-
[show abstract]
[hide abstract]
ABSTRACT: Decision-making under uncertainty has evolved into a mature field. However, in most parts of the existing decision theory,
one assumes decision makers have complete decision-relevant information. The standard framework is not capable to deal with
partial or fuzzy information, whereas, in reality, decision-relevant information about outcomes, probabilities, preferences
etc is inherently imprecise and as such described in natural language (NL). Nowadays, there is no decision theory with second-order
uncertainty in existence albeit real-world uncertainties fall into this category. This applies, in particular, to imprecise
probabilities expressed by terms such as likely, unlikely, probable, usually etc. We call such imprecise evaluations second-order information granules.
In this study, we develop a decision theory with second-order information granules. The first direction we consider is decision
making with fuzzy probabilities. The proposed theory differs from the existing ones as one that accumulates non-expected utility
paradigm with NL-described decision-relevant information. Linguistic preference relations and fuzzy utility functions are
used instead of their classical counterparts as forming a more adequate description of human preferences expressed under fuzzy
probabilities. Fuzzy probability distribution is incorporated into the suggested fuzzy utility model by means of a fuzzy number-valued
fuzzy measure instead of a real-valued non-additive probability. We provide representation theorems for a fuzzy utility function
described by a fuzzy number-valued Choquet integral with a fuzzy number-valued integrand and a fuzzy number-valued fuzzy measure.
The proposed theory is intended to solve decision problems when the environment of fuzzy states and fuzzy outcomes are characterized
by fuzzy probabilities. As the second direction in this realm we consider hierarchical imprecise probability models. Such
models allow us to take into account imprecision and imperfection of our knowledge, expressed by interval values of probabilities
of states of nature and degrees of confidence associated with such values. A decision-making process analysis and a choice
of the most preferable alternative subject to variation of intervals at the lower and upper levels of models and the types
of distribution on the sets of random values of probabilities of states of nature is also of significant interest.
We apply the developed theories and methodologies to solving real-world economic decision-making problems. The obtained results
show validity of the proposed approaches.
KeywordsDecision Making–Imprecise Probabilities–Fuzzy Utility–Fuzzy Function–Fuzzy Measure–Linguistic Preference–Second-Order Uncertainty–Choquet Integral
04/2011: pages 117-153;
-
[show abstract]
[hide abstract]
ABSTRACT: Experimental evidence has repeatedly shown that the widely used principle of maximization of expected utility has serious shortcomings. Non-expected utility theory suggests more adequate models. However, in these models utility functions and probabilities are mainly considered as real-valued functions whereas in reality human preferences are imprecise being described in natural language (NL). Nowadays a methodology for dealing with second-order uncertainty, or uncertainty<sup>2</sup> is not available, whereas, real-world uncertainties mainly fall into this category. In this paper we present an effective decision theory under uncertainty<sup>2</sup> when the environment of fuzzy events and fuzzy states are characterized by imprecise probabilities. The proposed theory includes a non-expected fuzzy utility function represented by a fuzzy integral with fuzzy-number-valued fuzzy measure generated by imprecise probabilities. The suggested theory encompasses the classical utility based decision analysis, cumulative Prospect theory and Choquet expected utility on bipolar scales. We apply this methodology for solving a real-life business problem.
Soft Computing, Computing with Words and Perceptions in System Analysis, Decision and Control, 2009. ICSCCW 2009. Fifth International Conference on; 10/2009
-
[show abstract]
[hide abstract]
ABSTRACT: 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 quantificati-
-
on (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.
IEEE Transactions on Systems Man and Cybernetics Part B (Cybernetics) 09/2009; · 3.08 Impact Factor
-
[show abstract]
[hide abstract]
ABSTRACT: In spite of great importance of fuzzy neural networks for solving wide range of real-world problems, unfortunately, little progress has been made in their development. In this study we have discussed recurrent neural networks with fuzzy weights and biases as adjustable parameters and internal feedback loops, which allows capturing dynamic response of a system without using external feedback through delays. In this case all the nodes are able to process linguistic information. As the main problem regarding fuzzy and recurrent fuzzy neural networks that limits their application range is the difficulty of proper adjustment of fuzzy weights and biases, we put an emphasize on the RFNN training algorithm. We have proposed the standard DEO-based method for learning of recurrent fuzzy neural network. The optimization method, customized for RFNN training, compares favorably with the existing gradient-based error minimization method as it is less complex and is more likely to locate the global minimum of network error. As the method does not require derivative information, it is very effective in case when dealing with different distance functions. Also, the considered global optimization algorithm can provide high accuracy of fuzzy mapping with relatively smaller network size. The RFNN was tested on a number of benchmark identification and time-series forecasting problems well-known in the literature as well as on application problems. Experimental results demonstrated very good performance on all considered problems.
09/2008; , ISBN: 978-953-7619-08-4
-
[show abstract]
[hide abstract]
ABSTRACT: It is known that one of the most spread forecasting methods is the time series analysis. A weakness of traditional crisp time
series forecasting methods is that they process only measurement based numerical information and cannot deal with the perception-based
historical data represented by linguistic values. Application of a new class of time series, a fuzzy time series whose values
are linguistic values, can overcome the mentioned weakness of traditional forecasting methods. In this paper we propose a
fuzzy recurrent neural network (FRNN) based time series forecasting method for solving forecasting problems in which the data
can be presented as perceptions and described by fuzzy numbers. The FRNN allows effectively handle fuzzy time series to apply
human expertise throughout the forecasting procedure and demonstrates more adequate forecasting results. Recurrent links in
FRNN also allow for simplification of the overall network structure (size) and forecasting procedure. Genetic algorithm-based
procedure is used for training the FRNN. The effectiveness of the proposed fuzzy time series forecasting method is tested
on the benchmark examples.
Soft Computing 12/2007; 12(2):183-190. · 1.88 Impact Factor
-
[show abstract]
[hide abstract]
ABSTRACT: Consumer demand for intelligent battery charges is increasing as portable electronic applications continue to grow. Fast charging
of battery packs is a problem which is difficult, and often expensive, to solve using conventional techniques. Conventional
techniques only perform a linear approximation of a nonlinear behavior of a battery packs. The battery charging is a nonlinear
electrochemical dynamic process and there is no exact mathematical model of battery. Better techniques are needed when a higher
degree of accuracy and minimum charging time are desired. In this paper we propose soft computing approach based on fuzzy
recurrent neural networks (RFNN) training by genetic algorithms to control batteries charging process. This technique does
not require mathematical model of battery packs, which are often difficult, if not impossible, to obtain. Nonlinear and uncertain
dynamics of the battery pack is modeled by recurrent fuzzy neural network. On base of this FRNN model, the fuzzy control rules
of the control system for battery charging is generated. Computational experiments show that the suggested approach gives
least charging time and least Tend-Tstart results according to the other intelligent battery charger works.
07/2007: pages 307-316;
-
[show abstract]
[hide abstract]
ABSTRACT: The paper analyses issues leading to errors in graphic object classifiers. The distance measures suggested in literature and used as a basis in traditional, fuzzy, and Neuro-Fuzzy classifiers are found to be not suitable for classification of non-stylized or fuzzy objects in which the features of classes are much more difficult to recognize because of significant uncertainties in their location and gray-levels. The authors suggest a neuro-fuzzy graphic object classifier with modified distance measure that gives better performance indices than systems based on traditional ordinary and cumulative distance measures. Simulation has shown that the quality of recognition significantly improves when using the suggested method.
Iranian journal of fuzzy systems 01/2004; 1:5-15. · 1.06 Impact Factor
-
[show abstract]
[hide abstract]
ABSTRACT: The paper analyses issues leading to errors in graphic object classifiers. The distance measures suggested in literature and used as a basis in Traditional, fuzzy, and Neuro-Fuzzy classifiers are found to be not very suitable for classification of non-stylized or fuzzy objects in which the features of classes are much more difficult to recognize because of significant uncertainties in their location and gray-levels. The authors suggest a Neuro-Fuzzy graphic object classifier with modified distance measure that gives better performance indices than systems based on traditional ordinary and cumulative distance measures. The simulation has shown that the quality of recognition significantly improves when using the suggested method.
Neural Networks, 2003. Proceedings of the International Joint Conference on; 08/2003
-
[show abstract]
[hide abstract]
ABSTRACT: Economic, ecology and business systems are often complex systems,
and are almost always characterized by imprecision and uncertainty. It
is known that in such cases distributed multi-agent intelligent system
based on soft computing is the most effective approach for systems
analysis, decision making, and control in such systems. The key problem
in constructing such systems is the problem of granulation, i.e.,
decomposition of the monolith intelligence of the whole system into
autonomous agents' intelligence. The work suggests a method for creation
of optimal knowledge bases of coordinating and cooperating intelligent
agents. The optimization includes determination of a rational number of
autonomous agent and fuzzy rules, optimal scaling factors, shapes and
centers of membership functions of fuzzy rules of agents' knowledge
bases, and optimal inference engine by using genetic algorithms.
Computer simulation of the multi-agent distributed system for
marketing-mix decision support system and demand forecasting are
provided
Fuzzy Systems, 2002. FUZZ-IEEE'02. Proceedings of the 2002 IEEE International Conference on; 02/2002
-
[show abstract]
[hide abstract]
ABSTRACT: This paper describes the concept of fuzzy regression analysis based on genetic algorithms. It is shown that the performance
of fuzzy regression models may be improved and fuzzy modeling technique can be simplified by incorporating genetic algorithms
into regression analysis procedure. The effectiveness of the proposed approach is illustrated through simulation of fuzzy
linear regression model obtained by other authors and comparison of the results. The paper further demonstrates the applications
of the approach to the manufacturing and business problems.
Soft Computing 01/2002; 6(6):470-475. · 1.88 Impact Factor
-
[show abstract]
[hide abstract]
ABSTRACT: The kernel of modern industrial technology, particularly CIM and
FMS is distributed artificial intelligence (DAI). This paper considers
the concept, construction principles, architecture, and interaction
mechanisms of agents of distributed intelligent systems for continuous
industrial branches, particularly, oil-refinery plants. The environment
of such plants is characterized by uncertainty, imprecision, missing and
incomplete data and knowledge, and is supposed to be fuzzy. Thus, a
fuzzy distributed multi-agent intelligent system (FDIS) is considered.
Rules and conventions of interactions between intelligent agents,
organization, structure, control strategy and communication in FDIS for
an oil refinery plant, are considered. Experimental results are given
concerning the FDIS in an oil-refinery plant
Fuzzy Information Processing Society, 1997. NAFIPS '97., 1997 Annual Meeting of the North American; 10/1997
-
[show abstract]
[hide abstract]
ABSTRACT: A hierarchical intelligent system for the catalytic cracking technological process control is suggested. It includes the fuzzy knowledge based level for decision making concerning the process optimal static mode; and the neuro fuzzy genetic based level for control of the dynamic of the process
Fuzzy Information Processing Society, 1996. NAFIPS. 1996 Biennial Conference of the North American; 07/1996
-
[show abstract]
[hide abstract]
ABSTRACT: In this paper the synthesis problems of industrial deterministic, fuzzy and adaptive controllers, based on neural technology are considered. Comparative results of considered classes of controllers are given. Results of application of neural controllers in the oil-refinery industry are discussed
Neural Networks, 1994. IEEE World Congress on Computational Intelligence., 1994 IEEE International Conference on;
-
[show abstract]
[hide abstract]
ABSTRACT: Contenido: Objetivos del soft computing; Fundamentos de la teoría de juegos difusos; Lógica difusa; Aplicaciones de los juegos difusos; Redes neurales artificiales; Razonamiento probabilístico; Algoritmos genéticos; Elementos de la teoría del caos; Tecnología neurodifusa; Combinación de algoritmos genéticos con redes neurales; Combinación de algoritmos genéticos con lógica difusa; Acercamiento neuro-difuso-genético; Otras combinaciones de los elementos del soft computing; Sistemas de soft computing basado en sistemas inteligentes distribuidos.
-
[show abstract]
[hide abstract]
ABSTRACT: 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.
Information Sciences.
-
[show abstract]
[hide abstract]
ABSTRACT: 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.
Applied Soft Computing.
-
[show abstract]
[hide abstract]
ABSTRACT: 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.
Fuzzy Sets and Systems.
