of Complex Fuzzy Logic and Complex Fuzzy Classes , 2011, Int. J. Comput. Commun. Control.

[26]  Chunshien Li,et al.  A novel self-organizing complex neuro-fuzzy approach to the problem of time series forecasting , 2013, Neurocomputing.

[27]  Paris A. Mastorocostas,et al.  An orthogonal least-squares method for recurrent fuzzy-neural modeling , 2003, Fuzzy Sets Syst..

[28]  Tharam S. Dillon,et al.  Delta-equalities of Complex Fuzzy Relations , 2010, 2010 24th IEEE International Conference on Advanced Information Networking and Applications.

[29]  Abraham Kandel,et al.  The Theory and Applications of Generalized Complex Fuzzy Propositional Logic , 2013, Soft Computing: State of the Art Theory and Novel Applications.

[30]  Musa Alci,et al.  Fuzzy rule-base driven orthogonal approximation , 2008, Neural Computing and Applications.

[31]  Chong Won Lee,et al.  Self-Organizing Fuzzy Controller for Multi-Objective Problem by Using Orthogonal Array and its Applications , 2002 .