Alexander P. Rotshtein

Cause and effect analysis by fuzzy relational equations and a genetic algorithm

This paper proposes using a genetic algorithm as a tool to solve the fault diagnosis problem. The fault diagnosis problem is based on a cause and effect analysis which is formally described by fuzzy relations. Fuzzy relations are formed on the basis of expert assessments. Application of expert fuzzy relations to restore and identify the causes through the observed effects requires the solution to a system of fuzzy relational equations. In this study this search for a solution amounts to solving a corresponding optimization problem. An optimization algorithm is based on the application of genetic operations of crossover, mutation and selection. The genetic algorithm suggested here represents an application in expert systems of fault diagnosis and quality control.

Diagnosis Problem Solving Using Fuzzy Relations

This paper deals with the restoration and the identification of the causes (diagnoses) through the observed effects (symptoms) on the basis of fuzzy relations and Zadehs compositional rule of inference. We propose an approach for building fuzzy systems of diagnosis, which enables solving fuzzy relational equations together with design and tuning of fuzzy relations on the basis of expert and experimental information. The essence of tuning consists of the selection such membership functions for fuzzy causes and effects, and also fuzzy relations, which minimize the difference between model and experimental results of diagnosis. The genetic algorithm is used for solving the optimization problem. The proposed approach is illustrated by the computer experiment and the real example of diagnosis.

Fuzzy Evidence in Identification, Forecasting and Diagnosis

The purpose of this book is to presenta methodology for designing and tuning fuzzyexpert systems in order to identify nonlinear objects; that is, to build input-output models using expert and experimental information. The results of these identifications are used for direct and inverse fuzzy evidence in forecasting and diagnosis problem solving. The book is organised as follows: Chapter 1 presents the basic knowledge about fuzzy sets, genetic algorithms and neural nets necessary for a clear understanding of the rest of this book. Chapter 2analyzesdirect fuzzy inference based on fuzzy if-then rules. Chapter 3is devoted to the tuning of fuzzy rulesfor direct inference using genetic algorithms and neural nets. Chapter4presents models and algorithms for extracting fuzzy rules from experimental data. Chapter 5 describesa method for solving fuzzy logic equationsnecessary for the inverse fuzzy inference indiagnostic systems. Chapters6 and 7 aredevoted to inverse fuzzy inferencebased on fuzzy relations andfuzzy rules. Chapter 8presents a method for extracting fuzzy relations from data. Allthe algorithms presented in Chapters 2-8 arevalidated by computer experiments and illustrated bysolving medical and technicalforecasting anddiagnosis problems. Finally, Chapter 9includes applications of the proposed methodology in dynamicand inventory control systems, prediction of results of football games,decisionmaking in road accident investigations, project management and reliability analysis.

Fuzzy multicriteria choice among alternatives: Worst-case approach

A method of multicriteria choice among alternatives under uncertainty is proposed. The method is based on the Bellman-Zadeh principle of intersection of fuzzy criteria and the Saaty 1–9 linguistic ratio scale. The novelty of the method consists in avoiding the laborious procedures of generating and processing paired comparison matrices. Instead of them, special relations based on comparison with the worst alternative and with the least important criterion are used. For the purposes of illustration, the method is illustrated by the problem of choosing a car.

Genetic Algorithm for Fuzzy Logical Equations Solving in Diagnostic Expert Systems

Application of the inverse logical inference in the expert systems of diagnosis is considered. The inverse logical inference allows to restore the causes by observed consequences using fuzzy relational matrix. Diagnosis decision finding requires fuzzy logical equations system solution. The genetic algorithm of optimization based on crossover, mutation and selection of the initial set of chromosomes is proposed for fuzzy logical equations system solving. Computer simulation illustrates the algorithm efficiency. The suggested genetic algorithm can find application in expert systems of technical and medical diagnosis and quality control.

Fuzzy algorithmic simulation of reliability: Control and correction resource optimization

Fuzzy models of reliability of algorithmic procedure based on membership functions that depend on parameters affecting the algorithm correct performance are considered. Statements of optimization problems of correction and control resources of linear algorithms with respect to reliability-cost criteria are formalized. The solution of the stated problems is illustrated by an example. The novelty of the approach consists in the fact that it does not use any statistical data and optimize parametric reliability of the system by choosing the control and correction resources in order to ensure the required or maximal possible correction level of performance for the given instability of input parameters.

Algebra of algorithms and fuzzy logic in system reliability analysis

A method for simulating system reliability based on the algebra of regular algorithms and fuzzy set theory is proposed. The reliability model is supported by a logic-algorithmic description of events associated with faults (failures and errors) occurred, detected and removed while the system is executing the task. The initial data for the simulation are membership functions and fuzzy IF-THEN rules that characterize whether the operator and logical elements of the model are executed correctly depending on the measurable parameters and influencing factors. Contraction-extension operations for membership functions help take into account the quality of checking and correction procedures. The result of application of the method is a multidimensional membership function that gives the distribution of correctness of task execution, depending on the parameters of objects and processes that compose the system. A fuzzy algorithmic algebra that represents formal rules of transition from operations in the algebra of regular algorithms to the corresponding operations over membership functions of operators and conditions is developed to implement the method.

Solution of a Diagnostics Problem on the Basis of Fuzzy Relations and a Genetic Algorithm

The use of backward logical inference in expert diagnostic systems is considered. To solve systems of fuzzy logic equations, a genetic algorithm based on the operations of crossover, mutation, and selection of an initial set of chromosomes is proposed. The efficiency of the algorithm proposed is illustrated by computer simulation.

Expert rules refinement by solving fuzzy relational equations

In this paper, an approach to expert rules refinement within the framework of fuzzy relational calculus is proposed. The system of fuzzy rules can be rearranged as a collection of linguistic solutions of fuzzy relational equations using the composite system of fuzzy terms. Resolution of fuzzy relational equations guarantees the optimal number of fuzzy rules for each output fuzzy term and the optimal geometry of input fuzzy terms for each linguistic solution.

Reliability Modeling and Optimization Using Fuzzy Logic and Chaos Theory

Fuzzy sets membership functions integrated with logistic map as the chaos generator were used to create reliability bifurcations diagrams of the system with redundancy of the components. This paper shows that increasing in the number of redundant components results in a postponement of the moment of the first bifurcation which is considered as most contributing to the loss of the reliability. The increasing of redundancy also provides the shrinkage of the oscillation orbit of the level of the system’s membership to reliable state. The paper includes the problem statement of redundancy optimization under conditions of chaotic behavior of influencing parameters and genetic algorithm of this problem solving. The paper shows the possibility of chaos-tolerant systems design with the required level of reliability.