Rafik A. Aliev

Fuzzy-genetic approach to aggregate production-distribution planning in supply chain management

Aggregate production-distribution planning (APDP) is one of the most important activities in supply chain management (SCM). When solving the problem of APDP, we are usually faced with uncertain market demands and capacities in production environment, imprecise process times, and other factors introducing inherent uncertainty to the solution. Using deterministic and stochastic models in such conditions may not lead to fully satisfactory results. Using fuzzy models allows us to remove this drawback. It also facilitates the inclusion of expert knowledge. However, the majority of existing fuzzy models deal only with separate aggregate production planning without taking into account the interrelated nature of production and distribution systems. This limited approach often leads to inadequate results. An integration of the two interconnected processes within a single production-distribution model would allow better planning and management. Due to the need for a joint general strategic plan for production and distribution and vague planning data, in this paper we develop a fuzzy integrated multi-period and multi-product production and distribution model in supply chain. The model is formulated in terms of fuzzy programming and the solution is provided by genetic optimization (genetic algorithm). The use of the interactive aggregate production-distribution planning procedure developed on the basis of the proposed fuzzy integrated model with fuzzy objective function and soft constraints allows sound trade-off between the maximization of profit and fillrate. The experimental results demonstrate high efficiency of the proposed method.

Fuzzy logic-based generalized decision theory with imperfect information

The existing decision models have been successfully applied to solving many decision problems in management, business, economics and other fields, but nowadays arises a need to develop more realistic decision models. The main drawback of the existing utility theories starting from von Neumann-Moregnstern expected utility to the advanced non-expected models is that they are designed for laboratory examples with simple, well-defined gambles which do not adequately enough reflect real decision situations. In real-life decision making problems preferences are vague and decision-relevant information is imperfect as described in natural language (NL). Vagueness of preferences and imperfect decision relevant information require using suitable utility model which would be fundamentally different to the existing precise utility models. Precise utility models cannot reflect vagueness of preferences, vagueness of objective conditions and outcomes, imprecise beliefs, etc. The time has come for a new generation of decision theories. In this study, we propose a decision theory, which is capable to deal with vague preferences and imperfect information. The theory discussed here is based on a fuzzy-valued non-expected utility model representing linguistic preference relations and imprecise beliefs.

Soft Computing and its Applications in Business and Economics

1 Introduction to Soft Computing.- 1.1 Basic Concepts of Soft Computing.- 2.2 Combination of Constituents of Soft Computing.- References.- 2. Constituent Methodologies of Soft Computing.- 2.1 Elements of Fuzzy Sets Theory.- 2.1.1 Fuzzy Sets and Operations Over Them.- 2.2.2 Mathematics of Fuzzy Computing.- 2.1.3 Fuzzy Logic and Approximate Reasoning.- 2.1.4 Probability and Fuzziness.- 2.1.5 Fuzzy Sets and Possibility Theory.- 2.2 Foundations of Neurocomputing.- 2.2.1 Basic Types and Architectures of Neural Networks.- 2.2.2 Learning Algorithms of Neural Networks.- 2.3 Probabilistic Computing.- 2.3.1 Bayesian Approach.- 2.3.2 Dempster-Shafer Theory of Belief.- 2.4 Evolutionary Computing.- 2.4.1 Evolution Programming and Genetic Algorithms.- 2.4.2 Computation with Genetic Algorithms.- 2.5 Chaotic Computing.- 2.5.1 Elements of Chaotic Computing.- 2.5.2 Non-Linear Dynamics and Chaotic Analysis.- 2.5.3 Empirical Chaotic Analysis.- References.- 3. Emerging Combined Soft Computing Technologies.- 3.1 Neuro-Fuzzy Technology.- 3.2 Neuro-Genetic Approach.- 3.3 Fuzzy Genetic Paradigm.- 3.4 Genetic Algorithms with Fuzzy Logic.- 3.5 Neuro-Fuzzy-Genetic Paradigm.- 3.6 Multi-Agent Distributed Intelligent Systems Paradigm.- 3.7 Computing with Words Technology.- References.- 4. Soft Computing Technologies in Business and Economic Forecasting.- 4.1 Neuro-Computing and Forecasting.- 4.2 Fuzzy Time Series Based Forecasting.- 4.3 Fuzzy Delphi Method.- 4.4 Soft Computing Based Forecasting Complex Time Series.- 4.5 Soft Computing Based Prediction Ensemble for Forecasting in Chaotic Time Series.- References.- 5 Soft Computing Based Decision Making and DSS.- 5.1 Fuzzy Linear Programming.- 5.2 Evolutionary Algorithm Based Fuzzy Linear Programming.- 5.3 Fuzzy Chaos Approach to Fuzzy Linear Programming Problem.- 5.4 Fuzzy-Probabilistic Scheduling for Oil Refinery.- 5.5 Fuzzy Decision Making.- 5.6 Multi-Agent Distributed Intelligent System Based on Fuzzy Decision Making.- 5.7 Soft Computing and Data Mining.- 5.8 Soft Computing Based Multi-Agent Marketing DSS.- 5.9 Hybrid DSS Based on Simulation and Genetic Algorithms.- 5.10 Soft Computing Based Alternatives Generations by Decision Support Systems.- References.- 6 Soft Computing in Marketing.- 6.1 Marketing Analysis of a Customers Purchasing Behavior.- 6.2 Customer Credit Evaluation.- 6.3 Soft Computing Based Fraud Detection.- 6.4 Fuzzy Evaluation of Service Quality.- 6.5 Application of Fuzzy Programming to Hospitals Service Performance Evaluating.- References.- 7 Soft Computing Applications in Operations Management.- 7.1 Application of Fuzzy Logic in Transportation Logistics.- 7.2 Scheduling Fuzzy Expert Systems with Probabilistic Reasoning for Oil Refineries.- 7.3 Detection and Withdrawal of Defect Parts in the Computer Aided Manufacturing of Evaporators.- 7.4 Genetic Algorithms Based Fuzzy Regression Analysis and Its Applications for Quality Evaluation.- 7.5 An Intelligent System for Diagnosis of the Oil-Refinery Plant.- 7.6 Neuro-Fuzzy Pattern Recognition in Manufacturing.- 7.7 Soft Computing Based Inventory Control.- 7.8 Fuzzy Project Scheduling.- 7.9 CW Based Decision Analysis on Risk Assessment of an Engineering Project.- References.- 8 Soft Computing in Finance.- 8.1 Soft Computing Based Stock Market Predicting System.- 8.2 Fuzzy Nonlinear Programming Approach to Portfolio Selection.- 8.3 Neuro-Fuzzy Approach to Modeling of Credit Risk in Trading Portfolios.- 8.4 A Fuzzy Approach to the Credit Portfolio Constructing.- 8.5 Soft Computing Based TDSS Multi-Agent Systems in Finance.- 8.6 Neural Nonlinear Modeling for Risk Management in Banking.- 8.7 Neuro-Fuzzy Loan Assessment System.- References.- 9 Soft Computing in Electronic Business.- 9.1 A Multi-Agent System for E-Commerce Decisions.- 9.2 Soft Computing and Personalization of Electronic Commerce.- 9.3 Risk Analysis in Electronic Commerce Using Fuzzy Weighted Average.- References.

Evolutionary algorithm-based learning of fuzzy neural networks. Part 2: Recurrent fuzzy neural networks

Fuzzy neural networks (FNN) as opposed to neuro-fuzzy systems, whose main task is to process numerical relationships, can process both numerical (measurement based) information and perception based information. In spite of great importance of fuzzy feed-forward and recurrent neural networks for solving wide range of real-world problems, today there are no effective training algorithm for them. Currently there are two approaches for training of FNN. First approach is based on application of the level-sets of fuzzy numbers and the back-propagation (BP) algorithm. The second approach involves using evolutionary algorithms to minimize error function and determine the fuzzy connection weights and biases. The method based on the second approach was proposed by the authors and published in Part 1 of this paper [R.A. Aliev, B. Fazlollahi, R. Vahidov, Genetic algorithm-based learning of fuzzy neural networks. Part 1: feed-forward fuzzy neural networks, Fuzzy Sets and Systems 118 (2001) 351-358]. In contrast to the BP and other supervised learning algorithms, evolutionary algorithms do not require nor use information about differentials, and hence, they are most effective in case where the derivative is very difficult to obtain or even unavailable. However, the main deficiency of the existing FNN based on the feed-forward architecture is its adherence to static problems. In case of dynamic or temporal problems there is a need for recurrent fuzzy neural networks (RFNN). Designing efficient training algorithms for RFNN has recently become an active research direction. In this paper we propose an effective differential evolution optimization (DEO) based learning algorithm for RFNN with fuzzy inputs, fuzzy weights and biases, and fuzzy outputs. The effectiveness of the proposed method is illustrated through simulation of benchmark forecasting and identification problems and comparisons with the existing methods. The suggested approach has also been used for real applications in an oil refinery plant for petrol production forecasting.

Genetic algorithm-based learning of fuzzy neural networks. Part 1: feed-forward fuzzy neural networks

In spite of great importance of fuzzy feed-forward and recurrent neural networks (FNN) for solving wide range of real-world problems, today there is no effective learning algorithm for FNN. In this paper we propose an effective genetic-based learning mechanism for FNN with fuzzy inputs, fuzzy weights expressed as LR-fuzzy numbers, and fuzzy outputs. The effectiveness of the proposed method is illustrated through simulation of fuzzy regression for quality evaluation and comparison with the widely used learning method based on α-cuts and fuzzy arithmetic. Finally, we demonstrate the use of the proposed learning procedure for calculating fuzzy-valued profit in an oligopolistic environment.

Logic-oriented neural networks for fuzzy neurocomputing

In this study, we concentrate on the fundamentals and essential development issues of logic-driven constructs of fuzzy neural networks. These networks, referred to as logic-oriented neural networks, constitute an interesting conceptual and computational framework that greatly benefits from the establishment of highly synergistic links between the technology of fuzzy sets (or granular computing, being more general) and neural networks. The most essential advantages of the proposed networks are twofold. First, the transparency of neural architectures becomes highly relevant when dealing with the mechanisms of efficient learning. Here the learning is augmented by the fact that domain knowledge could be easily incorporated in advance prior to any learning. This becomes possible given the compatibility between the architecture of the problem and the induced topology of the neural network. Second, once the training has been completed, the network can be easily interpreted and thus it directly translates into a series of truth-quantifiable logic expressions formed over a collection of information granules. The design process of the logic networks synergistically exploits the principles of information granulation, logic computing and underlying optimization including those biologically inspired techniques (such as particle swarm optimization, genetic algorithms and alike). We elaborate on the existing development trends, present key methodological pursuits and algorithms. In particular, we show how the logic blueprint of the networks is supported by the use of various constructs of fuzzy sets including logic operators, logic neurons, referential operators and fuzzy relational constructs.

DECISION THEORY WITH IMPRECISE PROBABILITIES

There is an extensive literature on decision making under uncertainty. Unfortunately, up to date there are no valid decision principles. Experimental evidence has repeatedly shown that widely used principle of maximization of expected utility has serious shortcomings. Utility function and nonadditive measures used in nonexpected utility models are mainly considered as real-valued functions whereas in reality decision-relevant information is imprecise and therefore is described in natural language. This applies, in particular, to imprecise probabilities expressed by terms such as likely, unlikely, probable, etc. The principal objective of the paper is the development of computationally effective methods of decision making with imprecise probabilities. We present representation theorems for a nonexpected fuzzy utility function under imprecise probabilities. We develop an effective decision theory when the environment of fuzzy events, fuzzy states, fuzzy relations and fuzzy constraints are characterized by imprecise probabilities. The suggested methodology is applied for a real-life decision-making problem.

Dynamic data mining technique for rules extraction in a process of battery charging

Battery charging controllers design and application is a growing industry direction. Fast and efficient charging of battery packs is a problem which is difficult and often expensive to solve using conventional techniques. The majority of existing works on intelligent charging systems are based on expert knowledge and heuristics. Not all features of the desired charging behavior can be attained by the hard-wired logic implemented by expert generated rules. Because the battery charging is a highly dynamic process and the chemical technology a battery uses varies significantly for different battery types, data mining technique can be of real importance for extracting the charging rules from the large databases, especially when the charging logic is to be continuously changed during the life of the battery dependent on the type and characteristics of the battery and utilization conditions. In this paper we use soft computing-based data mining technique for extraction of control rules for effective and fast battery charging process. The obtained rules were used for NiCd battery charging. The comparative performance evaluation was done among the existing charging control methods and the proposed system, which demonstrated a significant increase of performance (minimum charging time and minimum overheating) using the soft computing-based approach.

Z-Number-Based Linear Programming

Linear programming (LP) is the operations research technique frequently used in the fields of science, economics, business, management science, and engineering. Although it is investigated and applied for more than six decades, and LP models with different level of generalization of information about parameters including models with interval, fuzzy, generalized fuzzy, and random numbers are considered, until now there is no approach to account for reliability of information within the framework of LP.

Fundamentals of a Fuzzy-Logic-Based Generalized Theory of Stability

Stability is one of the fundamental concepts of complex dynamical systems including physical, economical, socioeconomical, and technical systems. In classical terms, the notion of stability inherently associates with any dynamical system and determines whether a system under consideration reaches equilibrium after being exposed to disturbances. Predominantly, this concept comes with a binary (Boolean) quantification (viz., we either quantify that systems are stable or not stable). While in some cases, this definition is well justifiable, with the growing complexity and diversity of systems one could seriously question the Boolean nature of the definition and its underlying semantics. This becomes predominantly visible in human-oriented quantification of stability in which we commonly encounter statements quantifying stability through some linguistic terms such as, e.g., absolutely unstable, highly unstable,. . ., absolutely stable, and alike. To formulate human-oriented definitions of stability, we may resort ourselves to the use of a so-called precisiated natural language, which comes as a subset of natural language and one of whose functions is redefining existing concepts, such as stability, optimality, and alike. Being prompted by the discrepancy of the definition of stability and the Boolean character of the concept itself, in this paper, we introduce and develop a generalized theory of stability (GTS) for analysis of complex dynamical systems described by fuzzy differential equations. Different human-centric definitions of stability of dynamical systems are introduced. We also discuss and contrast several fundamental concepts of fuzzy stability, namely, fuzzy stability of systems, binary stability of fuzzy system, and binary stability of systems by showing that all of them arise as special cases of the proposed GTS. The introduced definitions offer an important ability to quantify the concept of stability using some continuous quantification (that is through the use of degrees of stability). In this manner, we radically depart from the previous binary character of the definition. We establish some criteria concerning generalized stability for a wide class of continuous dynamical systems. Next, we present a series of illustrative examples which demonstrate the essence of the concept, and at the same time, stress that the existing Boolean techniques are not capable of capturing the essence of linguistic stability. We also apply the obtained results to investigate the stability of an economical system and show its usefulness in the design of nonlinear fuzzy control systems given some predefined degree of stability.