Showing papers in "International Journal of General Systems in 2005"
TL;DR: It is proved that the measure of fuzziness of a partition-based fuzzy rough set, FR(A), is equal to zero if and only if the set A is crisp and definable.
Abstract: This paper extends Pawlak's rough set onto the basis of a fuzzy partition of the universe of discourse. Some basic properties of partition-based fuzzy approximation operators are examined. To measure uncertainty in generalized fuzzy rough sets, a new notion of entropy of a fuzzy set is introduced. The notion is demonstrated to be adequate for measuring the fuzziness of a fuzzy event. The entropy of a fuzzy partition and conditional entropy are also proposed. These kinds of entropy satisfy some basic properties similar to those of Shannon's entropy. It is proved that the measure of fuzziness of a partition-based fuzzy rough set, FR(A), is equal to zero if and only if the set A is crisp and definable.
123 citations
TL;DR: An overview of three ANN architectures and the results of applying those ANNs for the detection and classification of malfunction, wear and damage of a gearbox operating under steady state conditions show the FLN learns more quickly and is more accurate in operation than the FFBP or the LVQ.
Abstract: Artificial neural networks (ANN) have been recognized as a powerful tool for classification and pattern recognition in various fields of applications. This paper presents an overview of three ANN architectures and the results of applying those ANNs for the detection and classification of malfunction, wear and damage of a gearbox operating under steady state conditions. The ANN models studied are: feed forward back propagation (FFBP), functional link network (FLN) and learning vector quantization (LVQ). Three artificial defects were deliberately introduced to the gearbox and these are: (1) loose key, (2) single tooth flank wear and (3) full tooth breakage (missing tooth). Vibration signals, collected from extensive experimentation, were analyzed using time and frequency domain descriptors that were used as feature vectors to feed the ANNs. The results show that, for this study, the FLN learns more quickly and is more accurate in operation than the FFBP or the LVQ. The LVQ algorithm exhibits faster rate of ...
78 citations
TL;DR: A generalized model of fuzzy rough sets based on general fuzzy relations are studied, properties and algebraic characterization of the model are revealed, and relationships between this model and related models are also discussed.
Abstract: The consideration of approximation problem of fuzzy sets in fuzzy information systems results in theory of fuzzy rough sets. This paper focuses on models of generalized fuzzy rough sets, a generalized model of fuzzy rough sets based on general fuzzy relations are studied, properties and algebraic characterization of the model are revealed, and relationships between this model and related models are also discussed.
77 citations
TL;DR: This paper is devoted to the study of a special kind of aggregation operators: commutative, non-decreasing binary operators F on [0,1] with annihilator and such that and .
Abstract: This paper is devoted to the study of a special kind of aggregation operators: commutative, non-decreasing binary operators F on [0,1] with annihilator and such that F(0,0) = 0 and F(1,1) = 1 . A characterization of this kind of operators is given, including many examples and properties in the general case. Special attention is paid to the associative case, leading to a characterization by means of a median expression. This type of operators can be viewed as a generalization of both uninorms and nullnorms.
53 citations
TL;DR: A generating function representation method for regular increasing monotone (RIM) quantifiers and a class of parameterized equidifferent RIM quantifier which has minimum variance generating function is proposed and its properties are analyzed.
Abstract: Comparing the large number of research papers on the ordered weighted averaging (OWA) operator, the researches on relative quantifier are relatively rare so far. In the present paper, based on the quantifier guided aggregation method with OWA operator which was proposed by Yager [“Quantifier guided aggregation using OWA operators”, Int. J. Intell. Syst., 11, pp. 49–73, 1996], a generating function representation method for regular increasing monotone (RIM) quantifiers is proposed. We extend the the properties of OWA operator to the RIM quantifier which is represented with a monotone function instead of the OWA weighting vector. A class of parameterized equidifferent RIM quantifier which has minimum variance generating function is proposed and its properties are also analyzed. The equidifferent RIM quantifier is consistent with its orness level for any aggregated elements, which can be used to represent the decision maker's preference.
51 citations
TL;DR: In this paper, the authors proposed the use of the maximum difference of entropies as a non-specificity measure for credal sets and studies its properties, and provided an algorithm to compute the most difficult part of the difference of entropy, the minimum of entropy.
Abstract: This paper proposes the use of the maximum difference of entropies as a non-specificity measure for credal sets and studies its properties. The main advantage of the new measure is that it does not only take into account the absolute imprecision of the credal set, but also the position of the credal set with respect to the uniform distribution. The paper provides an algorithm to compute the most difficult part of the difference of entropies, the minimum of entropy. The algorithm computes the exact minimum of entropy for order-2 capacities and it is based on the branch and bound technique with some additional procedures to prune the search.
31 citations
TL;DR: This paper can estimate the lower and upper bounds of the probability that the system is in a desirable state and proves that under reasonable assumptions, these estimates converge to the actual probability bounds.
Abstract: Based on a black box model of a complex system, and on intervals and probabilities describing the known information about the inputs, we want to estimate the system's reliability. This problem is motivated by a number of problem areas, most specifically in engineering reliability analysis under conditions of poor measurement and high complexity of system models. Using the results of tests performed on the system's computer model, we can estimate the lower and upper bounds of the probability that the system is in a desirable state. This is equivalent to using Monte-Carlo sampling to estimate cumulative belief and plausibility values of functionally propagated finite random intervals. In this paper, we prove that these estimates are correct in the sense that under reasonable assumptions, these estimates converge to the actual probability bounds.
29 citations
TL;DR: The basic properties of extended extremal fuzzy measure are considered and several variants of their representation are given and several transformation theorems are proved for extended lower and upper Sugeno integrals.
Abstract: The basic properties of extended extremal fuzzy measure are considered and several variants of their representation are given. In considering extremal fuzzy measures, several transformation theorems are proved for extended lower and upper Sugeno integrals. Extended extremal conditional fuzzy measures are defined. The notions of extremal fuzzy time moments and intervals are introduced and their monotone algebraic structures that form the most important part of the fuzzy instrument of modeling extremal fuzzy dynamic systems are discussed.
28 citations
TL;DR: Questions as to the ergodicity of EFDSs are considered, using the properties of both extended composition extremal fuzzy measures and -compositions over them, and sufficient conditions are proved for stationary CEFPs to be ergodic.
Abstract: New approaches in modeling the so-called extremal fuzzy dynamic systems (EFDSs) are developed. Applying the results of Parts I and II, fuzzy processes with possibilistic uncertainty, the source of which is extremal fuzzy time intervals, are constructed. Fuzzy-integral representations of controllable extremal fuzzy processes (CEFPs) are given. The dynamics of EFDSs is described. Questions as to the ergodicity of EFDSs are considered, using the properties of both extended composition extremal fuzzy measures and H_{ \omega } -compositions over them (Part II). Sufficient conditions are proved for stationary CEFPs to be ergodic.
25 citations
TL;DR: By considering sets of basic probability assignments, an appealing constructive approach to general interval probability is achieved, which allows for a very flexible modelling of uncertain knowledge.
Abstract: Dempster–Shafer theory allows to construct belief functions from (precise) basic probability assignments. The present paper extends this idea substantially. By considering sets of basic probability assignments, an appealing constructive approach to general interval probability is achieved, which allows for a very flexible modelling of uncertain knowledge.
24 citations
TL;DR: The notion of H-composition over extremal fuzzy measures is introduced, and some algebraic properties of the corresponding structures are discussed, which forms the most important part of the fuzzy instrument of modeling extremeal fuzzy dynamic systems.
Abstract: This paper continues the investigation of extremal fuzzy measures and their extensions started in Part I. Here, we consider the basic properties of composition extremal fuzzy measures. Several variants of their representations are given. The notion of H-composition over extremal fuzzy measures is introduced, and some algebraic properties of the corresponding structures, which forms the most important part of the fuzzy instrument of modeling extremal fuzzy dynamic systems, are discussed.
TL;DR: A new computational method is proposed for information-theoretic competitive learning that introduces the rth power of competitive unit activations used to accentuate actual competitive unitactivations and is called “accentuated information maximization”.
Abstract: In this paper, we propose a new computational method for information-theoretic competitive learning. We have so far developed information-theoretic methods for competitive learning in which competitive processes can be simulated by maximizing mutual information between input patterns and competitive units. Though the methods have shown good performance, networks have had difficulty in increasing information content, and learning is very slow to attain reasonably high information. To overcome the shortcoming, we introduce the rth power of competitive unit activations used to accentuate actual competitive unit activations. Because of this accentuation, we call the new computational method “accentuated information maximization”. In this method, intermediate values are pushed toward extreme activation values, and we have a high possibility to maximize information content. We applied our method to a vowel–consonant classification problem in which connection weights obtained by our methods were similar to those...
TL;DR: The main goal of this paper is to propose an axiomatic definition of measure of contradiction both for a set and between two sets and to examine how well some measures proposed throughout the fuzzy logic literature fit this definition.
Abstract: Several methods have been proposed within fuzzy logic for inferring new knowledge from the original premises. However, there must be some guarantee that the results contradict neither each other nor the initial information. In 1999, Trillas et al. introduced the concepts of both contradictory set and contradiction between two sets. Moreover, we established the need to study not only contradiction but also the degree of such contradiction in E. Castineira et al., “Degrees of contradiction in fuzzy sets theory”, Proceedings IPMU'02, 2002a, pp. 171–176, Annecy (France), E. Castineira et al., “Contradiccion entre dos conjuntos”, Actas ESTYLF'02, 2002b, pp. 379–383, Leon (Spain) (in Spanish) establishing some measures for this purpose. Nevertheless, contradiction could have been measured in some other way. Elena Castineira Holgado was born in Asturias (Spain). She received her Bachelor Degree in Mathematics from the Complutense University of Madrid in 1985, and her Ph.D. in Computer Sciences from the Techni...
TL;DR: This paper discusses the use of a cyclic genetic algorithm (CGA) to evolve control programs that produce gaits for actual hexapod robots and shows that the CGA successfully produces Gaits for both fully capable and disabled robots.
Abstract: A major facet of multi-legged robot control is locomotion. Each leg must move in such a manner that it efficiently produces thrust and provides maximum support. The motion of all the legs must be coordinated so that they are working together to provide constant stability while propelling the robot forward. In this paper, we discuss the use of a cyclic genetic algorithm (CGA) to evolve control programs that produce gaits for actual hexapod robots. Tests done in simulation and verified on the actual robot show that the CGA successfully produces gaits for both fully capable and disabled robots.
TL;DR: This paper compares the various definitions of independence and analyzes those definitions that are employed in the most significant uncertainty measures established in the literature for credal sets.
Abstract: A general way of representing incomplete information is to use closed and convex sets of probability distributions, which are also called credal sets. Each credal set is associated with uncertainty, whose amount is quantified by an appropriate uncertainty measure. One of the requisite properties of uncertainty measures is the property of additivity, which is associated with the concept of independence. For credal sets, the concept of independence is not unique. This means that different definitions of independence lead to different definitions of additivity for uncertainty measures. In this paper, we compare the various definitions of independence, but our principal aim is to analyze those definitions that are employed in the most significant uncertainty measures established in the literature for credal sets.
TL;DR: The paper presents an approach that implements KL for an intelligent decision support based on the paradigm of object-oriented constraint networks that makes it possible to perform problem solving by directly extracting slices of the common ontology and putting them into constraint solvers such as ILOG.
Abstract: An efficient knowledge sharing between multiple participating parties is required to provide for situation awareness and consequently to manage any networked organization. Thereby, it is necessary that the right knowledge from distributed sources is integrated and transferred to the right person within the right context at the right time to the right purpose. The aggregate of these interrelated activities is referred to as knowledge logistics (KL). The paper presents an approach that implements KL for an intelligent decision support. The approach assumes an ontological knowledge representation model based on the paradigm of object-oriented constraint networks. This makes it possible to perform problem solving by directly extracting slices of the common ontology and putting them into constraint solvers such as ILOG. Humanitarian relief operations are considered here as one of the approach applications what is illustrated via a case study of on-the-fly portable hospital configuration.
TL;DR: In this current paper the following problems are addressed: (1) extending the knowledge of a partially known probability distribution function to any point of a continuous sample space, (2) constructing an imprecise probability distribution based on theknowledge of a set of credible or confidence intervals, and (3) computing the lower and upper expected values of a random continuous variable.
Abstract: In this current paper the following problems are addressed: (1) extending the knowledge of a partially known probability distribution function to any point of a continuous sample space, (2) constructing an imprecise probability distribution based on the knowledge of a set of credible or confidence intervals, and (3) computing the lower and upper expected values of a random continuous variable. An example is provided.
TL;DR: This paper presents a novel addition to the current genetic programming techniques for solving differential equations, rather than using numerical approximation of derivatives during fitness evaluation, automatically computed analytical derivatives of the candidate solutions are employed.
Abstract: This paper presents a novel addition to the current genetic programming techniques for solving differential equations. Rather than using numerical approximation of derivatives during fitness evaluation, automatically computed analytical derivatives of the candidate solutions are employed. Because analytical derivatives are used, symbolic constants can be incorporated in the solution. This permits the development of a single solution for a range of material properties, boundary conditions or other design parameters. Additionally, for the special case of linear differential equations, a modified Gram–Schmidt algorithm is used to reduce the set of general solutions located by genetic programming to a basis set.
TL;DR: Efficient reinforcement learning through dynamic-form symbiotic evolution (DSE) is proposed for solving nonlinear control problems and was verified to be efficient and superior from comparisons with some traditional genetic algorithms.
Abstract: In this paper, efficient reinforcement learning through dynamic-form symbiotic evolution (DSE) is proposed for solving nonlinear control problems. Compared with traditional symbiotic evolution, DSE uses the sequential search-based dynamic evolution (SSDE) method to generate an initial population and to determine dynamic mutation points. Therefore, better chromosomes will be initially generated while better mutation points will be determined for performing dynamic mutation. The proposed DSE design method was applied to different control systems, including the cart-pole balancing system and the water bath temperature control system, and control problems were simulated on these systems. The proposed DSE method was verified to be efficient and superior for solving these control problems and from comparisons with some traditional genetic algorithms.
TL;DR: A LQR design methodology is presented to design a state-feedback decentralized high-gain analog controller, which gives the desired decentralized performance of the controlled analog system, and a prediction-based decentralized low-gain digital controller is developed from the decentralizedHigh Gain analog controller for the hybrid controlled system.
Abstract: Decentralized control is a practical control methodology for large-scale multivariable systems. This paper presents a LQR design methodology to design a state-feedback decentralized high-gain analog controller, which gives the desired decentralized performance of the controlled analog system. Then, a prediction-based decentralized low-gain digital controller is developed from the decentralized high-gain analog controller for the hybrid controlled system. As a result, the complexity and cost of hardware implementation of the controller can be significantly reduced. In order to improve the performance of the decentralized hybrid system, the evolutionary programming (EP) is employed to tune the observer-based decentralized tracker. Some examples are presented to illustrate the developed design methodology.
TL;DR: It is shown that the addressed problem can be solved in terms of the positive definite solutions to certain algebraic matrix inequalities to solve the stability analysis problem for a class of continuous stochastic time-delay systems with nonlinear disturbances, parameter uncertainties and possible actuator failures.
Abstract: This paper is concerned with the stabilization problem for a class of continuous stochastic time-delay systems with nonlinear disturbances, parameter uncertainties and possible actuator failures. Both the stability analysis and synthesis problems are considered. The purpose of the stability analysis problem is to derive easy-to-test conditions for the uncertain nonlinear time-delay systems to be stochastically, exponentially stable. The synthesis problem, on the other hand, aims to design state feedback controllers such that the closed-loop system is exponentially stable in the mean square for all admissible uncertainties, nonlinearities, time-delays and possible actuator failures. It is shown that the addressed problem can be solved in terms of the positive definite solutions to certain algebraic matrix inequalities. Numerical examples are provided to demonstrate the effectiveness of the proposed design method.
TL;DR: Systems Movement: Autobiographical Retrospectives is a special section of this Journal, the purpose of which is to produce, via invited autobiographical articles, historical information and insights regarding the thought processes and individual motivations of leading figures in the systems movement.
Abstract: Systems Movement: Autobiographical Retrospectives is a special section of this Journal, the purpose of which is to produce, via invited autobiographical articles, historical information and insights regarding the thought processes and individual motivations of leading figures in the systems movement. This valuable information is normally not included in regular publications that tend to focus on results rather than the creative process leading to those results. The autobiographical articles are likely to help us to improve our understanding of how, and why, the systems movement has progressed since its emergence in the mid-20th century. Each article in this section is published strictly by invitation extended to individual authors by the Editor, and is based on the recognition that these individuals have made major contributions to the systems movement.
TL;DR: A new approach, model theory approach, to small and medium scale transaction processing system (TPS) development, which provides a theoretical structure to information systems development so that systems development can be made an engineering discipline, and facilitates rapid systems development.
Abstract: This paper presents a new approach, model theory approach, to small and medium scale transaction processing system (TPS) development. A TPS of this paper is an information system designed to process day-to-day business event data at operational level of an organization. The paper is not concerned with data base construction but with transaction processing. The model theory approach is not a software engineering approach but a systems theory approach. In the approach a model of the target system, which is called a user model, is constructed in set theory using a formal system structure of a TPS. The user model is, then, compiled into an extended Prolog (extProlog) model. The extProlog is an extension of Prolog to meet requirements for management information system development. On compilation a standardized user interface (UI) called internal UI is attached. The extProlog model with the internal UI is, then, executed under control of another standardized UI called an external UI. Implementation is an integr...
TL;DR: A special class of generated n-contractive left-continuous t-subnorms is introduced, thus allowing to construct left-Continuous n- contractive t-norms by means of ordinal sums.
Abstract: Archimedean components of t-norms are shown to determine the degree of contractivity of the investigated t-norms. It is shown that Archimedean components play an important role also in the case of torsion t-norms. A special class of generated n-contractive left-continuous t-subnorms is introduced, thus allowing to construct left-continuous n-contractive t-norms by means of ordinal sums. Several examples of 3- and 4-contraction t-norms are given.
TL;DR: This paper investigates whether random set inclusion is preserved by non-interactivity and by stochastic independence, and proves that these hypotheses do not imply that (𝒵1, z 1) ⊆ (𝓂2, z 2), but imply that ($3, z 3).
Abstract: This paper investigates whether random set inclusion is preserved by non-interactivity and by stochastic independence. Let (𝒳1, x 1), (𝒳2, x 2) be two random sets on U 1 and U 2, respectively, and let (𝒴1, y 1), (𝒴2, y 2) be two consonant inclusions of theirs. Let (𝒵1, z 1) be the random relation on U 1 × U 2 obtained from (𝒳1, x 1) and (𝒳2, x 2) under the hypothesis of stochastic independence, and let (𝒵2, z 2) ((𝒵3, z 3), respectively) be the random relation on U 1 × U 2 obtained from (𝒴1, y 1), (𝒴2, y 2) under the hypothesis of non-interactivity (stochastic independence, respectively). We prove that these hypotheses do not imply that (𝒵1, z 1) ⊆ (𝒵2, z 2), but imply that (𝒵1, z 1) ⊆ (𝒵3, z 3).
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TL;DR: This paper determines the number and nature of fuzzy subsets of a finite set of n elements taking membership values in the real unit interval and introduces an equivalence relation on the set of all fuzzy subset.
Abstract: In this paper, we determine the number and nature of fuzzy subsets of a finite set of n elements taking membership values in the real unit interval. In order to do this we introduce an equivalence relation on the set of all fuzzy subsets. The important tools for studying this equivalence relation are that of a keychain, index of a keychain, and flags (maximal chains). These notions give rise to the idea of a pinned flag, their equivalences and an index of fuzzy subsets. Using these ideas we characterize the number of fuzzy subsets as the sum of a finite series of integral terms. These terms are enumerated by indices, each term representing the number of fuzzy subsets of a given index.
TL;DR: Trappezoidal rule is utilized together with Genetic Algorithm to convert a continuous-time system with input and state delays to an equivalent discrete-time one so that the states of the digitally controlled sampled-data system closely match those of the originally well-designed continuous- time system for a relatively longer sampling period.
Abstract: This paper utilizes trapezoidal rule together with Genetic Algorithm (GA) to convert a continuous-time system with input and state delays to an equivalent discrete-time one. A new method has been proposed to construct the hybrid control of sampled-data system with state and input delays via digital redesign which transforms the control law of a continuous-time system with state and input delays into an equivalent one of a sampled-data system so that the states of the digitally controlled sampled-data system closely match those of the originally well-designed continuous-time system for a relatively longer sampling period. An example is given to demonstrate that the proposed digital redesign is superior to the existing ones under a longer sampling period.
TL;DR: A new learning system called SSOLS, which combines functional-link neural networks, statistical hypothesis testing and self-organization of number of enhancement nodes, is introduced, which is simple, fast to compute, and very suitable for many real-world applications.
Abstract: In this paper, a new learning system called statistical, self-organizing learning system (SSOLS), which combines functional-link neural networks, statistical hypothesis testing and self-organization of number of enhancement nodes, is introduced. Its structure consists of two stages, a mapping stage and a learning stage. The input training vectors are initially mapped to the enhancement vectors in the mapping stage by multiplying with a random matrix, followed by pointwise nonlinear transformation. Starting with only one enhancement node, the enhancement layer incrementally adds an extra node in each iteration. In the learning stage, both the input vectors and the enhancement vectors are fed into a least squares learning module to obtain the estimated output vectors. This is made possible by choosing the output layer linear. The optimum dimension of the enhancement layer is determined by testing against a separate validation set. In this way, the number of enhancement nodes is also learned automatically. T...
TL;DR: An efficient input feature selection algorithm for modeling of systems based on modified definition of fuzzy-rough sets based on some natural properties of fuzzy t-norm and t-conorm operators is put forward, which is then utilized to construct improved Fuzzy-Rough Feature Selection algorithm.
Abstract: The aim of this paper is to provide an efficient input feature selection algorithm for modeling of systems based on modified definition of fuzzy-rough sets. Some of the critical issues concerning the complexity and convergence of the feature selection algorithm are discussed in detail. Based on some natural properties of fuzzy t-norm and t-conorm operators, the concept of fuzzy-rough sets on compact computational domain is put forward, which is then utilized to construct improved Fuzzy-Rough Feature Selection algorithm. Various mathematical properties of this new definition of fuzzy-rough sets are discussed from pattern classification viewpoint. Speedup factor as high as 622 has been achieved with proposed algorithm compared to recently proposed FRSAR, with improved model performance on selected set of features.
TL;DR: A neural network model that processes the whole input in parallel and organizes itself over time, and implements growing parallel SOM structure for any input and any output dimension.
Abstract: Self-organizing maps (SOM) have become popular for tasks in data visualization, pattern classification or natural language processing and can be seen as one of the major contemporary concepts for artificial neural networks. The general idea is to approximate a high dimensional and previously unknown input distribution by a lower dimensional neural network structure so that the topology of the input space is mapped closely. Not only is the general topology retained but the relative densities of the input space are reflected in the final output. Kohonen maps also have the property of neighbor influence. That is, when a neuron decides to move, it pulls all of its neighbors in the same direction modified by an elasticity factor. We present a SOM that processes the whole input in parallel and organizes itself over time. The main reason for parallel input processing lies in the fact that knowledge can be used to recognize parts of patterns in the input space that have already been learned. Thus, networks can be...