Showing papers in "International Journal of General Systems in 2010"
TL;DR: A new methodology for the analysis and forecasting of time series is proposed that directly employs two soft computing techniques: the fuzzy transform and the perception-based logical deduction, successfully applicable to robust long-time predictions.
Abstract: A new methodology for the analysis and forecasting of time series is proposed. It directly employs two soft computing techniques: the fuzzy transform and the perception-based logical deduction. Thanks to the use of both these methods, and to the innovative approach, consisting of the construction of several independent models, the methodology is successfully applicable to robust long-time predictions.
84 citations
TL;DR: This work proposes MENTOR, a methodology to support the development of a common reference ontology for a group of organisations sharing the same business domain, based on the mediator ontology (MO) concept, which assists the semantic transformations among each enterprise's ontology and the referential one.
Abstract: A community with knowledge organisation based on ontologies will enable an increase in the computational intelligence of its information systems. However, due to the worldwide diversity of communities, a high number of knowledge representation elements, which are not semantically coincident, have appeared representing the same segment of reality, becoming a barrier to business communications. Even if a domain community uses the same kind of technologies in its information systems, such as ontologies, it doesn't solve its semantics differences. In order to solve this interoperability problem, a solution is to use a reference ontology as an intermediary in the communications between the community enterprises and the outside, while allowing the enterprises to keep their own ontology and semantics unchanged internally. This work proposes MENTOR, a methodology to support the development of a common reference ontology for a group of organisations sharing the same business domain. This methodology is based on th...
65 citations
TL;DR: While Robert Rosen's work is the main focus of this article, an attempt is made to advance a perspective for the broad field of studies that developed around the notion of anticipation, including the circumstances of epistemological and gnoseological significance, leading to the articulation of the early hypotheses regarding anticipatory processes.
Abstract: Anticipation relates to the perception of change. Therefore, dynamics is the context for defining anticipation processes. Since preoccupation with change is as old as science itself, anticipation-related questions go back to the first attempts to explain why and how things change. However, as a specific concept, anticipation insinuates itself in the language of science in the writings of Whitehead, Burgers, Bennett, Feynman, Svoboda, Rosen, Nadin and Dubois, i.e. since 1929. While Robert Rosen’s work is the main focus of this article, an attempt is made to advance a perspective for the broad field of studies that developed around the notion of anticipation. Of particular interest are the circumstances of epistemological and gnoseological significance, leading to the articulation of the early hypotheses regarding anticipatory processes. Of no less interest to the scientific community are questions pertinent to complexity, adaptivity, purposiveness, time and computability as they relate to our understanding of anticipation.
53 citations
TL;DR: The results obtained are promising and point out the usefulness and strength of A-IFSs as a tool to account for more aspects of vague data and information.
Abstract: This paper is an improved and extended version of our previous work2 on typicality in terms of Atanassov's intuitionistic fuzzy sets (to be called A-IFSs, for short)3. We follow the line of reasoning known from psychological and cognitive sciences, in particular from linguistic experiments, and verify how those results work in the case of classification – a typical problem in computer science, decision sciences, etc. Our considerations concentrate on a typical example discussed in cognitive sciences – we investigate to which extent a linguistic representation in a psychological space (we start from nominal data – names are assigned to objects as labels) succeeds in predicting categories via A-IFSs. First, we consider a model of categories with a geometrical centroid model in which the similarity is defined in terms of a distance to centroids. Next, we verify if the extreme ideals, which are important in cognitive processes when categories are learnt in the presence of the alternative (contrast) category, ...
40 citations
TL;DR: The way in which this design of the representation is done by means of fuzzy sets, connectives and relations marks a distinction between the fuzzy and the formal logic methodologies, two different disciplines whose design process and agendas are not coincidental.
Abstract: This paper tries to show, from a theoretical perspective, the importance of designing well the representation of fuzzy systems whose behaviour is described by a linguistic description. The way in which this design of the representation is done by means of fuzzy sets, connectives and relations marks a distinction between the fuzzy and the formal logic methodologies, two different disciplines whose design process and agendas are not coincidental.
37 citations
TL;DR: The concept of the general relation mapping between two universes is proposed in order to construct the equivalence relation on one universe according to the given equivalences relation on the other universe based on the including degrees.
Abstract: Communication between information systems is a basic problem in granular computing. In current research, a homomorphism mapping between information systems is required. In this paper, the concept of the general relation mapping between two universes is proposed in order to construct the equivalence relation on one universe according to the given equivalence relation on the other universe based on the including degrees. The main properties of the mapping are studied, and it is proved that attribute reductions in the original system and image system are equivalent to each other under the given conditions. Finally, we also define the concept of fuzzy general relation mapping between two fuzzy information systems and give some properties.
20 citations
TL;DR: The relationships between positive-region reduction, Shannon entropy reduction and Liang entropy reduction are investigated and the change mechanisms for decision performance of a decision table induced by each of these three types of reduction approaches are analyzed.
Abstract: The given attribute reduction approach decides the decision performance of a reduced decision table, which can give a guidance for selecting one rule-extraction method in practical applications. The objective of this study is to compare the decision performance of positive-region reduction, Shannon entropy reduction and Liang entropy reduction. In this paper, the relationships between positive-region reduction, Shannon entropy reduction and Liang entropy reduction are first investigated. Then, by means of three evaluation indices (certainty measure, consistency measure and support measure), we systemically analyse these change mechanisms for decision performance of a decision table induced by each of these three types of reduction approaches. Finally, by numerical experiments, these change mechanisms of a decision table's decision performance are verified for the above-mentioned three attribute reductions.
20 citations
TL;DR: A combined approach, where the fuzzy analytic hierarchy process (AHP) and simulation come together, is presented to select the best computer-aided design (CAD) software out of the available options in the market.
Abstract: In this paper, a combined approach, where the fuzzy analytic hierarchy process (AHP) and simulation come together, is presented to select the best computer-aided design (CAD) software out of the available options in the market. The fuzzy AHP is used due to the vagueness and uncertainty of the judgements of a decision maker(s), because the crisp pair-wise comparison in the conventional AHP seems to be insufficient and imprecise to capture the right judgements of the decision maker(s). In this study, first the fuzzy AHP is used to reduce a possible number of alternatives for the CAD system to an acceptable level for further study, simulation analysis. Secondly, a simulation generator as an integrated part of the fuzzy AHP is used to try the remaining alternatives, on the generated model of a real-life product organisation in which the final alternative will be used. The results of simulation experiments are obtained, and then evaluated to reach to the ultimate CAD alternative.
19 citations
TL;DR: It is presented how the conceptually and numerically simple concept of a fuzzy linguistic database summary can be a very powerful tool for gaining much insight into the very essence of data.
Abstract: We present how the conceptually and numerically simple concept of a fuzzy linguistic database summary can be a very powerful tool for gaining much insight into the very essence of data. The use of linguistic summaries provides tools for the verbalisation of data analysis (mining) results which, in addition to the more commonly used visualisation, e.g. via a graphical user interface, can contribute to an increased human consistency and ease of use, notably for supporting decision makers via the data-driven decision support system paradigm. Two new relevant aspects of the analysis are also outlined which were first initiated by the authors. First, following Kacprzyk and Zadrozny, it is further considered how linguistic data summarisation is closely related to some types of solutions used in natural language generation (NLG). This can make it possible to use more and more effective and efficient tools and techniques developed in NLG. Second, similar remarks are given on relations to systemic functional lingu...
17 citations
TL;DR: The aim of this paper is to show that design of applied intelligent control systems requires different types of blending between fuzzy logic and conventional control systems.
Abstract: The aim of this paper is to show that design of applied intelligent control systems requires different types of blending between fuzzy logic and conventional control systems. Two alternative automotive applications – a manufacturing process control problem and an advisory system for fuel efficient driving – that benefit from both fuzzy and control theories are reviewed and different levels of prioritisations of both approaches are discussed based on the specificity of the applications.
17 citations
TL;DR: This paper provides an overview of working definitions of knowledge, ignorance, information and uncertainty and summarises formalised philosophical and mathematical framework for their analyses.
Abstract: This paper provides an overview of working definitions of knowledge, ignorance, information and uncertainty and summarises formalised philosophical and mathematical framework for their analyses It provides a comparative examination of the generalised information theory and the generalised theory of uncertainty It summarises foundational bases for assessing the reliability of knowledge constructed as a collective set of justified true beliefs It discusses system complexity for ancestor simulation potentials It offers value-driven communication means of knowledge and contrarian knowledge using memes and memetics
TL;DR: The results show that a simple network structure for both the multi-layer perceptron and radial basis function can produce equally good results, and that the best performing algorithm will strongly depend on the features of the datasets, and hence, there is not necessarily a single best classifier.
Abstract: Breast cancer is the second leading cause of cancer deaths in women today Sometimes, breast cancer can return after primary treatment A medical diagnosis of recurrent cancer is often a more challenging task than the initial one In this paper, we investigate the potential contribution of neural networks (NNs) to support health professionals in diagnosing such events The NN algorithms are tested and applied to two different datasets An extensive statistical analysis has been performed to verify our experiments The results show that a simple network structure for both the multi-layer perceptron and radial basis function can produce equally good results, not all attributes are needed to train these algorithms and, finally, the classification performances of all algorithms are statistically robust Moreover, we have shown that the best performing algorithm will strongly depend on the features of the datasets, and hence, there is not necessarily a single best classifier
TL;DR: The computational complexity of the problem of estimating information amount under different types of uncertainty, described by Shannon's entropy, is analysed.
Abstract: Measurement results (and, more generally, estimates) are never absolutely accurate: there is always an uncertainty, the actual value x is, in general, different from the estimate . Sometimes, we know the probability of different values of the estimation error , sometimes, we only know the interval of possible values of , sometimes, we have interval bounds on the cumulative distribution function of . To compare different measuring instruments, it is desirable to know which of them brings more information – i.e. it is desirable to gauge the amount of information. For probabilistic uncertainty, this amount of information is described by Shannon's entropy; similar measures can be developed for interval and other types of uncertainty. In this paper, we analyse the computational complexity of the problem of estimating information amount under different types of uncertainty.
TL;DR: An interval-valued rough intuitionistic fuzzy (IF) set model is presented by means of integrating the classical Pawlak rough set theory with the intervals-valued IF set theory.
Abstract: Rough set theory is a powerful tool for dealing with uncertainty, granuality and incompleteness of knowledge in information systems. This paper presents an interval-valued rough intuitionistic fuzzy (IF) set model by means of integrating the classical Pawlak rough set theory with the interval-valued IF set theory. In this paper, we first introduce some concepts and properties of interval-valued IF set theory. Then, the rough approximations of an interval-valued IF set in the classical Pawlak approximation space and the generalised Pawlak approximation space are respectively defined, and some fundamental properties of the approximation operators are studied. Furthermore, by employing cut sets of interval-valued IF sets, classical representations of interval-valued rough IF approximation operators are presented, and the connections between special binary relations and interval-valued rough IF approximation operators are constructed. Finally, we discuss the knowledge reduction and knowledge discovery of the ...
TL;DR: This paper proposes a heuristic method for attribute selection able to extract the more relevant features needed in the classification process to learn simplified and more significant belief decision rules in a quick time.
Abstract: In this paper, we deal with the problem of attribute selection from partially uncertain data based on rough sets without costly calculation. The uncertainty exists in decision attributes and is represented by the transferable belief model, one interpretation of the belief function theory. To solve this problem, we propose a heuristic method for attribute selection able to extract the more relevant features needed in the classification process. The simplification of the uncertain decision table using this heuristic method yields to learn simplified and more significant belief decision rules in a quick time. The experiments show interesting results based on two evaluation criteria such as the accuracy classification and the time complexity.
TL;DR: This paper shows that the SVM solution is stable under bounded perturbations of the data both in the linear programming and quadratic programming, and generalise for nonlinear discriminant functions.
Abstract: In this paper, we investigate the stability of linear and quadratic programming support vector machines (SVMs) with bounded noise in the input data using a robust optimisation model. For a linear discriminant function, this model is expressed as a second order cone optimisation problem. Using the concept of the kernel function, we generalise for nonlinear discriminant functions. Intuitively, it looks quite clear that large margin classifiers are robust in terms of bounded input noise. However, there is no theoretical analysis investigating this behaviour. We show that the SVM solution is stable under bounded perturbations of the data both in the linear programming and quadratic programming. Computational results are also presented for toy and real-world data.
TL;DR: By inserting fuzzy sets as payoff values in the game matrix, this work facilitates the procedure of formulations of payoff expectations by players by enabling them to use words when designing the preliminaries of the game.
Abstract: We explore the classical model of a two-player game to select the best strategies, where action is expected to maintain the values of a certain variable on the neutral level. By inserting fuzzy sets as payoff values in the game matrix, we facilitate the procedure of formulations of payoff expectations by players. Instead of making inconvenient decisions about the choice of accurate numerical entries of the matrix, the players are able to use words, which should simplify communication between them when designing the preliminaries of the game. The players also have the possibility of making a ranking of their favourite strategies. At the next stage of the play, we involve group decision-making in order to aggregate results coming from several paired games, when more than two players contradict each other.
TL;DR: The goal of this work is to extend the concept of the linguistic variable to the interval-valued case since there are some situations where their application would be justified, as can be seen in this paper.
Abstract: The goal of this work is to extend the concept of the linguistic variable to the interval-valued case since there are some situations where their application would be justified, as can be seen in this paper. After a brief introduction on fuzzy numbers and linguistic variables in [0, 1], we define the interval-valued linguistic variables and we study their behaviour through three properties. In the second part of the paper, we show their utility for replacing the absent values in an L-fuzzy context.
TL;DR: This paper establishes the theory basis for linguistic information processing and constructs the linguistic truth-valued concept lattice for a decision information system, and further utilises uncertainty reasoning to make the decision.
Abstract: Decision making with linguistic information is a research hotspot now. This paper begins by establishing the theory basis for linguistic information processing and constructs the linguistic truth-valued concept lattice for a decision information system, and further utilises uncertainty reasoning to make the decision. That is, we first utilise the linguistic truth-valued lattice implication algebra to unify the different kinds of linguistic expressions; second, we construct the linguistic truth-valued concept lattice and decision concept lattice according to the concrete decision information system and third, we establish the internal and external uncertainty reasoning methods and talk about the rationality of them. We apply these uncertainty reasoning methods into decision making and present some generation methods of decision rules. In the end, we give an application of this decision method by an example.
TL;DR: The notions of consistent and non-consistent marginals, which parallel those of epistemic independence, and unknown interaction and epistemic independent for random sets, respectively, are proposed.
Abstract: Random relations are random sets defined on a two-dimensional space (or higher). After defining the correlation for two variables constrained by a random relation as an interval, the effect of imprecision was studied by using a multi-valued mapping, whose domain is a space of joint random variables. This perspective led to the notions of consistent and non-consistent marginals, which parallel those of epistemic independence, and unknown interaction and epistemic independence for random sets, respectively. The calculation of the correlation bounds entails solving two optimisation problems that are NP-hard. When the entire random relation is available, it is shown that the hypothesis of non-consistent marginals leads to correlation bounds that are much larger (four orders of magnitude in some cases) than those obtained under the hypothesis of consistent marginals; this hierarchy parallels the hierarchy between probability bounds for unknown interaction and strong independence, respectively. Solutions of the...
TL;DR: Continuous aggregation functions, being invariant under any monotone bijective transformation, are discussed and characterised and the relevant role of simple medians in describingmonotone threshold Boolean functions is made apparent.
Abstract: Continuous aggregation functions, being invariant under any monotone bijective transformation, are discussed and characterised. As a basic tool for this characterisation, self-dual -valued capacities or their counterparts, self-dual monotone Boolean functions, are exploited. A generating role of is discussed. The relevant role of simple medians in describing monotone threshold Boolean functions is made apparent.
TL;DR: A hierarchical fuzzy hybrid structure consisting of a fuzzy discrete event dynamic system and a continuous variable dynamic system is constructed, which not only captures the hybrid continuous/discrete dynamics but also handles the uncertainties in states and state transitions.
Abstract: This paper presents a new approach to modelling and control of hybrid systems with both continuous variables and discrete events. Applying the fuzzy set theory, a hierarchical fuzzy hybrid structure consisting of a fuzzy discrete event dynamic system and a continuous variable dynamic system is constructed, which not only captures the hybrid continuous/discrete dynamics but also handles the uncertainties in states and state transitions. The identification of continuous and discrete components is developed, and the hybrid control is then synthesised by fuzzy IF–THEN rules embedded in the fuzzy interface. An example of the optimisation of a production line in manufacturing shows the efficacy of the proposed approach.
TL;DR: This paper proposes a numerical approach, the Random/Fuzzy (RaFu) method, whose aim is to determine an optimal numerical strategy so that computational costs are reduced to their minimum, using the theoretical frameworks mentioned above.
Abstract: The need to differentiate between epistemic and aleatory uncertainties is now well admitted by the risk analysis community. One way to do so is to model aleatory uncertainty by classical probability distributions and epistemic uncertainty by means of possibility distributions, and then propagate them by their respective calculus. The result of this propagation is a random fuzzy variable. When dealing with complex models, the computational cost of such a propagation quickly becomes too high. In this paper, we propose a numerical approach, the Random/Fuzzy (RaFu) method, whose aim is to determine an optimal numerical strategy so that computational costs are reduced to their minimum, using the theoretical frameworks mentioned above. We also give some means to take account of the resulting numerical error. The benefits of the RaFu method are shown by comparing it to previously proposed methods.
TL;DR: This paper deals with the assessment of the reliability of predictions made in the context of the fuzzy inductive reasoning methodology by means of two separate confidence measures, a proximity measure and a similarity measure.
Abstract: This paper deals with the assessment of the reliability of predictions made in the context of the fuzzy inductive reasoning methodology. The reliability of predictions is assessed by means of two separate confidence measures, a proximity measure and a similarity measure. A time series and a single-input/single-output system are used as two different applications to study the viability of these confidence measures.
TL;DR: A ‘useful’ fuzzy measure of integrated ambiguity is obtained by integration of fuzzy and probabilistic uncertainties with utility, and a new measure of fuzzy-directed divergence of a fuzzy set from another fuzzy set is proposed and its validity proved.
Abstract: In the present paper, a new concept of ‘useful’ fuzzy information, based on utility, is introduced by considering the uncertainties of fuzziness and probabilities of random events. A ‘useful’ fuzzy measure of integrated ambiguity is obtained by integration of fuzzy and probabilistic uncertainties with utility. A new ‘useful’ measure of fuzzy-directed divergence of a fuzzy set from another fuzzy set is proposed and its validity proved. Finally, the constrained optimisation of ‘useful’ fuzzy entropy and ‘useful’ fuzzy-directed divergence is studied.
TL;DR: This paper contains a short discussion and examples of the possibility for using the apparatus of generalised nets (GNs) for modelling of intelligent systems (ISs) and a formal definition of the concept of an IS is introduced and illustrated.
Abstract: This paper contains a short discussion and examples of the possibility for using the apparatus of generalised nets (GNs) for modelling of intelligent systems (ISs). A formal definition of the concept of an IS is introduced and illustrated. The GN approach for modelling is discussed and the architectural principles used in it are given. The modelling possibilities of the GNs are illustrated by the ideas for extensions of the concept of an expert system. A series of extensions of this concept are described. A GN model is given, which describes the process of construction of an IS. Some open problems are formulated. In the Appendix, short remarks on the concept of a GN are given: the definition and some components of the GN theory.
TL;DR: This article is based on my presentation at a symposium organised by Binghamton University (SUNY) on the occasion of my retirement and pays tribute to three great scholars, Antonín Svoboda, W. Ross Ashby and Lotfi A. Zadeh, who have decisively influenced my ideas and research work pertaining to the emergence of systems science.
Abstract: This article is based on my presentation at a symposium organised by Binghamton University (SUNY) on the occasion of my retirement. The purpose of the article is to pay tribute to three great scholars, Antonin Svoboda, W. Ross Ashby and Lotfi A. Zadeh, who have decisively influenced my ideas and research work pertaining to the emergence of systems science and to the study of the key role of uncertainty-based information in dealing with systems problems.
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TL;DR: This paper uses complete residuated lattices as the structures of truth degrees, covering thus the real unit interval with left-continuous t-norm and its residuum as an important but particular case and presents results describing central fuzzy sets and optimal central fuzzy set, provided similarity of fuzzy sets is assessed by Leibniz rule.
Abstract: Let B be a collection of fuzzy sets. What are the fuzzy sets which are sufficiently similar to every fuzzy set from B, i.e. ‘central’ fuzzy sets for B? Such a question naturally arises if B is large and one wishes to replace B by a single fuzzy set – the representative of B. In this paper, we develop a framework which enables us to answer this question and related ones. We use complete residuated lattices as the structures of truth degrees, covering thus the real unit interval with left-continuous t-norm and its residuum as an important but particular case. We present results describing central fuzzy sets and optimal central fuzzy sets, provided similarity of fuzzy sets is assessed by Leibniz rule.
TL;DR: A sheaf-theoretic framework for the representation of a quantum observable structure in terms of Boolean information sieves is proposed, based on the existence of a categorical adjunction, which establishes precise criteria of integrability and invariance of quantum information transfer by cohomological means.
Abstract: We propose a sheaf-theoretic framework for the representation of a quantum observable structure in terms of Boolean information sieves. The algebraic representation of a quantum observable structure in the relational local terms of sheaf theory effectuates a semantic transition from the axiomatic set-theoretic context of orthocomplemented partially ordered sets, la Birkhoff and Von Neumann, to the categorical topos-theoretic context of Boolean information sieves, la Grothendieck. The representation schema is based on the existence of a categorical adjunction, which is used as a theoretical platform for the development of a functorial formulation of information transfer, between quantum observables and Boolean localisation devices in typical quantum measurement situations. We also establish precise criteria of integrability and invariance of quantum information transfer by cohomological means.
TL;DR: A detailed representation of the elicitation process influenced by fuzzy rationality is given, and approximation of utilities in FR decision analysis does not depend on the probabilities, but the approximation of probabilities is dependent on preferences.
Abstract: It is widely recognised by decision analysts that real decision-makers always make estimates in an interval form. An overview of techniques to find an optimal alternative among such with imprecise and interval probabilities is presented. Scalarisation methods are outlined as most appropriate. A proper continuation of such techniques is fuzzy rational (FR) decision analysis. A detailed representation of the elicitation process influenced by fuzzy rationality is given. The interval character of probabilities leads to the introduction of ribbon functions, whose general form and special cases are compared with the p-boxes. As demonstrated, approximation of utilities in FR decision analysis does not depend on the probabilities, but the approximation of probabilities is dependent on preferences.