On generating the set of nondominated solutions of a linear programming problem with parameterized fuzzy numbers

The paper presents a new method for solving fully fuzzy linear programming problems with inequality constraints and parameterized fuzzy numbers, by means of solving multiobjective linear programming problems. The equivalence is proven between the set of nondominated solutions of the fully fuzzy linear programming problem and the set of weakly efficient solutions of the considered and related multiobjective linear problem. The whole set of nondominated solutions for a fully fuzzy linear programming problem is explicitly obtained by means of a finite generator set.The first author was partially supported by the research project MTM2017-89577-P (MINECO, Spain), and the second author was partially supported by Spanish Ministry of Economy and Competitiveness through grants AYA2016-75931-C2-1-P, AYA2015-68012-C2-1, AYA2014-57490-P, AYA2013-40611-P, and from the Consejería de Educación y Ciencia (Junta de Andalucía) through TIC-101, TIC-4075 and TIC-114

A proposal on reasoning methods in fuzzy rule-based classification systems

AbstractFuzzy Rule-Based Systems have been succesfully applied to pattern classification problems. In this type of classification systems, the classical Fuzzy Reasoning Method (FRM) classifies a new example with the consequent of the rule with the greatest degree of association. By using this reasoning method, we lose the information provided by the other rules with different linguistic labels which also represent this value in the pattern attribute, although probably to a lesser degree. The aim of this paper is to present new FRMs which allow us to improve the system performance, maintaining its interpretability. The common aspect of the proposals is the participation, in the classification of the new pattern, of the rules that have been fired by such pattern. We formally describe the behaviour of a general reasoning method, analyze six proposals for this general model, and present a method to learn the parameters of these FRMs by means of Genetic Algorithms, adapting the inference mechanism to the set of rules. Finally, to show the increase of the system generalization capability provided by the proposed FRMs, we point out some results obtained by their integration in a fuzzy rule generation process

A proposal on reasoning methods in fuzzy rule-based classification systems

Fuzzy Rule-Based Systems have been succesfully applied to pattern classification problems. In this type of classification systems, the classical Fuzzy Reasoning Method (FRM) classifies a new example with the consequent of the rule with the greatest degree of association. By using this reasoning method, we lose the information provided by the other rules with different linguistic labels which also represent this value in the pattern attribute, although probably to a lesser degree. The aim of this paper is to present new FRMs which allow us to improve the system performance, maintaining its interpretability. The common aspect of the proposals is the participation, in the classification of the new pattern, of the rules that have been fired by such pattern. We formally describe the behaviour of a general reasoning method, analyze six proposals for this general model, and present a method to learn the parameters of these FRMs by means of Genetic Algorithms, adapting the inference mechanism to the set of rules. Finally, to show the increase of the system generalization capability provided by the proposed FRMs, we point out some results obtained by their integration in a fuzzy rule generation process.CICYT TIC96-077

Machine Learning Methods for Fuzzy Pattern Tree Induction

This thesis elaborates on a novel approach to fuzzy machine learning, that is, the combination of machine learning methods with mathematical tools for modeling and information processing based on fuzzy logic. More specifically, the thesis is devoted to so-called fuzzy pattern trees, a model class that has recently been introduced for representing dependencies between input and output variables in supervised learning tasks, such as classification and regression. Due to its hierarchical, modular structure and the use of different types of (nonlinear) aggregation operators, a fuzzy pattern tree has the ability to represent such dependencies in a very exible and compact way, thereby offering a reasonable balance between accuracy and model transparency. The focus of the thesis is on novel algorithms for pattern tree induction, i.e., for learning fuzzy pattern trees from observed data. In total, three new algorithms are introduced and compared to an existing method for the data-driven construction of pattern trees. While the first two algorithms are mainly geared toward an improvement of predictive accuracy, the last one focuses on eficiency aspects and seeks to make the learning process faster. The description and discussion of each algorithm is complemented with theoretical analyses and empirical studies in order to show the effectiveness of the proposed solutions

Fuzzy Sets, Fuzzy Logic and Their Applications

The present book contains 20 articles collected from amongst the 53 total submitted manuscripts for the Special Issue “Fuzzy Sets, Fuzzy Loigic and Their Applications” of the MDPI journal Mathematics. The articles, which appear in the book in the series in which they were accepted, published in Volumes 7 (2019) and 8 (2020) of the journal, cover a wide range of topics connected to the theory and applications of fuzzy systems and their extensions and generalizations. This range includes, among others, management of the uncertainty in a fuzzy environment; fuzzy assessment methods of human-machine performance; fuzzy graphs; fuzzy topological and convergence spaces; bipolar fuzzy relations; type-2 fuzzy; and intuitionistic, interval-valued, complex, picture, and Pythagorean fuzzy sets, soft sets and algebras, etc. The applications presented are oriented to finance, fuzzy analytic hierarchy, green supply chain industries, smart health practice, and hotel selection. This wide range of topics makes the book interesting for all those working in the wider area of Fuzzy sets and systems and of fuzzy logic and for those who have the proper mathematical background who wish to become familiar with recent advances in fuzzy mathematics, which has entered to almost all sectors of human life and activity

Parametric Extension of the Most Preferred OWA Operator and Its Application in Search Engine's Rank

Most preferred ordered weighted average (MP-OWA) operator is a new kind of neat (dynamic weight) OWA operator in the aggregation operator families. It considers the preferences of all alternatives across the criteria and provides unique aggregation characteristics in decision making. In this paper, we propose the parametric form of the MP-OWA operator to deal with the uncertainty preference information, which includes MP-OWA operator as its special case, and it also includes the most commonly used maximum, minimum, and average aggregation operators. A special form of parametric MP-OWA operator with power function is proposed. Some properties of the parametric MP-OWA operator are provided and the advantages of them in decision making problems are summarized. The new proposed parametric MP-OWA operator can grasp the subtle preference information of the decision maker according to the application context through multiple aggregation results. They are applied to rank search engines considering the relevance of the retrieved queries. An search engine ranking example illustrates the application of parametric MP-OWA operator in various decision situations

FPGA design methodology for industrial control systems—a review

This paper reviews the state of the art of fieldprogrammable gate array (FPGA) design methodologies with a focus on industrial control system applications. This paper starts with an overview of FPGA technology development, followed by a presentation of design methodologies, development tools and relevant CAD environments, including the use of portable hardware description languages and system level programming/design tools. They enable a holistic functional approach with the major advantage of setting up a unique modeling and evaluation environment for complete industrial electronics systems. Three main design rules are then presented. These are algorithm refinement, modularity, and systematic search for the best compromise between the control performance and the architectural constraints. An overview of contributions and limits of FPGAs is also given, followed by a short survey of FPGA-based intelligent controllers for modern industrial systems. Finally, two complete and timely case studies are presented to illustrate the benefits of an FPGA implementation when using the proposed system modeling and design methodology. These consist of the direct torque control for induction motor drives and the control of a diesel-driven synchronous stand-alone generator with the help of fuzzy logic

Development of FPGA based Standalone Tunable Fuzzy Logic Controllers

Soft computing techniques differ from conventional (hard) computing, in that unlike hard computing, it is tolerant of imprecision, uncertainty, partial truth, and approximation. In effect, the role model for soft computing is the human mind and its ability to address day-to-day problems. The principal constituents of Soft Computing (SC) are Fuzzy Logic (FL), Evolutionary Computation (EC), Machine Learning (ML) and Artificial Neural Networks (ANNs). This thesis presents a generic hardware architecture for type-I and type-II standalone tunable Fuzzy Logic Controllers (FLCs) in Field Programmable Gate Array (FPGA). The designed FLC system can be remotely configured or tuned according to expert operated knowledge and deployed in different applications to replace traditional Proportional Integral Derivative (PID) controllers. This re-configurability is added as a feature to existing FLCs in literature. The FLC parameters which are needed for tuning purpose are mainly input range, output range, number of inputs, number of outputs, the parameters of the membership functions like slope and center points, and an If-Else rule base for the fuzzy inference process. Online tuning enables users to change these FLC parameters in real-time and eliminate repeated hardware programming whenever there is a need to change. Realization of these systems in real-time is difficult as the computational complexity increases exponentially with an increase in the number of inputs. Hence, the challenge lies in reducing the rule base significantly such that the inference time and the throughput time is perceivable for real-time applications. To achieve these objectives, Modified Rule Active 2 Overlap Membership Function (MRA2-OMF), Modified Rule Active 3 Overlap Membership Function (MRA3-OMF), Modified Rule Active 4 Overlap Membership Function (MRA4-OMF), and Genetic Algorithm (GA) base rule optimization methods are proposed and implemented. These methods reduce the effective rules without compromising system accuracy and improve the cycle time in terms of Fuzzy Logic Inferences Per Second (FLIPS). In the proposed system architecture, the FLC is segmented into three independent modules, fuzzifier, inference engine with rule base, and defuzzifier. Fuzzy systems employ fuzzifier to convert the real world crisp input into the fuzzy output. In type 2 fuzzy systems there are two fuzzifications happen simultaneously from upper and lower membership functions (UMF and LMF) with subtractions and divisions. Non-restoring, very high radix, and newton raphson approximation are most widely used division algorithms in hardware implementations. However, these prevalent methods have a cost of more latency. In order to overcome this problem, a successive approximation division algorithm based type 2 fuzzifier is introduced. It has been observed that successive approximation based fuzzifier computation is faster than the other type 2 fuzzifier. A hardware-software co-design is established on Virtex 5 LX110T FPGA board. The MATLAB Graphical User Interface (GUI) acquires the fuzzy (type 1 or type 2) parameters from users and a Universal Asynchronous Receiver/Transmitter (UART) is dedicated to data communication between the hardware and the fuzzy toolbox. This GUI is provided to initiate control, input, rule transfer, and then to observe the crisp output on the computer. A proposed method which can support canonical fuzzy IF-THEN rules, which includes special cases of the fuzzy rule base is included in Digital Fuzzy Logic Controller (DFLC) architecture. For this purpose, a mealy state machine is incorporated into the design. The proposed FLCs are implemented on Xilinx Virtex-5 LX110T. DFLC peripheral integration with Micro-Blaze (MB) processor through Processor Logic Bus (PLB) is established for Intellectual Property (IP) core validation. The performance of the proposed systems are compared to Fuzzy Toolbox of MATLAB. Analysis of these designs is carried out by using Hardware-In-Loop (HIL) test to control various plant models in MATLAB/Simulink environments

Fuzzy Mathematics

This book provides a timely overview of topics in fuzzy mathematics. It lays the foundation for further research and applications in a broad range of areas. It contains break-through analysis on how results from the many variations and extensions of fuzzy set theory can be obtained from known results of traditional fuzzy set theory. The book contains not only theoretical results, but a wide range of applications in areas such as decision analysis, optimal allocation in possibilistics and mixed models, pattern classification, credibility measures, algorithms for modeling uncertain data, and numerical methods for solving fuzzy linear systems. The book offers an excellent reference for advanced undergraduate and graduate students in applied and theoretical fuzzy mathematics. Researchers and referees in fuzzy set theory will find the book to be of extreme value