Fuzzy Vector Research Articles

Consolidity analysis for fully fuzzy functions, matrices, probability and statistics

The paper presents a comprehensive review of the know-how for developing the systems consolidity theory for modeling, analysis, optimization and design in fully fuzzy environment. The solving of systems consolidity theory included its development for handling new functions of different dimensionalities, fuzzy analytic geometry, fuzzy vector analysis, functions of fuzzy complex variables, ordinary differentiation of fuzzy functions and partial fraction of fuzzy polynomials. On the other hand, the handling of fuzzy matrices covered determinants of fuzzy matrices, the eigenvalues of fuzzy matrices, and solving least-squares fuzzy linear equations. The approach demonstrated to be also applicable in a systematic way in handling new fuzzy probabilistic and statistical problems. This included extending the conventional probabilistic and statistical analysis for handling fuzzy random data. Application also covered the consolidity of fuzzy optimization problems. Various numerical examples solved have demonstrated that the new consolidity concept is highly effective in solving in a compact form the propagation of fuzziness in linear, nonlinear, multivariable and dynamic problems with different types of complexities. Finally, it is demonstrated that the implementation of the suggested fuzzy mathematics can be easily embedded within normal mathematics through building special fuzzy functions library inside the computational Matlab Toolbox or using other similar software languages.

The mean square error of a random fuzzy vector based on the support function and the Steiner point

Metrics between fuzzy values are a topic with interest for different purposes. Among them, statistics with fuzzy data is growing in modelling and techniques largely through the use of suitable distances between such data. This paper introduces a generalized (actually, parameterized) L2 metric between fuzzy vectors which is based on their representation in terms of their support function and Steiner points. Consequently, the metric takes into account the deviation in ‘central location’ (represented by the Steiner points) and the deviation in ‘shape’ (represented by a deviation defined in terms of the support function and Steiner points). Then, sufficient conditions can be given for this representation to characterize fuzzy vectors, which is valuable for different aims, like optimization studies. Properties of the metric are analyzed and its application to quantify the mean (square) error of a fuzzy value in estimating the value of a fuzzy vector-valued random element is examined. Some immediate implications from this mean error are finally described.

Adaptive fuzzy vector control for a doubly-fed induction motor

This paper presents a new adaptive fuzzy vector controller (AFVC) to handle the torque and speed tracking problem of a doubly-fed induction motor (DFIM) as an alternative to classical PI based vector control method generally used for its simplicity. However, the control performance of DFIM is still influenced by the variations of the parameters, the external load disturbances and perturbations in practical applications. Then, it is difficult to achieve high control performances of DFIM by using conventional PI-type control techniques. The proposed AFVC scheme uses adaptive fuzzy systems to reasonably approximate the uncertain dynamics appearing in the DFIM, relaxing thereby the usual modeling requirement about the DFIM dynamics. Of fundamental interest, it is shown that all the closed-loop signals are bounded and the tracking errors exponentially converge to a residual set. Probing simulation results are given to emphasize the effectiveness of the proposed AFVC system with respect to the usual feedback linearization based vector control (FLVC) system.

The Vector Control System of Induction Motor Based on Fuzzy Control

Classical control theory method often cannot obtain good static and dynamic performance in speed control system of asynchronous motor that is multivariable, nonlinear and strong coupling. However, with the application of modern control theory, it can effectively improve the operating performance of system in a complicated environment. This paper introduces the basic principle of vector control system and establishes the simulation model of vector control system of asynchronous motor. Meanwhile, according to fuzzy control theory, this paper shows a design of fuzzy controller and it is applied to the vector control system of speed adjusting module. Finally, it uses Matlab/Simulink to simulate and it verifies that Fuzzy vector control system response faster has better stability and stronger robust performance compared to the traditional vector control. Key words: induction motor; vector control; fuzzy control

Classification of Apple Varieties Using FT-NIR Spectroscopy and Possibilistic Learning Vector Quantization

Red Fuji, Huaniu and Gala were classified by Fourier transform near infrared (FT-NIR) spectroscopy and possibilistic learning vector quantization (PLVQ) which was proposed to solve the noise sensitivity problem of fuzzy learning vector quantization (PLVQ). Firstly, apple NIR spectra were measured by FT-NIR spectrophotometer. Secondly, principal component analysis (PCA) was used to compress the dimensionality of NIR spectra which was high dimensional. Thirdly, fuzzy c-means (FCM) clustering was run to termination to obtain the cluster vectors for PLVQ. Finally, PLVQ was performed to classify the data. Experimental results showed that this classification method was fast, nondestructive and effective for classifying the variety of apples.

Rapid Classification of Pork NIR Speca Using PCA and FLVQ

Pork storage time is relevant to its freshness which influences pork quality. To achieve the rapid and effective discrimination of pork storage time, near infrared spectroscopy was used to collect the near infrared reflectance (NIR) spectra of pork in different storage time. The high-dimensional NIR spectra was firstly compressed by principal component analysis (PCA) and then classified by fuzzy learning vector quantization (FLVQ). PCA plus FLVQ is a completely unsupervised learning algorithm which finds hidden patterns in unlabeled data. Experimental results showed that PCA plus FLVQ could classify pork NIR spectra effectively.

A Study of the Assessment on Air Quality on Fuzzy Comprehensive Index

This paper discusses the assessment problem on air quality. It will firstly make analysis on part irrationality of existing AQI and then introduces into concept of fuzzy mathematics on this basis. It makes index assessment on regional air quality according to 6 index values of selected air quality. Firstly, it will use fuzzy mathematics as basis to establish model of fuzzy comprehensive index and adopt weighting method of excess multiple considering each index to determine the weight, secondly it uses membership function of half-step trapezoidal method to determine its membership grade and makes compound operation to obtain fuzzy comprehensive assessment matrix, finally it makes fuzzy vector uniformization to get the new air quality index as well as uses national standard as reference limits to divide it into 6 grades and comprehensively makes index assessment on air quality.

VAGUE FIELDS AND VAGUE VECTOR SPACES

The notions of vague fields and vague vector spaces with member- ship and non-membership function values taking in unit interval of real numbers are introduced, which generalize the existing notions of fuzzy field , fuzzy vector spaces, and studied various properties.

Pattern Recognition Based on Fuzzy Set and Genetic Algorithm

In this paper, we consider a soft computing approach to pattern classification. Our basic tools for soft computing are fuzzy relational calculus (FRC) and genetic algorithm (GA). We introduce a new interpretation of multidimensional fuzzy implication (MFI) to represent our knowledge about the training data set. We also consider the notion of a fuzzy pattern vector to handle the fuzzy information granules of the quantized pattern space and to represent a population of training patterns in the quantized pattern space. The construction of the pattern classifier is essentially based on the estimate of a fuzzy relation Ri between the antecedent clause and consequent clause of each one-dimensional fuzzy implication. For the estimation of Ri we use floating point representation of GA. Thus a set of fuzzy relations is formed from the new interpretation of MFI. This set of fuzzy relations is termed as the core of the pattern classifier. Once the classifier is constructed the non-fuzzy features of a test pattern can be classified. The performance of the proposed scheme is tested on synthetic data. Subsequently, we use the proposed scheme for the vowel classification problem of an Indian language. Finally, a benchmark of performance is established by considering multiplayer perception (MLP), support vector machine (SVM) and the present method. The Abalone, Hosse Colic and Pima Indians data sets, obtained from UCL database repository are used for the said benchmark study. This new tool for pattern classification is very effective for classification of patterns under vegue and imprecise environment. It can provide multiple classification under overlapped classes.

Research on Mine Gas Accident Multi-Factor Fuzzy Comprehensive Safety Evaluation

Gas accident is one of the most common accidents in coal mine in china. This paper argues that the gas dangerousness is determined by many factors which are difficult to quantitative risk, and deems these factors are quantified and fuzzy comprehensive evaluation, comprehensive evaluation, which are benefit evaluation and master the coal mine’s gas safety level, and determine the safety investment direction and improve the benefit of safety investment that will reduce the coal mine gas occurrence probability, so as to reduce and avoid the happening of coal mine gas accident. The basic steps: first, to analyze and master all kinds of gas accident reasons; Second, to determine the assemble of the gas risk factors evaluation, determine the evaluation grade assemble; Third, to proceed the single factor evaluation, determine fuzzy relationship matrix and the fuzzy weight vector of evaluation factor, and to choose the appropriate composition operator, vector analysis with the result of fuzzy comprehensive evaluation; Finally, people will take corresponding measures to prevent according to the result of evaluation that shows safety weaknesses.

Solving fully fuzzy polynomials using feed-back neural networks

Recently, there has been a considerable amount of interest and practice in solving many problems of several applied fields by fuzzy polynomials. In this paper, we have designed an artificial fuzzified feed-back neural network. With this design, we are able to find a solution of fully fuzzy polynomial with degree n. This neural network can get a fuzzy vector as an input, and calculates its corresponding fuzzy output. It is clear that the input–output relation for each unit of fuzzy neural network is defined by the extension principle of Zadeh. In this work, a cost function is also defined for the level sets of fuzzy output and fuzzy target. Next a learning algorithm based on the gradient descent method will be defined that can adjust the fuzzy connection weights. Finally, our approach is illustrated by computer simulations on numerical examples. It is worthwhile to mention that application of this method in fluid mechanics has been shown by an example.

Properties of Fuzzy Inner Product Spaces

In this paper, natural inner product structure for the space of fuzzyn−tuples is introduced. Also we have introduced the ortho vector, stochastic fuzzy vectors, ortho - stochastic fuzzy vectors, ortho-stochastic fuzzy matrices and the concept of orthogonal complement of fuzzy vector subspace of a fuzzy vector space.

Intuitionistic Fuzzy Multiple Attribute Decision Making Method Based on Closeness Degree

Closeness degree is a metric similar levels between two fuzzy sets. This paper extends the closeness degree to the filed of intuitionistic fuzzy multiple attribute decision making. First it defines the closeness degree of two intuitionistic fuzzy vector, then proposes a method based on closeness degree to solve intuitionistic fuzzy multi-attribute decision making problems with the known weights, and demonstrates the effectiveness of this method with examples at last.

English

English

Implementation of a new fuzzy vector control of induction motor

The aim of this paper is to present a new approach to control an induction motor using type-1 fuzzy logic. The induction motor has a nonlinear model, uncertain and strongly coupled. The vector control technique, which is based on the inverse model of the induction motors, solves the coupling problem. Unfortunately, in practice this is not checked because of model uncertainties. Indeed, the presence of the uncertainties led us to use human expertise such as the fuzzy logic techniques. In order to maintain the decoupling and to overcome the problem of the sensitivity to the parametric variations, the field-oriented control is replaced by a new block control. The simulation results show that the both control schemes provide in their basic configuration, comparable performances regarding the decoupling. However, the fuzzy vector control provides the insensitivity to the parametric variations compared to the classical one. The fuzzy vector control scheme is successfully implemented in real-time using a digital signal processor board dSPACE 1104. The efficiency of this technique is verified as well as experimentally at different dynamic operating conditions such as sudden loads change, parameter variations, speed changes, etc. The fuzzy vector control is found to be a best control for application in an induction motor.

Operation and ordering of fuzzy sets, and fuzzy set-valued convex mappings

For fuzzy mathematical models using general fuzzy sets rather than fuzzy numbers or fuzzy vectors, operations (addition and scalar multiplication) and orderings of fuzzy sets are needed, and the concept of fuzzy set-valued convex mappings is important. In the present paper, fundamental properties of operations, orderings, and fuzzy set-valued convex mappings for general fuzzy sets are investigated systematically.

On the global solution of a fuzzy linear system

The global solution of a fuzzy linear system contains the crisp vector solution of a real linear system. So discussion about the global solution of a n ×n fuzzy linear system A˜ x = ˜ b with a fuzzy number vector b in the right hand side and crisp a coefficient matrix A is considered. The advantage of the paper is developing a new algorithm to find the solution of such system by considering a global solution based upon the concept of a convex fuzzy numbers. At first the existence and uniqueness of the solution are introduced and then the related theorems and properties about the solution are proved in details. Finally the method is illustrated by solving some numerical examples.

Detection of Moving Objects with Fuzzy Color Coherence Vector

Background subtraction is a popular method for detecting foreground that is widely adopted as the fundamental processing for advanced applications such as tracking and surveillance. Color coherence vector (CCV) includes both the color distribution information (histogram) and the local spatial relationship information of colors. So it overcomes the weakness of the conventional color histogram for the representation of an object. In this paper, we introduce a fuzzy color coherence vector (FCCV) based background subtraction method. After applying the fuzzyc-means clustering to color coherence subvectors and color incoherence subvectors, we develop a region-based fuzzy statistical feature for each pixel based on the fuzzy membership matrices. The features are extracted from consecutive frames to build the background model and detect the moving objects. The experimental results demonstrate the effectiveness of the proposed approach.

Fuzzy optimization model for land use change

There are some important questions in Land use change literature, for instance How much land to allocate to each of a number of land use type in order to maximization of (household or individual) rent -paying ability, minimization of environmental impacts or maximization of population income. In this paper, we want to investigate them and propose mathematical models to find an answer for these questions. Since Most of the parameters in this process are linguistics and fuzzy logic is a powerful tools to handle them, a fuzzy linear programming model is used in model building. To this end, Fuzzy Linear Programming Problem(FLP) with fuzzy related system of constraint and fuzzy coefficient vector in the objective function, that is a full fuzzy system of simultaneous equations with fuzzy objective function is discussed. The related production operations in the objective function and in the constrains are performed in the basis of standard production between fuzzy numbers. The constraint which can be take into account depend on the case but representative objective include: Lower and upper limits on land use, availability of Labour and so on.

The Generalized Inverse of Atanassov's Intuitionistic Fuzzy Matrices

In this paper, a method is presented to find generalized inverse (g-inverse) of Atanassov's intuitionistic fuzzy matrix (AIFM). Also, the idea of standard basis for Atanassov's intuitionistic fuzzy vectors is introduced. Some results regarding the g-inverse of AIFM are studied. An application of g-inverse is provided at the end of the paper.