Interval fuzzy probability method for power transformer multiple fault diagnosis

Accurately diagnosing power transformer faults is critical to improving the operational reliability of power systems. Although some researchers have made great efforts to improve the accuracy of transformer fault diagnosis, accurate diagnosis of multiple faults is still a difficult problem. In order to improve the accuracy of transformer multiple faults diagnosis, a multiple fault diagnosis method based on interval fuzzy probability is proposed. Different from the previous methods which provide single-value probability, this method use probability interval to represent the occurrence degree of various possible faults, which can objectively predict the potential faults that occurring in a transformer and provide a more reasonable explanation for the diagnosis results. In the proposed method, the interval fuzzy set is used to describe the evaluation of state variables and the interval fuzzy probability model based on interval weighted average is applied to integrate the fault information. The representative matrix of fault types based on fuzzy preference relationship is established to estimate the relative importance of each gas in the dissolved gases. The proposed method can provide the probability of probable faults in transformer, help engineers quickly determine the type and location of faults, and improve the accuracy of diagnosis and maintenance efficiency of transformer. The effectiveness of the method is verified with case studies.

Conditional Intuitionistic Fuzzy Mean Value

The conditional mean value has applications in regression analysis and in financial mathematics, because they are used in it. We can find papers from recent years that use the conditional mean value in fuzzy cases. As the intuitionstic fuzzy sets are an extension of fuzzy sets, we will try to define a conditional mean value for the intuitionistic fuzzy case. The conditional mean value in crisp intuitionistic fuzzy events was first studied by V. Valenčáková in 2009. She used Gödel connectives. Her approach can only be used for special cases of intuitionistic fuzzy events, therefore, we want to define a conditional mean value for all elements of a family of intuitionistic fuzzy events. In this paper, we define the conditional mean value for intuitionistic fuzzy events using Lukasiewicz connectives. We use a Kolmogorov approach and the notions from a classical probability theory for construction. B. Riečan formulated a conditional intuitionistic fuzzy probability for intuitionistic fuzzy events using an intuitionistic fuzzy state in 2012. In classical cases, there exists a connection between the conditional probability and the conditional mean value, therefore we show a connection between the conditional intuitionistic fuzzy probability induced by the intuitionistic fuzzy state and the conditional intuitionistic fuzzy mean value.

Fuzzy probability based person recognition in smart environments

Biometric features are used to verify the people identity in the living places like smart apartments. To increase the chance of classification and recognition rate, the recognizing procedure contains various steps such as detection of silhouette from the gait profile, silhouette segmentation, reading features from the silhouette, classification of features and finally recognition of person using its probability value. Person recognition accuracy will be oscillated and declined due to blockage, radiance and posture variance problems. In the proposed work, the gait profile will be formed by capturing the gait of a targeted person in stipulated time to reach the destination. From the profile the silhouettes are detected using frame difference and segmented from the background using immediate thresholding and features are extracted from the silhouette using gray-level covariance matrix and optimized feature set is formed using PSO. These optimized features are fused, trained and classified using nearest neighbor support vectors. The fuzzy probability method is used for recognizing the person based on the probability value of the authentic and imposter scores. The relationship between the CMS, TPR, TNR and F-rate are calculated for 1 : 1 matcher from the gallery set. The performance of the classifiers are found to be perfect by plotting the DET graph and ROC curve. The proposed fuzzy probability theory is mingled with GLCMPSO and NSFV method for human recognition purpose. The performance of the proposed is proved to be acceptable for recognition with the optimal parameters (Entropy, SSIM, PSNR, CQM) calculation From the work, it is clear that, the rank probability is proportional to the match score value of the silhouette stored in the gallery.

Multi-objective Optimization of Tree Trunk Axes in Glulam Beam Design Considering Fuzzy Probability Based Random Fields

Deterministic design and a priori parameters are used in traditional optimization approaches. The material characteristics of solid wood are not deterministic in reality. Hence, realistic optimization and simulation methods need to take the uncertainties of parameters into account. The uncertainty characteristics of wood are mainly originated in natural variation. In addition to this, incertitudes from lack of knowledge are inherent. Accordingly, the aleatoric approach of randomness can be expanded to a polymorphic uncertainty model. Fuzzy probability based randomness is used in this work. Therefore, the epistemic approach of fuzziness is taken into account. The distribution functions of random variables are parametrized by fuzzy variables. So coupling of both, aleatoric and epistemic uncertainties, is involved.Interactions of fuzzy variables and crosscorrelations of random variables are considered among and within the parameters. Crosscorrelated random fields are used to represent spatial variation of material parameters. The autocovariance structures are modeled structurally dependent on the tree trunk axes. FEM results are applied as basic solutions of a loaded timber structure. A local orthotropic material formulation with respect to specifically located tree trunk axes is used. The optimal positions of the tree trunk axes for each wooden log are examined as design parameters. Polymorphic uncertainty is used to describe a priori parameters. The developed methods for uncertainty analysis are embedded in an automated and parallelized optimization processing. An analysis of a two-tier glulam beam, according to a purlin of a timber roof construction, is shown as numerical example for the optimization framework.

SELECTION OF LOCATIONS FOR GROUND BASED OPTICAL SURVEILLANCE DEVICES BASED ON THE FUZZY PROBABILITY MODEL

When choosing the location of groundbased optical surveillance devices (NOSN), the problem arises of evaluating the suitability of a particular area of terrain or choosing the best of a number of considered ones, provided that the ability to perform professional tasks with specified characteristics is quantified. A method for solving this problem is proposed by constructing a fuzzyprobability model of a generalized (integral) indicator of the quality of NOS placements based on the knowledge and experience of experts. Such an indicator is determined by a systemically confirmed set of seven linguistic variables included in the factor space for constructing a fuzzy probability model in the form of a nonlinear polynomial expression. At the same time, the dependent variablethe ability to perform the task with the specified characteristicsindirectly determines the degree of the best placement of the NOS, taking into account its astroclimate. Practical recommendations on the choice and justification of the factor space are given, the main stages of constructing a fuzzy probability model are shown, and the degree of adequacy of calculations based on it to the actual ability to perform tasks with specified characteristics, evaluated by independent experts, for the locations of NOS in various geographical regions of the Russian Federation.

A note on mean value and dispersion of intuitionistic fuzzy events

In this paper, we compare two definitions of mean value and dispersion for intuitionistic fuzzy events. We show the connection between these two definitions and we introduce some types of mean values induced by intuitionistic fuzzy state and by intuitionistic fuzzy probability.

Martingale Convergence Theorem for the Conditional Intuitionistic Fuzzy Probability

For the first time, the concept of conditional probability on intuitionistic fuzzy sets was introduced by K. Lendelová. She defined the conditional intuitionistic fuzzy probability using a separating intuitionistic fuzzy probability. Later in 2009, V. Valenčáková generalized this result and defined the conditional probability for the MV-algebra of inuitionistic fuzzy sets using the state and probability on this MV-algebra. She also proved the properties of conditional intuitionistic fuzzy probability on this MV-algebra. B. Riečan formulated the notion of conditional probability for intuitionistic fuzzy sets using an intuitionistic fuzzy state. We use this definition in our paper. Since the convergence theorems play an important role in classical theory of probability and statistics, we study the martingale convergence theorem for the conditional intuitionistic fuzzy probability. The aim of this contribution is to formulate a version of the martingale convergence theorem for a conditional intuitionistic fuzzy probability induced by an intuitionistic fuzzy state m. We work in the family of intuitionistic fuzzy sets introduced by K. T. Atanassov as an extension of fuzzy sets introduced by L. Zadeh. We proved the properties of the conditional intuitionistic fuzzy probability.

Conditional intuitionistic fuzzy probability and martingale convergence theorem using IF-probability

The aim of this paper is to formulate the conditional intuitionistic fuzzy probability and a version of martingale convergence theorem with respect an intuitionistic fuzzy probability. Since the intuitionistic fuzzy probability can be decomposed to two intuitionistic fuzzy states, we can use the results holding for intuitionistic fuzzy states.