ANCFIS: A Neurofuzzy Architecture Employing Complex Fuzzy Sets

Zhifei, Chen; Aghakhani, Sara; Man, Jianghong; Dick, Scott

doi:10.1109/tfuzz.2010.2096469

Cited by 127 publications

(71 citation statements)

References 56 publications

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“…Complex-valued fuzzy sets have been indeed successfully used in practical applications; see, e.g., [1,4,6,13,24] -and our analysis explains why. Let us show, on several examples, that they indeed help to reconstruct the membership values d i .…”

Section: How Good Are Complex-valued Degrees In Practice?mentioning

confidence: 70%

50 Years of fuzzy: from discrete to continuous to – Where?

Kreinovich

Nguyen

Kosheleva

et al. 2015

IFS

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Abstract. While many objects and processes in the real world are discrete, from the computational viewpoint, discrete objects and processes are much more difficult to handle than continuous ones. As a result, a continuous approximation is often a useful way to describe discrete objects and processes. We show that the need for such an approximation explains many features of fuzzy techniques, and we speculate on to which promising future directions of fuzzy research this need can lead us.Keywords: fuzzy techniques, discrete, continuous, interval-valued fuzzy, complex-valued fuzzy, computing with words, dynamical fuzzy logic, chemical kinetics, non-additive measures, symmetry Fuzzy Techniques as an Easier-to-Compute Continuous Approximation for Difficult-to-Compute Discrete Objects and ProcessesDiscrete objects and processes are ubiquitous. Many real-life objects are processes are discrete. On the macro level, there is an abrupt transition in space between physical bodies, there is an abrupt transition in time when, e.g., a glass breaks or a person changes his/her opinion. On the micro level, matter consists of discrete atoms and molecules, with abrupt transitions between different states of an atom.Continuous problems are easier to compute. While discrete objects and processes are ubiquitous in nature, from the computational viewpoint, it is often much easier to handle continuous problems. This may sound * Corresponding author. E-mail: vladik@utep.edu.counter-intuitive, since intuitively, if we restrict our search or optimization to only integer values, the problem would become easier -but it is not. For example, in the continuous case, it is relatively easy to find a solution x 1 , . . . , x n to a system of linearmany known feasible algorithms for that), the problem becomes NP-hard (computationally intractable) if we only allow discrete values of x i ; see, e.g., [9,28].Similarly, in the continuous case, it is relatively easy to find the values x 1 , . . . , x n that minimize a given quadratic function f (x 1 , . . . , x n ): it is sufficient to solve the corresponding system of linear equations ∂f ∂x i = 0. However, optimization of quadratic functions for discrete inputs, e.g., for x i ∈ {0, 1}, is NPhard [9,28]. Continuous approximations of discrete objects and processes are ubiquitous in physics. Because dealing with discrete objects and processes is often computationally complicated, physicists often approximate discrete objects with continuous ones. For example, it is not feasible to describe the changes in atmosphere by tracing all 10 23 molecules, but approximate equations that describe the atmosphere as a continuous field leads to many useful weather predictions. Similar, a solid body -in effect, a collection of atoms -is well described by a continuous density field, and an atomic nucleus -a collection of protons and neutrons -is well described by a continuous (liquid) model; see, e.g., [8].Such approximations are also useful in analyzing social phenomena. For example, in analyzing how epidemics spread, ...

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Section: How Good Are Complex-valued Degrees In Practice?mentioning

confidence: 70%

50 Years of fuzzy: from discrete to continuous to – Where?

Kreinovich

Nguyen

Kosheleva

et al. 2015

IFS

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“…Data modelling is the foundation of forecasting demands of regional infrastructure services. Data mining, statistics, and machine learning techniques and methods have been widely used in building forecast models [4][5][6] . Existing modelling techniques and methods may not suit infrastructure practices.…”

Section: Data-driven Forecasting Challengesmentioning

confidence: 99%

Data-Driven Forecasts of Regional Demand for Infrastructure Services

Wickramasuriya²,

Perez³

et al. 2014

Proceedings of the International Symposium for Next Generation Infrastructure

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Abstract:The socio-economic development and liveability of a region are affected to a great extent by the region's infrastructure services. Data-driven forecasting the demands for infrastructure utilities (for example, electricity, water, and waste) of a region becomes a challenging issue in the situation of highly integrative infrastructure networks and restricted data sharing, which involves handling temporary and spatial infrastructure utility data simultaneously and modelling the correlations between different infrastructure utilities and their interactions with relevant socio-economic and environmental indicators. Data mining and complex fuzzy set techniques are used to implement this kind of analytical capability in SMART Infrastructure Dashboard (SID). The developed forecasting method and technique can be used by local governmental agencies, infrastructure service designers and providers, and local communities for better governance, planning and delivering of effective and efficient infrastructure service and facility. It can also provide support evidence for a region's long-term sustainable planning and development.

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“…In recent years, complex fuzzy sets have been successfully used in complex fuzzy inference systems for various applications, such as time series prediction [2][3][4][5][6][7][8], function approximation [9][10][11], and image restoration [12,13]. A complex fuzzy set A on a universe of discourse U is a mapping from U to the unit disc in the complex plane.…”

Section: Introductionmentioning

confidence: 99%

“…When we apply these orthogonal methods to complex fuzzy systems, the concept of orthogonality should be considered. (2) Recently, complex fuzzy sets have been used in image restoration [12,13] and signal processing [1,23]. In these applications, various orthogonal data, such as orthogonal signals and orthogonal images, are often considered.…”

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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ANCFIS: A Neurofuzzy Architecture Employing Complex Fuzzy Sets

Cited by 127 publications

References 56 publications

50 Years of fuzzy: from discrete to continuous to – Where?

50 Years of fuzzy: from discrete to continuous to – Where?

Data-Driven Forecasts of Regional Demand for Infrastructure Services

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

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