Showing papers on "Fuzzy associative matrix published in 2008"

Fuzzy Modeling and Fuzzy Control

Abstract: preparation of statements that are fair, clear, and helpful to courts; and responding to questions by judges and juries.” The author does a good job of meeting these goals through discussions on how to quantify DNA evidence for presentation in court or preparing legal statements. This book will be helpful to statisticians and others with technical backgrounds, who might be called on as expert witnesses in deciding what kind of information is considered a valid evidence and what should be presented. For example, in Chapter 8, the author mentions that an expert witness needs sufficient information to answer two questions for a jury: (1) How likely is the evidence if the defendant s is guilty? and (2) how likely is the evidence if s is innocent and i is the true culprit? The author discusses different ways to answer these questions. Although the writing in this book is fairly nontechnical, some mathematical theory behind the results is presented, but not for courtroom statements. It is given for forensic scientists to provide insight into the reasoning behind results. The concept of p-value is very difficult to understand for those unfamiliar with statistical terminology. The author presents this concept in plain English in very easy-to-understand language without actually mentioning the term “pvalue.” Although the concepts of hypotheses testing are used in discussions from the beginning, it is introduced formally only at the end of Chapter 8, where the standard definition of p-value also is given. Similarly, the discussions include descriptions of the concepts of conditional probabilities and two types of error rates, which also are not easy to understand for members of a jury. The errors of logic, referred to as the prosecutor’s fallacy and the defendant’s fallacy, are described using simple examples. An interesting discussion also shows how a lower level of language comprehension by jurors can lead to confusion about differences in P(A|B) and P(B|A). There is more emphasis on evaluating evidence using likelihood ratios and the Bayes theorem. In today’s world of expanding use of scientific methods to resolve conflicts by the judicial system and recent increases in use of DNA profiling as evidence, there is a need for more literature that describes these concepts in simple language. This book is a good example of how statistics can be explained in plain English to a nontechnical audience, a skill that every statistician needs to master for improved communication.

Fuzzy Modeling with Spatial Information for Geographic Problems

Abstract: Reasoning About Regions, Relations, and Fields.- Fuzzy Reasoning about Geographic Regions.- Combined Extraction of Directional and Topological Relationship Information from 2D Concave Objects.- Field Based Methods for the Modeling of Fuzzy Spatial Data.- Modeling Localities with Fuzzy Sets and GIS.- Fuzzy Classification.- Mining Weather Data Using Fuzzy Cluster Analysis.- Modelling the Fuzzy Spatial Extent of Geographical Entities.- Multi-Dimensional Interpolations with Fuzzy Sets.- Talking Space - A Social & Fuzzy Logical GIS Perspective On Modelling Spatial Dynamics.- A Valuation of the Reliability of a GIS Based on the Fuzzy Logic in a Concrete Case Study.- Fuzzy Representations of Landscape Features.- Fuzziness and Ambiguity in Multi-Scale Analysis of Landscape Morphometry.- Fuzzy Representation of Special Terrain Features Using a Similarity-based Approach.- Decision Making with GIS and Fuzzy Sets.- Spatial Decision-Making Using Fuzzy Decision Tables: Theory, Application and Limitations.- Spatial Decision Making Using Fuzzy GIS.- Spatially Explicit Individual-Based Ecological Modeling with Mobile Fuzzy Agents.

Chaos synchronization using fuzzy logic controller

Abstract: The design of a rule-based controller for a class of master-slave chaos synchronization is presented in this paper. In traditional fuzzy logic control (FLC) design, it takes a long time to obtain the membership functions and rule base by trial-and-error tuning. To cope with this problem, we directly construct the fuzzy rules subject to a common Lyapunov function such that the master–slave chaos systems satisfy stability in the Lyapunov sense. Unlike conventional approaches, the resulting control law has less maximum magnitude of the instantaneous control command and it can reduce the actuator saturation phenomenon in real physic system. Two examples of Duffing–Holmes system and Lorenz system are presented to illustrate the effectiveness of the proposed controller.

Elementary Fuzzy Matrix Theory and Fuzzy Models for Social Scientists

Abstract: This book gives the basic notions of fuzzy matrix theory and its applications to simple fuzzy models. The approach is non-traditional in order to attract many students to use this methodology in their research. The traditional approach of mathematicians has conditioned students of sociology in such a manner that they are averse to using mathematical tools. Six simple types of fuzzy models that make use of fuzzy matrices are given. These models are distinct because they are time-dependent and can even be used for statistical data. The Fuzzy Cognitive Maps models gives the hidden pattern. Fuzzy Relational Maps model not only gives the hidden pattern but also gives the inter-relations between two sets of disjoint attributes. The Bidirectional Associative Memories model analyzes data depending on the time-period, while the Fuzzy Associative Memories model can give the gradation of importance of each attribute. Finally, the Fuzzy Relational Equation model is capable of giving a solution closer to the predicted solution. All the models are illustrated through elaborate examples of particular social problems.

Fuzzy Number Intuitionistic Fuzzy Arithmetic Aggregation Operators

Abstract: A fuzzy number intuitionistic fuzzy set (FNIFS) is a generalization of intuitionistic fuzzy set. The fundamental characteristic of FNIFS is that the values of its membership function and non-membership function are trigonometric fuzzy numbers rather than exact numbers. In this paper, we define some operational laws of fuzzy number intuitionistic fuzzy numbers, and, based on these operational laws, develop some new arithmetic aggregation operators, such as the fuzzy number intuitionistic fuzzy weighted averaging (FIFWA) operator, the fuzzy number intuitionistic fuzzy ordered weighted averaging (FIFOWA) operator and the fuzzy number intuitionistic fuzzy hybrid aggregation (FIFHA) operator for aggregating fuzzy number intuitionistic fuzzy information. Furthermore, we give an application of the FIFHA operator to multiple attribute decision making based on fuzzy number intuitionistic fuzzy information. Finally, an illustrative example is given to verify the developed approach.

Systematic design of a stable type-2 fuzzy logic controller

Abstract: Stability is one of the more important aspects in the traditional knowledge of automatic control. Type-2 fuzzy logic is an emerging and promising area for achieving intelligent control (in this case, fuzzy control). In this work we use the fuzzy Lyapunov synthesis as proposed by Margaliot and Langholz [M. Margaliot, G. Langholz, New Approaches to Fuzzy Modeling and Control: Design and Analysis, World Scientific, Singapore, 2000] to build a Lyapunov stable type-1 fuzzy logic control system, and then we make an extension from a type-1 to a type-2 fuzzy logic control system, ensuring the stability on the control system and proving the robustness of the corresponding fuzzy controller.

Fuzzy risk analysis based on fuzzy numbers with different shapes and different deviations

Abstract: In this paper, we present a new method for fuzzy risk analysis based on fuzzy numbers with different shapes and different deviations. First, we present a new method for ranking trapezoidal fuzzy numbers based on their shapes and deviations. Then, we use some examples to compare the proposed method with the existing methods for ranking fuzzy numbers. Finally, we use the proposed fuzzy ranking method to present a new fuzzy risk analysis algorithm to deal with fuzzy risk analysis problems. The proposed fuzzy risk analysis algorithm is more flexible and simpler than the existing methods due to the fact that it allows the evaluating values to be represented by trapezoidal fuzzy numbers with different shapes and different deviations.

Fuzzy Linear Regression Model

Abstract: To estimate the parameters of fuzzy linear regression model with crisp input and fuzzy output, we construct a method based on minimizing the least square errors, and propose some relative conclusions including normal equations, minimum solution, unique solution and their analytical expressions of fuzzy parameters. Finally, one numerical example is used to illustrate our proposed methods reasonable.

Fuzzy number intuitionistic fuzzy geometric aggregation operators and their application to decision making

Abstract: A fuzzy number intuitionistic fuzzy set is a generalization of intuitionistic fuzzy set. For the fuzzy number intuitionistic fuzzy information aggregating problems, some operational laws of fuzzy number intuitionistic fuzzy numbers are defined, based on which some new geometric aggregation operators are developed, such as the fuzzy number intuitionistic fuzzy weighted geometric (FIFWG) operator, the fuzzy number intuitionistic fuzzy ordered weighted geometric (FIFOWG) operator and the fuzzy number intuitionistic fuzzy hybrid geometric (FIFHG) operator. Based on these operators, an approach for solving uncertain multiple attribute group decision making problems is proposed, in which the attribute weights are completely known and the attribute values are fuzzy number intuitionistic fuzzy numbers. Finally, an illustrative example show the effectiveness of the proposed approach.

A review and classification of fuzzy mathematical programs

Abstract: In this article, a review of fuzzy mathematical programming models according to fuzzy components is given. Fifteen types of the fuzzy mathematical programming models are identified in the proposed classification. All possible combinations of fuzzy components are considered in classifying fuzzy mathematical programs. Existing solution procedures which were proposed in the literature for solving fuzzy mathematical programs are also reviewed and discussed in the paper.

Fuzzy Control System Design via Fuzzy Lyapunov Functions

Abstract: This correspondence deals with the problems of analysis and design for a class of continuous-time Takagi-Sugeno fuzzy control systems. Sufficient conditions for the stability of fuzzy control systems are derived based on a fuzzy Lyapunov function. Both parallel and nonparallel distributed compensation controllers are considered. Sufficient conditions for the solvability of the controller design problem are given in the form of linear matrix inequalities. Unlike the fuzzy Lyapunov function approaches reported in the literature, the bound of the time derivatives of the fuzzy basis functions is not required in the proposed approaches. The effectiveness of the proposed approaches is shown through a numerical example.

On line learning fuzzy rule-based system structure from data streams

Abstract: A new approach to fuzzy rule-based systems structure identification in on-line (possibly real-time) mode is described in this paper It expands the so called evolving Takagi-Sugeno (eTS) approach by introducing self-learning aspects not only to the number of fuzzy rules and system parameters but also to the number of antecedent part variables (inputs) The approach can be seen as online sensitivity analysis or online feature extraction (if in a classification application, eg in eClass which is the classification version of eTS) This adds to the flexibility and self-learning capabilities of the proposed system In this paper the mechanism of formation of new fuzzy sets as well as of new fuzzy rules is analyzed from the point of view of on-line (recursive) data density estimation Fuzzy system structure simplification is also analyzed in on-line context Utility- and age-based mechanisms to address this problem are proposed The rule-base structure evolves based on a gradual update driven by; i) information coming from the new data samples; ii) on-line monitoring and analysis of the existing rules in terms of their utility, age, and variables that form them The theoretical theses are supported by experimental results from a range of real industrial data from chemical, petro-chemical and car industries The proposed methodology is applicable to a wide range of fault detection, prediction, and control problems when the input or feature channels are too many

Compact fuzzy association rule-based classifier

Abstract: Classification is one of the most popular data mining techniques applied to many scientific and industrial problems. The efficiency of a classification model is evaluated by two parameters, namely the accuracy and the interpretability of the model. While most of the existing methods claim their accurate superiority over others, their models are usually complex and hardly understandable for the users. In this paper, we propose a novel classification model that is based on easily interpretable fuzzy association rules and fulfils both efficiency criteria. Since the accuracy of a classification model can be largely affected by the partitioning of numerical attributes, this paper discusses several fuzzy and crisp partitioning techniques. The proposed classification method is compared to 15 previously published association rule-based classifiers by testing them on five benchmark data sets. The results show that the fuzzy association rule-based classifier presented in this paper, offers a compact, understandable and accurate classification model.

On copulas, quasicopulas and fuzzy logic

Abstract: We investigate (quasi)copulas as possible truth functions of fuzzy conjunction which is not necessarily associative and present some axiom systems for such fuzzy logics. In particular, we study an expansion of ?ukasiewicz (infinite valued propositional) logic by a new connective interpreted as an arbitrary quasicopula (and also by a new connective interpreted as the residuum of the copula). Main results concern standard completeness.

Sampled-data fuzzy controller for continuous nonlinear systems

Abstract: The sampled-data fuzzy control of nonlinear systems is presented. The consequents of the fuzzy controller rules are linear sampled-data sub-controllers. As a result, the fuzzy controller is a weighted sum of some linear sampled-data sub-controllers that can be implemented by a microcontroller or a digital computer to lower the implementation cost. Consequently, a hybrid fuzzy controller consisting of continuous-time grades of memberships and discrete-time sub-controller is obtained. The system stability of the fuzzy control system is investigated on the basis of Lyapunov-based approach. The sampling activity introduces discontinuity to complicate the system dynamics and make the stability analysis difficult. The proposed fuzzy controller exhibits a favourable property to alleviate the conservativeness of the stability analysis. Furthermore, linear matrix inequality-based performance conditions are derived to guarantee the system performance of the fuzzy control system. An application example is given to illustrate the merits of the proposed approach.

Studying interval valued matrix games with fuzzy logic

Abstract: Matrix games have been widely used in decision making systems. In practice, for the same strategies players take, the corresponding payoffs may be within certain ranges rather than exact values. To model such uncertainty in matrix games, we consider interval-valued game matrices in this paper; and extend the results of classical strictly determined matrix games to fuzzily determined interval matrix games. Finally, we give an initial investigation into mixed strategies for such games.

Learning consistent, complete and compact sets of fuzzy rules in conjunctive normal form for regression problems

Abstract: When a flexible fuzzy rule structure such as those with antecedent in conjunctive normal form is used, the interpretability of the obtained fuzzy model is significantly improved. However, some important problems appear related to the interaction among this set of rules. Indeed, it is relatively easy to get inconsistencies, lack of completeness, redundancies, etc. Generally, these properties are ignored or mildly faced. This paper, however, focuses on the design of a multiobjective genetic algorithm that properly considers all these properties thus ensuring an effective search space exploration and generation of highly legible and accurate fuzzy models.

Building an Associative Classifier Based on Fuzzy Association Rules

Abstract: Classification based on association rules is considered to be effective and advantageous in many cases. However, there is a so-called "sharp boundary" problem in association rules mining with quantitative attribute domains. This paper aims at proposing an associative classification approach, namely Classification with Fuzzy Association Rules (CFAR), where fuzzy logic is used in partitioning the domains. In doing so, the notions of support and confidence are extended, along with the notion of compact set in dealing with rule redundancy and conflict. Furthermore, the corresponding mining algorithm is introduced and tested on benchmarking datasets. The experimental results revealed that CFAR generated better understandability in terms of fewer rules and smother boundaries than the traditional CBA approach while maintaining satisfactory accuracy.

Fuzzy Classification on Relational Databases

Abstract: The fuzzy logic theory proposed by Zadeh (1965) is based on intuitive reasoning and takes into account human subjectivity and imprecision. Unlike statistical data mining techniques such as cluster or regression analysis, fuzzy logic enables the use of nonnumerical values and introduces the notion of linguistic variables (Zadeh, 1975a, 1975b, 1975c). Using linguistic terms and variables hides AbstrAct

Intuitionistic fuzzy left k-ideals of semirings

Abstract: We introduce the notion of intuitionistic fuzzy left k-ideals of semirings and investigate their properties and connections with left k-ideals of the corresponding semirings Next we give some important characterizations of intuitionistic fuzzy left k-ideals of different type and describe various methods of constructions of such intuitionistic fuzzy sets Finally, we propose some natural classification of intuitionistic fuzzy left k-ideals