Fuzzy Convolution Research Articles

Meticulous fuzzy convolution C means for optimized big data analytics: adaptation towards deep learning

In this new era, any business, industrial production, etc. are in need of information in analytics to start and continue its new move towards increasing their outcomes, efficiency, and performance. In this way, many analytics and analytics software’s are making promising results and trying to make more efficient solutions for the betterment of tomorrow. Many basic algorithms like K-means family, FCM family, etc. are used for the process. Nevertheless, processing the insignificant data, which is no way useful and may sometimes distracts the significant features that are most needed, a Deep Learning approach is used before Big-Data analytics. On the other hand, the features of the significant data should have more in-depth understanding to explore more possibilities that could help the better tomorrow. Here we propose a Meticulous Fuzzy Convolution C-Means (MFCCM) algorithm by mutating the nature of Convolutional Neural Network (CNN) to adopt the nature of significant feature understanding of deep learning method. The main novel idea behind this algorithm is to process the data through the optimized Big-Data algorithm through the process of effective feature selection. Here the process involves the enhancement of Deep Learning algorithm (CNN) with the FCM to select the significant features. This algorithm shows promising results as it gives better segmentation even in the presence of variance noisy data.

Многофакторная оценка конкурентоспособности университетов с применением нечеткого метода максиминной свертки

Многофакторная оценка конкурентоспособности университетов с применением нечеткого метода максиминной свертки

Fuzzy model predictive control of non-linear processes using convolution models and foraging algorithms

In this paper, a fuzzy model predictive control (FMPC) approach is introduced to design a control system for nonlinear processes. The proposed control strategy has been successfully employed for representative, benchmark chemical processes. Each nonlinear process system is described by fuzzy convolution models, which comprise a number of quasi-linear fuzzy implications (FIs). Each FI is employed to describe a fuzzy-set based relation between control input and model output. A quadratic optimization problem is then formulated, which minimizes the difference between the model predictions and the desired trajectory over a predefined predictive horizon and the requirement of control energy over a shorter control horizon. The present work proposes to solve this optimization problem by employing a contemporary population-based evolutionary optimization strategy, called the Bacterial Foraging Optimization (BFO) algorithm. The solution of this optimization problem is utilized to determine optimal controller parameters. The utility of the proposed controller is demonstrated by applying it to two non-linear chemical processes, where this controller could achieve better performances than those achieved by similar competing controller, under various operating conditions and design considerations. Further comparisons between various stochastic optimization algorithms have been reported and the efficacy of the proposed approach over similar optimization based algorithms has been concluded employing suitable performance indices.

A fuzzy convolution model for radiobiologically optimized radiotherapy margins

In this study we investigate the use of a new knowledge-based fuzzy logic technique to derive radiotherapy margins based on radiotherapy uncertainties and their radiobiological effects. The main radiotherapy uncertainties considered and used to build the model were delineation, set-up and organ motion-induced errors. The radiobiological effects of these combined errors, in terms of prostate tumour control probability and rectal normal tissue complication probability, were used to formulate the rule base and membership functions for a Sugeno type fuzzy system linking the error effect to the treatment margin. The defuzzified output was optimized by convolving it with a Gaussian convolution kernel to give a uniformly varying transfer function which was used to calculate the required treatment margins. The margin derived using the fuzzy technique showed good agreement compared to current prostate margins based on the commonly used margin formulation proposed by van Herk et al (2000 Int. J. Radiat. Oncol. Biol. Phys. 47 1121–35), and has nonlinear variation above combined errors of 5 mm standard deviation. The derived margin is on average 0.5 mm bigger than currently used margins in the region of small treatment uncertainties where margin reduction would be applicable. The new margin was applied in an intensity modulated radiotherapy prostate treatment planning example where margin reduction and a dose escalation regime were implemented, and by inducing equivalent treatment uncertainties, the resulting target and organs at risk doses were found to compare well to results obtained using currently recommended margins.

Fuzzy approximation by fuzzy convolution type operators

Here we introduce and study four sequences of naturally arising fuzzy integral operatorsof convolution type that are integral analogs of known fuzzy wavelet type operators, defined via a scaling function. Their fuzzy convergence with rates to the fuzzy unit operator is established through fuzzy inequalities involving the fuzzy modulus of continuity. Also, their high-order fuzzy approximation is given similarly by involving the fuzzy modulus of continuity of the N th order ( N ≥ 1) H-fuzzy derivative of the engaged fuzzy number valued function. The fuzzy global smoothness preservation property of these operators is demonstrated also.

Hybrid Fuzzy Convolution Model and its Application in Predictive Control

In this paper a new method for synthesizing nonlinear, control-oriented process models is presented. The proposed hybrid fuzzy convolution model (HFCM) consists of a steady-state fuzzy model and a gain-independent impulse response model. The proposed HFCM is applied in model based predictive control of a laboratory-scale electrical water-heater. Simulation and real-time studies confirm that the method is capable of controlling this delayed and distributed parameter system with a strong nonlinear feature.

Hybrid fuzzy convolution modelling and identification of chemical process systems

This paper looks at a new method of modelling nonlinear dynamic processes, using grid-type Takagi-Sugeno fuzzy models and a priori knowledge. The proposed hybrid fuzzy convolution dynamic model consists of a non-linear fuzzy steady-state static and a gainindependent impulse response model-based dynamic part. The modelling of nonlinear pH processes is chosen as a realistic case study for demonstration of the proposed modelling approach. The off-line identified hybrid fuzzy convolution model is shown to be capable of modelling the nonlinear process and providing better multiple-step prediction than the conventional grid-type Takagi-Sugeno fuzzy model.

Fuzzy model predictive control

A fuzzy model predictive control (FMPC) approach is introduced to design a control system for a highly nonlinear process. In this approach, a process system is described by a fuzzy convolution model that consists of a number of quasi-linear fuzzy implications. In controller design, prediction errors and control energy are minimized through a two-layered iterative optimization process. At the lower layer, optimal local control policies are identified to minimize prediction errors in each subsystem. A near optimum is then identified through coordinating the subsystems to reach an overall minimum prediction error at the upper layer. The two-layered computing scheme avoids extensive online nonlinear optimization and permits the design of a controller based on linear control theory. The efficacy of the FMPC approach is demonstrated through three examples.

Fuzzy and rule-based image convolution

An image can be sharpened by high pass filtering of its discrete Fourier transform or by an equivalent convolution processing in the spatial domain. Edge detection is a form of drastic sharpening with conversion to black and white. The approach taken here to sharpening and edge detection, as well as smoothing and other processing is to use a ‘smart’ convolution mask that makes rule-based decisions. Upon employing gains in the rule consequents, we achieve a type of fuzzy convolution of the output pixels. We also enlarge images using our new type of fuzzy interpolation to obtain higher resolution, detect edges with the rules and then reduce to the original size to obtain better edges than by merely applying the edge detection rules to the original image. We provide examples of sharpening directly with our rules. We also provide examples of edge detection both with and without the enlargement–reduction process.

FUZZY NUMBER SUBTRACTION CONVOLUTION ON THE CM-2

The running time of data-parallel algorithms can be reduced by avoiding global reduction operations. Using fuzzy number subtraction convolution as an example, this paper illustrates how data-parallel programs can be restructured to eliminate global reduction operations. This is done by using techniques from systolic array design. The algorithms are programmed in CM Fortran and have been run on a Connection Machine CM-2. The running time results show that advantages can be achieved in a considerable domain of the problem size space. At the same time the results show that for obtaining shortest running times different algorithms have to be used in different domains.