Showing papers in "International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems in 2004"
TL;DR: The concepts of information entropy, rough entropy and knowledge granulation in rough set theory are introduced, and the relationships among those concepts are established.
Abstract: Rough set theory is a relatively new mathematical tool for use in computer applications in circumstances which are characterized by vagueness and uncertainty. In this paper, we introduce the concepts of information entropy, rough entropy and knowledge granulation in rough set theory, and establish the relationships among those concepts. These results will be very helpful for understanding the essence of concept approximation and establishing granular computing in rough set theory.
320 citations
TL;DR: This paper introduces the extended geometric mean (EGM), extended arithmetical averaging (EAA) operator, extended ordered weighted averaged (EOWA) operator and extendedordered weighted geometric (EowG) operator; and proposes approaches to ranking the alternatives in the group decision-making problems.
Abstract: In this paper, we define two types of linguistic preference relations (multiplicative linguistic preference relation and additive linguistic preference relation), and study some of their desirable properties. We introduce the extended geometric mean (EGM) operator, extended arithmetical averaging (EAA) operator, extended ordered weighted averaging (EOWA) operator and extended ordered weighted geometric (EOWG) operator. An approach based on the EGM and EOWG operators and multiplicative linguistic preference relations and an approach based on the EAA and EOWA operators and additive linguistic preference relations are proposed to ranking the alternatives in the group decision-making problems. Finally, we give a numerical example to illustrate the developed approaches.
295 citations
TL;DR: This paper considers the problem of rank-based fuzzy sets, a generalization of ordinary fuzzy sets which are characterized by a membership function and a non-membership function.
Abstract: Intuitionistic fuzzy sets are a generalization of ordinary fuzzy sets which are characterized by a membership function and a non-membership function. In this paper we consider the problem of rankin...
138 citations
TL;DR: In this paper, similarity measures between type-2 fuzzy sets are given and the axiom definition and properties of these measures are provided and for practical use, it is shown how to compute the similarities between Gaussian type- 2 fuzzy sets.
Abstract: In this paper, we give similarity measures between type-2 fuzzy sets and provide the axiom definition and properties of these measures. For practical use, we show how to compute the similarities between Gaussian type-2 fuzzy sets. Yang and Shih's [22] algorithm, a clustering method based on fuzzy relations by beginning with a similarity matrix, is applied to these Gaussian type-2 fuzzy sets by beginning with these similarities. The clustering results are reasonable consisting of a hierarchical tree according to different levels.
82 citations
TL;DR: The capabilities of the Choquet integral aggregation are extended by allowing the ordering to be induced by some values other then those being aggregated, which allows for an induced Choquet Choquet Integral aggregation operator to be considered.
Abstract: We discuss the OWA and Choquet integral aggregation operators and point out the central role the ordering operation plays in these operators. We extend the capabilities of the Choquet integral aggregation by allowing the ordering to be induced by some values other then those being aggregated. This allows us to consider an induced Choquet Choquet integral aggregation operator. We look at the properties of this operator. We then look at its applications. Among the applications considered are aggregations guided by linguistic and other ordinal structures. We look at the use of induced aggregation in nearest neighbor methods. We also consider the Choquet aggregation of complex objects such as matrices and vectors.
77 citations
TL;DR: The general applicability of fuzzy arithmetic based on sparse grids to compute expensive multivariate functions of fuzzy numbers is illustrated by computing two dynamic systems subjected to uncertain parameters as well as uncertain initial conditions.
Abstract: Fuzzy arithmetic provides a powerful tool to introduce uncertainty into mathematical models. With Zadeh's extension principle, one can obtain a fuzzy-valued extension of any real-valued objective function. An efficient and accurate approach to compute expensive multivariate functions of fuzzy numbers is given by fuzzy arithmetic based on sparse grids. In this paper, we illustrate the general applicability of this new method by computing two dynamic systems subjected to uncertain parameters as well as uncertain initial conditions. The first model consists of a system of delay differential equations simulating the periodic outbreak of a disease. In the second model, we consider a multibody mechanism described by an algebraic differential equation system.
53 citations
TL;DR: Methods applicable to associative operators, means and Choquet integral based operators with respect to a universal fuzzy measure are discussed, and special attention is paid to k-order additive symmetric fuzzy measures.
Abstract: This paper treats the problem of fitting general aggregation operators with unfixed number of arguments to empirical data. We discuss methods applicable to associative operators (t-norms, t-conorms, uninorms and nullnorms), means and Choquet integral based operators with respect to a universal fuzzy measure. Special attention is paid to k-order additive symmetric fuzzy measures.
46 citations
TL;DR: The classification of multivariate time-varying data finds application in several fields, such as economics, finance, marketing research, psychometrics, bioinformatics, medicine, signal processing, and more.
Abstract: The classification of multivariate time-varying data finds application in several fields, such as economics, finance, marketing research, psychometrics, bioinformatics, medicine, signal processing,...
45 citations
TL;DR: The definition and properties of intuitionistic fuzzy implication operators are presented and the expression obtained when fuzzy implication and coimplication operators are applied to different aggregations of degrees of truth and non-truth of the propositions are studied.
Abstract: In this paper we present the definition and properties of intuitionistic fuzzy implication operators. We study the expression obtained from said operators when fuzzy implication and coimplication operators are applied to different aggregations of degrees of truth and non-truth of the propositions.
36 citations
TL;DR: Fuzzy cognitive maps are signed directed graphs used to model the evolution of scenarios with time as mentioned in this paper, which can be useful in decision support for predicting future states given an initial state.
Abstract: Fuzzy cognitive maps are signed directed graphs used to model the evolution of scenarios with time. FCMs can be useful in decision support for predicting future states given an initial state. Genet...
36 citations
TL;DR: In this paper, the authors deal with division situations where individual claims can vary within closed intervals and remove uncertainty of claims by weighting in a consistent way the upper and lower bounds of the claim intervals.
Abstract: The paper deals with division situations where individual claims can vary within closed intervals. Uncertainty of claims is removed by weighting in a consistent way the upper and lower bounds of the claim intervals. Deterministic division problems with the obtained compromise claims are then considered and classical division rules from the bankruptcy literature are used to generate several procedures leading to efficient and reasonable rules for division problems under interval uncertainty of claims.
TL;DR: Theories of fuzzy sets and rough sets have emerged as two major mathematical approaches for managing uncertainty that arises from inexact, noisy, or incomplete information.
Abstract: Theories of fuzzy sets and rough sets have emerged as two major mathematical approaches for managing uncertainty that arises from inexact, noisy, or incomplete information. They are generalizations...
TL;DR: By using the relative fuzzy topology a new kind of dynamics is considered, a method for constructing relative semi-dynamical systems is presented and an extension of the notion of conjugate relation is presented.
Abstract: In this paper by using the relative fuzzy topology a new kind of dynamics is considered. A method for constructing relative semi-dynamical systems is presented. Relative fixed points and relative sinks are also studied. New results on invariant sets without any similarity in usual mathematics are deduced. Furthermore an extension of the notion of conjugate relation is presented.
TL;DR: In this article, it was shown that the only way to build a group is to use strict t-norms, and that there is no way to construct a ring with t-conorms.
Abstract: We consider the interval ]-1, 1[ and intend to endow it with an algebraic structure like a ring. The motivation lies in decision making, where scales that are symmetric w.r.t. 0 are needed in order to represent a kind of symmetry in the behaviour of the decision maker. A former proposal due to Grabisch was based on maximum and minimum. In this paper, we propose to build our structure on t-conorms and t-norms, and we relate this construction to uninorms. We show that the only way to build a group is to use strict t-norms, and that there is no way to build a ring. Lastly, we show that the main result of this paper is connected to the theory of ordered Abelian groups.
TL;DR: This work describes a simple application of the new intuitionistic OWA operator which aggregates a set of intuitionistic fuzzy sets Ai in multiple-expert multiple-criteria decision-making.
Abstract: The OWA (Ordered Weighted Average) operator is a powerful non-linear operator for aggregating a set of inputs ai,i∈{1,2,…,M}. In the original OWA operator the inputs are crisp variables ai. This restriction was subsequently removed by Mitchell and Schaefer who by application of the extension principle defined a fuzzy OWA operator which aggregates a set of ordinary fuzzy sets Ai. We continue this process and define an intuitionistic OWA operator which aggregates a set of intuitionistic fuzzy sets Ai. We describe a simple application of the new intuitionistic OWA operator in multiple-expert multiple-criteria decision-making.
TL;DR: The well-known Egoroff's theorem in classical measure theory is established on monotone non-additive measure spaces and Taylor's theorem, which concerns almost everywhere convergence of measurable function sequence in classical measures theory, is generalized.
Abstract: In this paper, the well-known Egoroff's theorem in classical measure theory is established on monotone non-additive measure spaces. Taylor's theorem, which concerns almost everywhere convergence of measurable function sequence in classical measure theory, is also generalized. The converse problem of the theorems are discussed, and a necessary and sufficient condition for the Egoroff's theorem is obtained on semicontinuous fuzzy measure space with S-compactness.
TL;DR: A simple form of imputation is to estimate missing values by max-t & min-s compositions, which is an extension of Yang and Shih's n-step procedure and a clustering algorithm for the similarity-relation matrix is proposed.
Abstract: It is well known that an intuitionistic fuzzy relation is a generalization of a fuzzy relation. In fact there are situations where intuitionistic fuzzy relations are more appropriate. This paper discusses the fuzzy clustering based on intuitionistic fuzzy relations. On the basis of max-t & min-s compositions, we discuss an n-step procedure which is an extension of Yang and Shih's [17] n-step procedure. A similarity-relation matrix is obtained by beginning with a proximity-relation matrix using the proposed n-step procedure. Then we propose a clustering algorithm for the similarity-relation matrix. Numerical comparisons of three critical max-t & min-s compositions: max-t1 & min-s1, max-t2 & min-s2 and max-t3 & min-s3, are made. The results show that max-t1 & min-s1 compositions has better performance. Sometimes, data may be missed with an incomplete proximity-relation matrix. Imputation is a general and flexible method for handling missing-data problem. In this paper we also discuss a simple form of imputation is to estimate missing values by max-t & min-s compositions.
TL;DR: In this paper, a concept of chance distribution is originally presented for bifuzzy variable, and the linearity of expected value operator of bifBuzzy variable is proved.
Abstract: A fuzzy variable is a function from a possibility space to the set of real numbers, while a bifuzzy variable is a function from a possibility space to the set of fuzzy variables. In this paper, a concept of chance distribution is originally presented for bifuzzy variable, and the linearity of expected value operator of bifuzzy variable is proved. Furthermore, bifuzzy simulations are designed and illustrated by some numerical experiments.
TL;DR: Applications of fuzzy linguistic methods in syntactic pattern recognition are described, and fuzzy acceptors in relationship with formal –fuzzy languages and – fuzzy grammars are studied.
Abstract: –fuzzy acceptors in relationship with formal –fuzzy languages and –fuzzy grammars are studied, where is a bounded chain. Applications of fuzzy linguistic methods in syntactic pattern recognition are described.
TL;DR: Weak and strong laws of large numbers (WLLN's and SLLN’s) for weighted sums of independent (not necessarily identically distributed) fuzzy set-valued random variables in the sense of the extended Hausdorff metric are presented.
Abstract: In this paper, we shall present weak and strong laws of large numbers (WLLN's and SLLN's) for weighted sums of independent (not necessarily identically distributed) fuzzy set-valued random variables in the sense of the extended Hausdorff metric , based on the result of set-valued random variable obtained by Taylor and Inoue32,33. This work is a continuation of Li and Ogura20.
TL;DR: A new method of estimating fuzzy multivariable linear and nonlinear regression models using triangular fuzzy numbers is presented, obtained by implementing a dual version of the ridge regression procedure for linear models.
Abstract: This paper presents a new method of estimating fuzzy multivariable linear and nonlinear regression models using triangular fuzzy numbers. This estimation method is obtained by implementing a dual version of the ridge regression procedure for linear models. It allows us to perform fuzzy nonlinear regression by constructing a fuzzy linear regression in a high dimensional feature space for the data set with crisp inputs and fuzzy output. Experimental results are then presented, which indicate the performance of this algorithm.
TL;DR: The fuzzy mapping was established by integrating objective information and subjective information in the design process, such as expert's knowledge, designer's preferences and customer's requirements, where the fuzzy sets, fuzzy mapping and fuzzy transition were used.
Abstract: The contents and meanings of mapping relationships between physical domain and function domain in different design stages, such as conceptual design, detail design and enhancement design, were analyzed. According to the analysis results, the fuzzy mapping between physical domain and function domain in different design stages was established by integrating objective information and subjective information in the design process, such as expert's knowledge, designer's preferences and customer's requirements, where the fuzzy sets, fuzzy mapping and fuzzy transition were used. The property table of structure behavior parameters was established based on the fuzzy mapping relationships. The fuzzy mapping is very important to optimize product structure, perfect product function, meet the diversified and individual requirements of customers. Finally, an example was used to illustrate the fuzzy mapping relationships between physical domain and function domain in different design stages.
TL;DR: The author introduces the notion of fuzzy IC-bags and does some characterizations of them and notes that under the conditions of uncertainty, where the counts of objects are not fixed, then the interval counts can occur with different fuzzy membership grades for each particular object in the collection.
Abstract: In the present paper, the author introduces the notion of fuzzy IC-bags and does some characterizations of them. The concepts of fuzzy base sets, base equivalent fuzzy IC-Bags, cardinally equispaced fuzzy IC-Bags, and cardinally equivalent fuzzy IC-Bags have been developed. The types of peak elements, and the concerned types of peak membership grades have been discussed. It is observed that the collection of any particular type of peak elements together with their membership grades actually form fuzzy bags. A set of operations on fuzzy IC-Bags have been defined and some propositions have been proved. We note that under the conditions of uncertainty, where the counts of objects are not fixed, then the interval counts can occur with different fuzzy membership grades for each particular object in the collection, and the framework for fuzzy IC-Bags provides us with the opportunity to justify and model the organized complexity as a part of the associated intolerance embedded in the subjective patterns.
TL;DR: The proposed model uses convex polyhedral membership functions to represent vague aspirations of the decision maker and enriches the existing satisficing methods for fuzzy multi-objective linear programming in a more practical way with the effective method based on convex cone.
Abstract: A fuzzy multi-objective decision-making with nonlinear membership functions is proposed in this paper by assuming that the decision maker has a fuzzy goal for each objective function The fuzzy goals can be quantified by convex polyhedral membership functions, which are expressed by linguistic terms The concept of the convex cone is used to formulate a normalized convex polyhedral penalty function, which can also be considered conversely as a convex polyhedral membership function The most desirable value of membership functions are selected to be reference membership values of achievement of convex polyhedral membership functions that can be viewed as the extension of the idea of reference point method The formulated model can be solved by existing linear programming solvers and can find the satisficing solution for the decision maker, which can be derived efficiently from among an M-Pareto optimal solution set together with the trade-off rates between the membership functions The proposed model uses convex polyhedral membership functions to represent vague aspirations of the decision maker It enriches the existing satisficing methods for fuzzy multi-objective linear programming in a more practical way with the effective method based on convex cone
TL;DR: In this article, the authors proposed an approach to transform the fuzzy decision-making problem into crisp one by using the compositional rule of inference and signed distance to obtain the order of different alternatives and subsequently obtain the best alternative.
Abstract: An assessment of a set of alternatives under certain evaluation criteria has difficulty in dealing with the priority of these alternatives, especially with a lack of precise information in an uncertain environment. Fuzzy numbers are usually applied to represent the imprecise numerical measurements of different alternatives. In this study statistical data are used to derive level (1-α,1-β) interval-valued fuzzy numbers to represent unknown alternative effectiveness scores, after which, by using the compositional rule of inference and signed distance to transform the fuzzy decision making problem into crisp one, one can conveniently obtain the order of these different alternatives and subsequently obtain the best alternative. The approach presented is computationally efficiency, and its underlying concepts are simple and comprehensible. By using this extended generalized method, two cases of an organizational type of rapid-transit-system selection problem are presented as examples to illustrate the applicability of the interval-valued fuzzy numbers and ranking system for decision making. The key contribution of the method is the seamless integration of the statistical data, interval-valued fuzzy number and signed distance to analyze multicriteria decision making problem. The innovation introduced in the model concerns interval-valued fuzzy number which is recognized as a determinant of the effectiveness score in fuzzy relation matrix.
TL;DR: Numerical results show that the proposed FCML algorithm presents good accuracy and is recommended as a new tool for the parameter estimation of the logistic regression mixture models.
Abstract: Distribution mixtures are used as models to analyze grouped data. The estimation of parameters is an important step for mixture distributions. The latent class model is generally used as the analysis of mixture distributions for discrete data. In this paper, we consider the parameter estimation for a mixture of logistic regression models. We know that the expectation maximization (EM) algorithm was most used for estimating the parameters of logistic regression mixture models. In this paper, we propose a new type of fuzzy class model and then derive an algorithm for the parameter estimation of a fuzzy class logistic regression model. The effects of the explanatory variables on the response variables are described. The focus is on binary responses for the logistic regression mixture analysis with a fuzzy class model. An algorithm, called a fuzzy classification maximum likelihood (FCML), is then created. The mean squared error (MSE) based accuracy criterion for the FCML and EM algorithms to the parameter estimation of logistic regression mixture models are compared using the samples drawn from logistic regression mixtures of two classes. Numerical results show that the proposed FCML algorithm presents good accuracy and is recommended as a new tool for the parameter estimation of the logistic regression mixture models.
TL;DR: Experimental results on the WebKB corpus show that, by fusing the plain text information and the hyperlink structure information, much better classification performance can be achieved.
Abstract: A method to assign fuzzy labels to unlabeled hypertext documents based on hyperlink structure information is first proposed. Then, the construction of the fuzzy transductive support vector machines is described. Also, an algorithm to train the fuzzy transductive support vector machines is presented. While in the transductive support vector machines all the test examples are treated equally, in the fuzzy transductive support vector machines, test examples are treated discriminatively according to their fuzzy labels, hence a more reliable decision function. Experimental results on the WebKB corpus show that, by fusing the plain text information and the hyperlink structure information, much better classification performance can be achieved.
TL;DR: This paper presents the definition of integral of fuzzy mappings from the fuzzy number space E into E, and discusses its properties and calculation, and provides a method of robustness estimates for the traffic volumes passing a road each day.
Abstract: In this paper, we present the definition of integral of fuzzy mappings from the fuzzy number space E into E, and discuss its properties and calculation. And as an application of the integral, we provide a method of robustness estimates for the traffic volumes passing a road each day (24 hours). In addition, we also give another example of the integral characterizing the distance travelled in an imprecise or uncertain environment of time and speed.
TL;DR: A knowledge-based system that mimics human supervisory control performance is developed in the context of dynamic planning involving simulated search and rescue missions using ground based autonomous robots and uninhabited aerial vehicles.
Abstract: With the increases in the levels of automation and computerization, supervisory control systems are becoming increasingly common in commercial and military applications. A supervisory control system consists of one or more human operators interacting with highly automated components such as those seen in satellite ground control, flexible manufacturing systems, or nuclear power plants. Humans typically perform cognitively intense tasks such as monitoring, planning, real-time control, and troubleshooting, and are ultimately responsible for the safe and efficient operation of the overall system. Although developments on supervisory control have led to useful applications in interface design and automation, there is a scarcity of research that empirically evaluates human decision making in supervisory control through emulation of task performance using knowledge-based systems. In the context of dynamic planning involving simulated search and rescue missions using ground based autonomous robots and uninhabited aerial vehicles, we developed a knowledge-based system that mimics supervisory control performance. This paper describes the application domain, the details of the simulation model, and the implementation and assessment of a knowledge-based system that mimics human supervisory control performance.
TL;DR: Ad-hoc wireless networks are power constrained as the nodes operate with limited battery energy, and transactions through each mobile node must be controlled to maximize the lifetime of these networks.
Abstract: Ad-hoc wireless networks are power constrained as the nodes operate with limited battery energy. To maximize the lifetime of these networks, transactions through each mobile node must be controlled...