Another approach to reasoning about uncertainty, with a different mathematical basis, is fuzzy logic. Brief history: Standard classical (Boolean) logic (Aristotle, c 50BC; Boole, 1854) uses two possible truth values: • A statement may be true (truth value 1) or false (truth value 0) Łukasiewicz logic (early 20th century): three truth values: • 2, 1 and 0 represent, respectively, “true”, “false” and “unknown” or “irrelevant” • This was further extended to an infinite-valued logic, where real numbers in the range [0,1] represent varying degrees of truth. Only of academic interest, until... Lotfi Zadeh (1965) introduced fuzzy set theory and fuzzy logic, and promoted these as a way of reasoning about uncertainty in computer systems.

Fuzzy SETS AND FUZZY LOGIC

This paper deals with the quadratic stability conditions of fuzzy control systems that relax the existing conditions reported in the previous literatures. Two new conditions are proposed and shown to be useful in analyzing and designing fuzzy control systems. The first one employs the S-procedure to utilize information regarding the premise parts of the fuzzy systems. The next one enlarges the class of fuzzy control systems, whose stability is ensured by representing the interactions among the fuzzy subsystems in a single matrix and solving it by linear matrix inequality. The relationships between the suggested stability conditions and the conventional well-known stability conditions reported in the previous literatures are also discussed, and it is shown in a rigorous manner that the second condition of this paper includes the conventional conditions. Finally, some examples and simulation results are presented to illustrate the effectiveness of the stability conditions.

New approaches to relaxed quadratic stability condition of fuzzy control systems

This paper presents a review of the developments in the field of diagnosis of electrical machines and drives based on artificial intelligence (AI). It covers the application of expert systems, artificial neural networks (ANNs), and fuzzy logic systems that can be integrated into each other and also with more traditional techniques. The application of genetic algorithms is considered as well. In general, a diagnostic procedure starts from a fault tree developed on the basis of the physical behavior of the electrical system under consideration. In this phase, the knowledge of well-tested models able to simulate the electrical machine in different fault conditions is fundamental to obtain the patterns characterizing the faults. The fault tree navigation performed by an expert system inference engine leads to the choice of suitable diagnostic indexes, referred to a particular fault, and relevant to build an input data set for specific AI (NNs, fuzzy logic, or neuro-fuzzy) systems. The discussed methodologies, that play a general role in the diagnostic field, are applied to an induction machine, utilizing as input signals the instantaneous voltages and currents. In addition, the supply converter is also considered to incorporate in the diagnostic procedure the most typical failures of power electronic components. A brief description of the various AI techniques is also given; this highlights the advantages and the limitations of using AI techniques. Some applications examples are also discussed and areas for future research are also indicated.

Recent developments of induction motor drives fault diagnosis using AI techniques

Preface. 1 Introduction. 1.1 Characteristics of Expert Systems. 1.2 Neural Nets. 1.3 Symbolic Reasoning. 1.4 Developing a Rule-Based Expert System. 1.5 Fuzzy Rule-Based Systems. 1.6 Problems in Learning How to Construct Fuzzy Expert Systems. 1.7 Tools for Learning How to Construct Fuzzy Expert Systems. 1.8 Auxiliary Reading. 1.9 Summary. 1.10 Questions. 2 Rule-Based Systems: Overview. 2.1 Expert Knowledge: Rules and Data. 2.2 Rule Antecedent and Consequent. 2.3 Data-Driven Systems. 2.4 Run and Command Modes. 2.5 Forward and Backward Chaining. 2.6 Program Modularization and Blackboard Systems. 2.7 Handling Uncertainties in an Expert System. 2.8 Summary. 2.9 Questions. 3 Fuzzy Logic, Fuzzy Sets, and Fuzzy Numbers: I. 3.1 Classical Logic. 3.2 Elementary Fuzzy Logic and Fuzzy Propositions. 3.3 Fuzzy Sets. 3.4 Fuzzy Relations. 3.5 Truth Value of Fuzzy Propositions. 3.6 Fuzzification and Defuzzification. 3.7 Questions. 4 Fuzzy Logic, Fuzzy Sets, and Fuzzy Numbers: II. 4.1 Introduction. 4.2 Algebra of Fuzzy Sets. 4.3 Approximate Reasoning. 4.4 Hedges. 4.5 Fuzzy Arithmetic. 4.6 Comparisons between Fuzzy Numbers. 4.7 Fuzzy Propositions. 4.8 Questions. 5 Combining Uncertainties. 5.1 Generalizing AND and OR Operators. 5.2 Combining Single Truth Values. 5.3 Combining Fuzzy Numbers and Membership Functions. 5.4 Bayesian Methods. 5.5 The Dempster-Shafer Method. 5.6 Summary. 5.7 Questions. 6 Inference in an Expert System I. 6.1 Overview. 6.2 Types of Fuzzy Inference. 6.3 Nature of Inference in a Fuzzy Expert System. 6.4 Modification and Assignment of Truth Values. 6.5 Approximate Reasoning. 6.6 Tests of Procedures to Obtain the Truth Value of a Consequent from the Truth Value of Its Antecedent. 6.7 Summary. 6.8 Questions. 7 Inference in a Fuzzy Expert System II: Modification of Data and Truth Values. 7.1 Modification of Existing Data by Rule Consequent Instructions. 7.2 Modification of Numeric Discrete Fuzzy Sets: Linguistic Variables and Linguistic Terms. 7.3 Selection of Reasoning Type and Grade-of-Membership Initialization. 7.4 Fuzzification and Defuzzification. 7.5 Non-numeric Discrete Fuzzy Sets. 7.6 Discrete Fuzzy Sets: Fuzziness, Ambiguity, and Contradiction. 7.7 Invalidation of Data: Non-monotonic Reasoning. 7.8 Modification of Values of Data. 7.9 Modeling the Entire Rule Space. 7.10 Reducing the Number of Classification Rules Required in the Conventional Intersection Rule Configuration. 7.11 Summary. 7.12 Questions. 8 Resolving Contradictions: Possibility and Necessity. 8.1 Definition of Possibility and Necessity. 8.2 Possibility and Necessity Suitable for MultiStep Rule-Based Fuzzy Reasoning. 8.3 Modification of Truth Values During a Fuzzy Reasoning Process. 8.4 Formulation of Rules for Possibility and Necessity. 8.5 Resolving Contradictions Using Possibility in a Necessity-Based System. 8.6 Summary. 8.7 Questions. 9 Expert System Shells and the Integrated Development Environment (IDE). 9.1 Overview. 9.2 Help Files. 9.3 Program Editing. 9.4 Running the Program. 9.5 Features of General-Purpose Fuzzy Expert Systems. 9.6 Program Debugging. 9.7 Summary. 9.8 Questions. 10 Simple Example Programs. 10.1 Simple FLOPS Programs. 10.2 Numbers.fps. 10.3 Sum.fps. 10.4 Sum.par. 10.5 Comparison of Serial and Parallel FLOPS. 10.6 Membership Functions, Fuzzification and Defuzzification. 10.7 Summary. 10.8 Questions. 11 Running and Debugging Fuzzy Expert Systems I: Parallel Programs. 11.1 Overview. 11.2 Debugging Tools. 11.3 Debugging Short Simple Programs. 11.4 Isolating the Bug: System Modularization. 11.5 The Debug Run. 11.6 Interrupting the Program for Debug Checks. 11.7 Locating Program Defects with Debug Commands. 11.8 Summary. 11.9 Questions. 12 Running and Debugging Expert Systems II: Sequential Rule-Firing. 12.1 Data Acquisition: From a User Versus Automatically Acquired. 12.2 Ways of Solving a Tree-Search Problem. 12.3 Expert Knowledge in Rules auto1.fps. 12.4 Expert Knowledge in a Database: auto2.fps. 12.5 Other Applications of Sequential Rule Firing. 12.5.1 Missionaries and Cannibals. 12.6 Rules that Make Themselves Refireable: Runaway Programs and Recursion. 12.7 Summary. 12.8 Questions. 13 Solving "What?" Problems when the Answer is Expressed in Words. 13.1 General Methods. 13.2 Iris.par: What Species Is It? 13.3 Echocardiogram Pattern Recognition. 13.4 Schizo.par. 13.5 Discussion. 13.6 Questions. 14 Programs that Can Learn from Experience. 14.1 General Methods. 14.2 Pavlov1.par: Learning by Adding Rules. 14.3 Pavlov2.par: Learning by Adding Facts to Long-Term Memory. 14.4 Defining New Data Elements and New: RULEGEN.FPS. 14.5 Most General Way of Creating New Rules and Data Descriptors. 14.6 Discussion. 14.7 Questions. 15 Running On-Line in Real-Time. 15.1 Overview of On-Line Real-Time Work. 15.2 Input/Output On-Line in Real-Time. 15.3 On-Line Real-Time Processing. 15.4 Types of Rules Useful in Real-Time On-Line Work. 15.5 Memory Management. 15.6 Development of On-Line Real-Time Programs. 15.7 Speeding Up a Program. 15.8 Debugging Real-Time Online Programs. 15.9 Discussion. 15.10 Questions. Appendix. Answers. References. Index.

Fuzzy expert systems and fuzzy reasoning

http://temp.ecosystemassessments.net/system/resources/W1siZiIsIjIwMTUvMDUvMTMvMDgvMTIvMzcvNDc2L1VORVBfRVNWYWx1YXRpb25fNl9FY29sb2dpY2FsX0Vjb25vbWljc19SZXZpZXdfbXVsdGlfY3JpdGVyaWEucGRmIl1d/UNEP_ESValuation_6_Ecological%20Economics%20Review%20multi-criteria.pdf

Charles Aschmann

Papers

Applied fuzzy systems