Discrete complex fuzzy logic

Tamir, Dan E.; Teodorescu, Horia-Nicolai; Kandel, Abraham

doi:10.1109/nafips.2012.6291020

Cited by 14 publications

(12 citation statements)

References 24 publications

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“…Our definition of complex propositional logic presented in Sect. 3 [10,36], closely follows ŁΠ, the system used by Běhounek et al For clarity, we reintroduce some of the important notions, notations, and concepts from that paper.…”

Section: Propositional Fuzzy Logicmentioning

confidence: 99%

“…Another important extension to the theory of fuzzy logic and fuzzy sets, namely complex fuzzy logic (CFL) and complex fuzzy sets (CFS), has been developed by Kandel and his coauthors [10,[33][34][35][36]. Moses et al introduced an aggregation of two fuzzy sets into one complex fuzzy set [33].…”

Section: Introductionmentioning

confidence: 99%

“…In this context A, provides a restriction on a real-valued variable X and B is a restriction on the degree of certainty that X is A [32]. Nevertheless, this concept is used to qualify the reliability of fuzzy quantities rather than to define complex fuzzy sets [10,36].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Complex Fuzzy Sets and Complex Fuzzy Logic an Overview of Theory and Applications

Tamir,

Rishe,

Kandel

2015

Fifty Years of Fuzzy Logic and Its Applications

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Fuzzy Logic, introduced by Zadeh along with his introduction of fuzzy sets, is a continuous multi-valued logic system. Hence, it is a generalization of the classical logic and the classical discrete multi-valued logic (e.g. Łukasiewicz' three/many-valued logic). Throughout the years Zadeh and other researches have introduced extensions to the theory of fuzzy setts and fuzzy logic. Notable extensions include linguistic variables, type-2 fuzzy sets, complex fuzzy numbers, and Z-numbers. Another important extension to the theory, namely the concepts of complex fuzzy logic and complex fuzzy sets, has been investigated by Kandel et al. This extension provides the basis for control and inference systems relating to complex phenomena that cannot be readily formalized via type-1 or type-2 fuzzy sets. Hence, in recent years, several researchers have used the new formalism, often in the context of hybrid neuro-fuzzy systems, to develop advanced complex fuzzy logic-based inference applications. In this chapter we reintroduce the concept of complex fuzzy sets and complex fuzzy logic and survey the current state of complex fuzzy logic, complex fuzzy sets theory, and related applications.

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Section: Propositional Fuzzy Logicmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Complex Fuzzy Sets and Complex Fuzzy Logic an Overview of Theory and Applications

Tamir,

Rishe,

Kandel

2015

Fifty Years of Fuzzy Logic and Its Applications

Self Cite

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“…The proposed CFL was extended to generalized propositional CFL, applicable in multidimensional fuzzy propositional and predicate logic, through definitions in [10] based on fuzzy Łukasiewicz logical system [11]. Tamir et al [12] proposed an extended complex post-logical system (ECPS) based on the extended Post system (EPS) of order p > 2 by DiZenzo [13]. One of the possible applications of the proposed system is in discrete processes such as digital signal processing (DSP), real-time applications, and embedded systems.…”

Section: Complex Fuzzy Sets and Logicmentioning

confidence: 99%

Time-Series Forecasting via Complex Fuzzy Logic

Yazdanbakhsh

Dick

2014

Frontiers of Higher Order Fuzzy Sets

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Adaptive neuro-complex-fuzzy inference system (ANCFIS) is a neurofuzzy system that employs complex fuzzy sets for time-series forecasting. One of the particular advantages of this architecture is that each input to the network is a windowed segment of the time series, rather than a single lag as in most other neural networks. This allows ANCFIS to predict even chaotic time series very accurately, using a small number of rules. Some recent findings, however, indicate that published results on ANCFIS are suboptimal; they could be improved by changing how the length of an input window is determined, and/or subsampling the input window.We compare the performance of ANCFIS using three different approaches to defining an input window, across six time-series datasets. These include chaotic datasets and time series up to 20,000 observations in length. We found that the optimal choice of input formats was dataset dependent, and may be influenced by the size of the dataset. We finally develop a recommended approach to determining input windows that balances the twin concerns of accuracy and computation time. IntroductionTime-series forecasting has emerged as the first major application of complex fuzzy sets and logic, which were first described by Ramot in [1]. Beginning in 2007, complex-valued neuro-fuzzy systems were developed to inductively learn forecasting models; these include the adaptive neuro-complex-fuzzy inference system (ANCFIS) architecture [2], and the family of complex neuro-fuzzy system (CNFS) architectures [3]. Both ANCFIS and CNFS are modifications of the well-known ANFIS architecture, in which complex fuzzy sets and complex-valued network signals are used. These architectures showed that complex fuzzy sets were naturally useful in creating very accurate forecasting models. ANCFIS in particular is also very parsimonious;

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“…Thus a complex fuzzy set is a set of vectors in the complex plane. This idea of membership vectors greatly inspired how definition of complex fuzzy sets operations [14,15] and complex fuzzy logic systems [16][17][18][19][20][21] and how to measures the difference between two complex fuzzy sets [22][23][24].…”

Section: Introductionmentioning

confidence: 99%

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

Dai

2017

Symmetry

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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.

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Discrete complex fuzzy logic

Cited by 14 publications

References 24 publications

Complex Fuzzy Sets and Complex Fuzzy Logic an Overview of Theory and Applications

Complex Fuzzy Sets and Complex Fuzzy Logic an Overview of Theory and Applications

Time-Series Forecasting via Complex Fuzzy Logic

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

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