Showing papers on "Fuzzy associative matrix published in 2015"

Fault Diagnosis of Electric Power Systems Based on Fuzzy Reasoning Spiking Neural P Systems

Abstract: This paper proposes a graphic modeling approach, fault diagnosis method based on fuzzy reasoning spiking neural P systems (FDSNP), for power transmission networks. In FDSNP, fuzzy reasoning spiking neural P systems (FRSN P systems) with trapezoidal fuzzy numbers are used to model candidate faulty sections and an algebraic fuzzy reasoning algorithm is introduced to obtain confidence levels of candidate faulty sections, so as to identify faulty sections. FDSNP offers an intuitive illustration based on a strictly mathematical expression, a good fault-tolerant capacity due to its handling of incomplete and uncertain messages in a parallel manner, a good description for the relationships between protective devices and faults, and an understandable diagnosis model-building process. To test the validity and feasibility of FDSNP, seven cases of a local subsystem in an electrical power system are used. The results of case studies show that FDSNP is effective in diagnosing faults in power transmission networks for single and multiple fault situations with/without incomplete and uncertain SCADA data, and is superior to four methods, reported in the literature, in terms of the correctness of diagnosis results.

On Equivalence of FIS and ELM for Interpretable Rule-Based Knowledge Representation

Abstract: This paper presents a fuzzy extreme learning machine (F-ELM) that embeds fuzzy membership functions and rules into the hidden layer of extreme learning machine (ELM). Similar to the concept of ELM that employed the random initialization technique, three parameters of F-ELM are randomly assigned. They are the standard deviation of the membership functions, matrix-C (rule-combination matrix), and matrix-D [don’t care (DC) matrix]. Fuzzy if-then rules are formulated by the rule-combination Matrix of F-ELM, and a DC approach is adopted to minimize the number of input attributes in the rules. Furthermore, F-ELM utilizes the output weights of the ELM to form the target class and confidence factor for each of the rules. This is to indicate that the corresponding consequent parameters are determined analytically. The operations of F-ELM are equivalent to a fuzzy inference system. Several benchmark data sets and a real world fault detection and diagnosis problem have been used to empirically evaluate the efficacy of the proposed F-ELM in handling pattern classification tasks. The results show that the accuracy rates of F-ELM are comparable (if not superior) to ELM with distinctive ability of providing explicit knowledge in the form of interpretable rule base.

A Parameterized Nonlinear Programming Approach to Solve Matrix Games With Payoffs of I-Fuzzy Numbers

Abstract: The aim of this paper is to develop a new methodology for solving matrix games with payoffs of Atanassov's intuitionistic fuzzy (I-fuzzy) numbers. In this methodology, we define the concepts of I-fuzzy numbers and the value-index and ambiguity-index and develop a difference-index-based ranking method, which is proven to be a total order. By doing this, the parameterized nonlinear programming models are derived from a pair of auxiliary I-fuzzy mathematical programming models, which are used to determine solutions of matrix games with payoffs of I-fuzzy numbers. The validity and applicability of the models and method proposed in this paper are illustrated with a practical example.

Fuzzy Differential Equations in Various Approaches

Abstract: 1. Introduction. -2. Basic Concepts. -3. Fuzzy Calculus. -4. Fuzzy Differential Equations. -Mathematical Background. -Index.

Fuzzy Granular Structure Distance

Abstract: A fuzzy granular structure refers to a mathematical structure of the collection of fuzzy information granules granulated from a dataset, while a fuzzy information granularity is used to measure its uncertainty. However, the existing forms of fuzzy information granularity have two limitations. One is that when the fuzzy information granularity of one fuzzy granular structure equals that of the other, one can say that these two fuzzy granular structures possess the same uncertainty, but these two fuzzy granular structures may be not equivalent to each other. The other limitation is that existing axiomatic approaches to fuzzy information granularity are still not complete, under which when the partial order relation among fuzzy granular structures cannot be found, their coarseness/fineness relationships will not be revealed. To address these issues, a so-called fuzzy granular structure distance is proposed in this study, which can well discriminate the difference between any two fuzzy granular structures. Besides this advantage, the fuzzy granular structure distance has another important benefit: It can be used to establish a generalized axiomatic constraint for fuzzy information granularity. By using the axiomatic constraint, the coarseness/fineness of any two fuzzy granular structures can be distinguished. In addition, through taking the fuzzy granular structure distances of a fuzzy granular structure to the finest one and the coarsest one into account, we also can build a bridge between fuzzy information granularity and fuzzy information entropy. The applicable analysis on 12 real-world datasets shows that the fuzzy granular structure distance and the generalized fuzzy information granularity have much better performance than existing methods.

Fuzzy arithmetic on LR fuzzy numbers with applications to fuzzy programming

Abstract: In practice, some special LR fuzzy numbers, like the triangular fuzzy number, the Gaussian fuzzy number and the Cauchy fuzzy number, are widely used in many areas to deal with various vague information. With regard to these special LR fuzzy numbers, called regular LR fuzzy numbers in this paper, an operational law is proposed for fuzzy arithmetic, providing a novel approach to analytically and exactly calculating the inverse credibility distribution of some specific arithmetical operations based on the credibility measure. As an application of the operational law, an equivalent form of the expected value operator as well as a theorem for computing the expected value of strictly monotone functions is suggested. Finally, we utilize the operational law to construct a solution framework of fuzzy programming with parameters of regular LR fuzzy numbers, and such type of fuzzy programming problems can be handled by the operational law as the classic deterministic programming without any particular solving techniques.

Intuitionistic fuzzy logics as tools for evaluation of Data Mining processes

Abstract: The Intuitionistic Fuzzy Sets (IFSs), proposed in 1983, are extensions of fuzzy sets. Some years after their introduction, sequentially, intuitionistic fuzzy propositional logic, intuitionistic fuzzy predicate logic, intuitionistic fuzzy modal logic and intuitionistic fuzzy temporal logic have been introduced, presented here shortly. During the last 25years, different intuitionistic fuzzy tools have been used for evaluation of objects from the area of the Artificial Intelligence, as expert systems (having, e.g. facts and rules, with intuitionistic fuzzy degrees of validity and non-validity), decision making processes (having, e.g. intuitionistic fuzzy estimations of the criteria), neural networks, pattern recognitions, metaheuristic algorithms, etc. Short review of these legs of research is offered, with some concrete ideas of possible new directions of study. On this basis, a non-formal discussion is raised on the benefits of applying various elements of intuitionistic fuzzy logics as tools for evaluation of Data Mining processes.

An introduction to fuzzy soft topological spaces

Abstract: The aim of this study is to dene fuzzy soft topology which will be compatible to the fuzzy soft theory and investigate some of its fundamental properties. Firstly, we recall some basic properties of fuzzy soft sets and then we give the denitions of cartesian product of two fuzzy soft sets and projection mappings. Secondly, we introduce fuzzy soft topology and fuzzy soft continuous mapping. Moreover, we induce a fuzzy soft topology after given the denition of a fuzzy soft base. Also, we obtain an initial fuzzy soft topology and give the denition of product fuzzy soft topology. Finally, we prove that the category of fuzzy soft topological spaces FSTOP is a topological category over SET:

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

Abstract: 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.

A new definition for defuzzification of generalized fuzzy numbers and its application

Abstract: In this paper, a new approach for defuzzification of generalized fuzzy numbers is established. This method uses the incentre point of a triangle where the three bisector lines of its angles meet. Coordinates of incentre point can also be easily calculated by the "Mathematica" package to solve problems of defuzzification and ranking fuzzy numbers. Some numerical examples are illustrated to show the utility of proposed method.

Fuzzy control for uncertainty nonlinear systems with dual fuzzy equations

Abstract: Many uncertain nonlinear systems can be modeled by the linear-in-parameter model, and the parameters are uncertain in the sense of fuzzy numbers. Fuzzy equations can be used to model these nonlinear systems. The solutions of the fuzzy equations are the controllers. In this paper, we give the controllability condition for the fuzzy control via dual fuzzy equations. Two types of neural networks are applied to approximate the solutions of the fuzzy equations. These solutions are then transformed into the fuzzy controllers. The novel methods are validated with five benchmark examples.

A New Approach to Multi-variable Fuzzy Forecasting Using Picture Fuzzy Clustering and Picture Fuzzy Rule Interpolation Method

Abstract: In this paper, a new approach to multi-variable fuzzy forecasting using picture fuzzy clustering and picture fuzzy rule interpolation techniques is proposed Firstly, we partition dataset into clusters using picture fuzzy clustering algorithm Secondly, we construct picture fuzzy rules based on given clusters Finally, we determine the predicted outputs based on the picture fuzzy rule interpolation scheme Our proposed approach is applied to forecast the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) data The experimental results indicate that our method predicts better forecasting results than some relevant ones

Analysis of the Fuzzy Controllability Property and Stabilization for a Class of T–S Fuzzy Models

Abstract: In this paper, the controllability property for a class of Takagi–Sugeno (T–S) fuzzy models is analyzed, while a fully nonlinear stabilizer is designed in a practical way. It is shown that global fuzzy stabilizers can be constructed in a nonconservative way by means of a relatively simple approach. The existence of such controllers depends on the fuzzy controllability conditions, which are derived in a straightforward way. The main advantage of the proposed approach is that the convergence of the closed-loop system can be imposed arbitrarily. Some examples are given in order to illustrate the validity of the method. Finally, the proposed controller is applied on an underactuated system known as “pendubot” and the results are compared with an stabilizer designed on the basis of LMIs.

On the relationship among F-transform, fuzzy rough set and fuzzy topology

Abstract: The objective of this work is to associate the concepts of fuzzy rough sets and fuzzy topologies/co-topologies with the F-transforms. The notions of the direct \(F^{\uparrow }\) and \(F^{\downarrow }\)-transforms are extended to the case where they are applied to an L-valued function on a space with an L-valued fuzzy partition. It is shown that these F-transforms are particular cases of upper and lower fuzzy approximation operators. Moreover, every F-transform component induces a continuous map between two associated fuzzy topological spaces or fuzzy co-topological spaces.

Genetic optimization of fuzzy fractional PD+I controllers

Abstract: Fractional order calculus is a powerful emerging mathematical tool in science and engineering. There is currently an increasing interest in generalizing classical control theories and developing novel control strategies. The genetic algorithms (GA) are a stochastic search and optimization methods based on the reproduction processes found in biological systems, used for solving engineering problems. In the context of process control, the fuzzy logic usually means variables that are described by imprecise terms, and represented by quantities that are qualitative and vague. In this article we consider the development of an optimal fuzzy fractional PD+I controller in which the parameters are tuned by a GA. The performance of the proposed fuzzy fractional control is illustrated through some application examples.

Dynamical Models of Stock Prices Based on Technical Trading Rules Part I: The Models

Abstract: In this paper, we use fuzzy systems theory to convert the technical trading rules commonly used by stock practitioners into excess demand functions which are then used to drive the price dynamics. The technical trading rules are recorded in natural languages where fuzzy words and vague expressions abound. In Part I of this paper, we will show the details of how to transform the technical trading heuristics into nonlinear dynamic equations. First, we define fuzzy sets to represent the fuzzy terms in the technical trading rules; second, we translate each technical trading heuristic into a group of fuzzy IF–THEN rules; third, we combine the fuzzy IF–THEN rules in a group into a fuzzy system; and finally, the linear combination of these fuzzy systems is used as the excess demand function in the price dynamic equation. We transform a wide variety of technical trading rules into fuzzy systems, including moving average rules, support and resistance rules, trend line rules, big buyer, big seller, and manipulator rules, band and stop rules, and volume and relative strength rules. Simulation results show that the price dynamics driven by these technical trading rules are complex and chaotic, and some common phenomena in real stock prices such as jumps, trending, and self-fulfilling appear naturally.

An analysis of fully fuzzy linear programming with fuzzy decision variables through logistics network design problem

Abstract: Recently, there is a growing attention by the researchers to solve and interpret the analysis of fully fuzzy linear programming problems in which all of the parameters as well as the decision variables are considered as fuzzy numbers. Under a fully uncertain environment where all of the data are stated as fuzzy, presenting the reasonable range of values for the decision variables may be comparatively better than the currently available crisp solutions so as to provide ranges of flexibility to decision makers. However, there is still a scarcity of solution methodologies on fuzzy mathematical programs with fuzzy decision variables. Based on this motivation, a new parametric method which is mainly based on α-cut representation of fuzzy intervals is proposed in this paper by incorporating the decision maker's attitude toward risk. In order to illustrate validity and practicality of the proposed method, it is applied to a generic reverse logistics network design model including fuzzy decision variables. To the best of our knowledge, this is the first study in the literature which presents fuzzy efficient solutions and analysis for a fully fuzzy reverse logistics network design problem with fuzzy decision variables. The provided solutions by the proposed method are also compared to the available solution methodologies from the literature in terms of computational efficiency, solution quality and ease of use. By using the proposed method, the decision makers can be supported by yielding fuzzy efficient solutions under different uncertainty levels and risk attitudes. The computational results have also shown that more reliable and necessarily precise solutions can be generated by the proposed method for a risk-averse decision maker.

Bayesian network construction using a fuzzy rule based approach for medical decision support

Abstract: This study proposes a novel method for the construction of efficient and convenient Bayesian networks BNs and influence diagrams regarding medical problems based on fuzzy rules The general methodology that was developed is able to address decisions based on fuzzy medical rules that connect symptoms with the severity/rating scale of a disease These fuzzy rules are rich enough to cover a large variety of medical decisions The method overcomes the major disadvantage of Bayesian nets, that is, the need of a vast amount of subjective probabilities Instead of filling conditional probability tables in BNs, physicians report their knowledge in the form of fuzzy rules The knowledge of these rules after defuzzification is transformed according to certain equations into probabilities This becomes possible, categorizing the rules into certain types For each type of rule, a mathematical expression is determined, which sets correctly the conditional probabilities that relate a symptom with its child severity A particular example of assessing pulmonary infections and making decisions on severity degree was explored, implementing a decision support system DSS to show the functionality of the proposed methodology The developed front-end DSS was evaluated and proved capable to drive fair decisions close to those obtained by physicians

FRULER: Fuzzy Rule Learning through Evolution for Regression

Abstract: In regression problems, the use of TSK fuzzy systems is widely extended due to the precision of the obtained models. Moreover, the use of simple linear TSK models is a good choice in many real problems due to the easy understanding of the relationship between the output and input variables. In this paper we present FRULER, a new genetic fuzzy system for automatically learning accurate and simple linguistic TSK fuzzy rule bases for regression problems. In order to reduce the complexity of the learned models while keeping a high accuracy, the algorithm consists of three stages: instance selection, multi-granularity fuzzy discretization of the input variables, and the evolutionary learning of the rule base that uses the Elastic Net regularization to obtain the consequents of the rules. Each stage was validated using 28 real-world datasets and FRULER was compared with three state of the art enetic fuzzy systems. Experimental results show that FRULER achieves the most accurate and simple models compared even with approximative approaches.

A novel associative classification model based on a fuzzy frequent pattern mining algorithm

Abstract: We propose a novel efficient fuzzy associative classification approach.We exploit a fuzzy version of the FP-Growth algorithm.We perform an experimental analysis on 17 classification datasets.We compare our approach with three well-known associative classifiers. Associative classification models are based on two different data mining paradigms, namely pattern classification and association rule mining. These models are very popular for building highly accurate classifiers and have been employed in a number of real world applications.During the last years, several studies and different algorithms have been proposed to integrate associative classification models with the fuzzy set theory, leading to the so-called fuzzy associative classifiers.In this paper, we propose a novel efficient fuzzy associative classification approach based on a fuzzy frequent pattern mining algorithm. Fuzzy items are generated by discretizing the input variables and defining strong fuzzy partitions on the intervals resulting from these discretizations. Then, fuzzy associative classification rules are mined by employing a fuzzy extension of the FP-Growth algorithm, one of the most efficient frequent pattern mining algorithms. Finally, a set of highly accurate classification rules is generated after a pruning stage.We tested our approach on seventeen real-world datasets and compared the achieved results with the ones obtained by using both a non-fuzzy associative classifier, namely CMAR, and two recent state-of-the-art classifiers, namely FARC-HD and D-MOFARC, based on fuzzy association rules. Using non-parametric statistical tests, we show that our approach outperforms CMAR and achieves accuracies similar to FARC-HD and D-MOFARC.

Matrix Games with Intuitionistic Fuzzy Pay-offs

Abstract: In this paper two person zero sum matrix games are considered in which elements of payoff matrix are expressed with triangular intuitionistic fuzzy numbers (TIFNs). The purpose of this paper is to develop a solution methodology for solving such types of matrix games. For this, a pair of auxiliary intuitionistic fuzzy programming (IFP) models for each player are established. Then these two IFP problems are transformed into conventional crisp linear programming problems by defining a suitable defuzzification function to determine optimal strategies for each player and value of the game. The proposed method in this paper is illustrated with a numerical example to show the validity and applicability.

The intelligence of dual simplex method to solve linear fractional fuzzy transportation problem

Abstract: An approach is presented to solve a fuzzy transportation problem with linear fractional fuzzy objective function. In this proposed approach the fractional fuzzy transportation problem is decomposed into two linear fuzzy transportation problems. The optimal solution of the two linear fuzzy transportations is solved by dual simplex method and the optimal solution of the fractional fuzzy transportation problem is obtained. The proposed method is explained in detail with an example.

A duality approach for solving bounded linear programming problems with fuzzy variables based on ranking functions and its application in bounded transportation problems

Abstract: There are several methods, in the literature, for solving fuzzy variable linear programming problems fuzzy linear programming in which the right-hand-side vectors and decision variables are represented by trapezoidal fuzzy numbers. In this paper, the shortcomings of some existing methods are pointed out and to overcome these shortcomings a new method based on the bounded dual simplex method is proposed to determine the fuzzy optimal solution of that kind of fuzzy variable linear programming problems in which some or all variables are restricted to lie within lower and upper bounds. To illustrate the proposed method, an application example is solved and the obtained results are given. The advantages of the proposed method over existing methods are discussed. Also, one application of this algorithm in solving bounded transportation problems with fuzzy supplies and demands is dealt with. The proposed method is easy to understand and to apply for determining the fuzzy optimal solution of bounded fuzzy variable linear programming problems occurring in real-life situations.