Showing papers on "Fuzzy number published in 2008"
TL;DR: In this paper, fuzzy logic is viewed in a nonstandard perspective and the cornerstones of fuzzy logic-and its principal distinguishing features-are: graduation, granulation, precisiation and the concept of a generalized constraint.
1,253 citations
TL;DR: A procedure based on the DIFWA operator is developed to solve the dynamic intuitionistic fuzzy multi-attribute decision making (DIF-MADM) problems where all the decision information about attribute values takes the form of intuitionism fuzzy numbers collected at different periods.
571 citations
TL;DR: A fuzzy TOPSIS based methodology is applied to solve the solid waste transshipment site selection problem in Istanbul, Turkey and the criteria weights are calculated by using the AHP.
417 citations
TL;DR: A fuzzy AHP approach is proposed to determine the level of faulty behavior risk (FBR) in work systems and faulty behavior is prevented before occurrence and work system safety is improved.
412 citations
TL;DR: An algorithm for determining the optimal membership degrees with respect to a given goal function is created, and a measure is introduced that is able to identify outlier vertices that do not belong to any of the communities, bridges that have significant membership in more than one single community, and regular Vertices that fundamentally restrict their interactions within their own community.
Abstract: We consider the problem of fuzzy community detection in networks, which complements and expands the concept of overlapping community structure. Our approach allows each vertex of the graph to belong to multiple communities at the same time, determined by exact numerical membership degrees, even in the presence of uncertainty in the data being analyzed. We create an algorithm for determining the optimal membership degrees with respect to a given goal function. Based on the membership degrees, we introduce a measure that is able to identify outlier vertices that do not belong to any of the communities, bridge vertices that have significant membership in more than one single community, and regular vertices that fundamentally restrict their interactions within their own community, while also being able to quantify the centrality of a vertex with respect to its dominant community. The method can also be used for prediction in case of uncertainty in the data set analyzed. The number of communities can be given in advance, or determined by the algorithm itself, using a fuzzified variant of the modularity function. The technique is able to discover the fuzzy community structure of different real world networks including, but not limited to, social networks, scientific collaboration networks, and cortical networks, with high confidence.
393 citations
TL;DR: This paper defines the concepts of association matrix and equivalent association matrix, and introduces some methods for calculating the association coefficients of IFSs, and proposes a clustering algorithm for IFS's, which is extended to cluster interval-valued intuitionistic fuzzy sets (IVIFSs).
385 citations
01 Jun 2008
TL;DR: To investigate the system stability, an interval type-2 Takagi-Sugeno (T-S) fuzzy model is proposed to represent the nonlinear plant subject to parameter uncertainties, which allows the introduction of slack matrices to handle the parameter uncertainties in the stability analysis.
Abstract: This paper presents the stability analysis of interval type-2 fuzzy-model-based (FMB) control systems. To investigate the system stability, an interval type-2 Takagi-Sugeno (T-S) fuzzy model, which can be regarded as a collection of a number of type-1 T-S fuzzy models, is proposed to represent the nonlinear plant subject to parameter uncertainties. With the lower and upper membership functions, the parameter uncertainties can be effectively captured. Based on the interval type-2 T-S fuzzy model, an interval type-2 fuzzy controller is proposed to close the feedback loop. To facilitate the stability analysis, the information of the footprint of uncertainty is used to develop some membership function conditions, which allow the introduction of slack matrices to handle the parameter uncertainties in the stability analysis. Stability conditions in terms of linear matrix inequalities are derived using a Lyapunov-based approach. Simulation examples are given to illustrate the effectiveness of the proposed interval type-2 FMB control approach.
382 citations
TL;DR: An efficient centroid type-reduction strategy for general type-2 fuzzy set that usually needs only several resolution of @a value such that the defuzzified value converges to a real value.
361 citations
TL;DR: In this paper, a fuzzy analytical hierarchy process (AHP) model is proposed to deal with the uncertainty and vagueness involved in the mapping of one's preference to an exact number or ratio.
305 citations
TL;DR: An optimization model based on the maximizing deviation method, by which the attribute weights can be determined, is established and another optimization model is established for the special situations where the information about attribute weights is completely unknown.
Abstract: With respect to multiple attribute decision making problems with intuitionistic fuzzy information, some operational laws of intuitionistic fuzzy numbers, score function and accuracy function of intuitionistic fuzzy numbers are introduced. An optimization model based on the maximizing deviation method, by which the attribute weights can be determined, is established. For the special situations where the information about attribute weights is completely unknown, we establish another optimization model. By solving this model, we get a simple and exact formula, which can be used to determine the attribute weights. We utilize the intuitionistic fuzzy weighted averaging (IFWA) operator to aggregate the intuitionistic fuzzy information corresponding to each alternative, and then rank the alternatives and select the most desirable one(s) according to the score function and accuracy function. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.
290 citations
TL;DR: This paper proposes a self-evolving interval type-2 fuzzy neural network (SEIT2FNN) with online structure and parameter learning, which is applied to simulations on nonlinear plant modeling, adaptive noise cancellation, and chaotic signal prediction.
Abstract: This paper proposes a self-evolving interval type-2 fuzzy neural network (SEIT2FNN) with online structure and parameter learning. The antecedent parts in each fuzzy rule of the SEIT2FNN are interval type-2 fuzzy sets and the fuzzy rules are of the Takagi-Sugeno-Kang (TSK) type. The initial rule base in the SEIT2FNN is empty, and the online clustering method is proposed to generate fuzzy rules that flexibly partition the input space. To avoid generating highly overlapping fuzzy sets in each input variable, an efficient fuzzy set reduction method is also proposed. This method independently determines whether a corresponding fuzzy set should be generated in each input variable when a new fuzzy rule is generated. For parameter learning, the consequent part parameters are tuned by the rule-ordered Kalman filter algorithm for high-accuracy learning performance. Detailed learning equations on applying the rule-ordered Kalman filter algorithm to the SEIT2FNN consequent part learning, with rules being generated online, are derived. The antecedent part parameters are learned by gradient descent algorithms. The SEIT2FNN is applied to simulations on nonlinear plant modeling, adaptive noise cancellation, and chaotic signal prediction. Comparisons with other type-1 and type-2 fuzzy systems in these examples verify the performance of the SEIT2FNN.
TL;DR: An analytic hierarchical process (AHP) based on fuzzy numbers multi-attribute method is proposed for the evaluation and justification of an advanced manufacturing system and an example of machine tool selection is used to illustrate and validate the proposed approach.
Abstract: Investment evaluation methods play an important role in today's competitive manufacturing environment. Shrinking profit margins and diversification require careful analysis of investments and decisions regarding these investments are crucial for the survival of the manufacturing industry. Both economic evaluation criterion and strategic criteria such as flexibility, quality improvement, which are not quantitative in nature, are considered for evaluation. Much has been written about the deficiencies of traditional models for justifying advanced manufacturing systems. The use of fuzzy set theory allows incorporating unquantifiable, incomplete and partially known information into the decision model. In this paper, an analytic hierarchical process (AHP) based on fuzzy numbers multi-attribute method is proposed for the evaluation and justification of an advanced manufacturing system. Finally, an example of machine tool selection is used to illustrate and validate the proposed approach.
TL;DR: An algorithm using discernibility matrix to compute all the attributes reductions is developed and shows that the idea in this paper is feasible and valid.
Abstract: Fuzzy rough sets are the generalization of traditional rough sets to deal with both fuzziness and vagueness in data. The existing researches on fuzzy rough sets are mainly concentrated on the construction of approximation operators. Less effort has been put on the attributes reduction of databases with fuzzy rough sets. This paper mainly focuses on the attributes reduction with fuzzy rough sets. After analyzing the previous works on attributes reduction with fuzzy rough sets, we introduce formal concepts of attributes reduction with fuzzy rough sets and completely study the structure of attributes reduction. An algorithm using discernibility matrix to compute all the attributes reductions is developed. Based on these lines of thought, we set up a solid mathematical foundation for attributes reduction with fuzzy rough sets. The experimental results show that the idea in this paper is feasible and valid.
01 Jun 2008
TL;DR: F fuzzyDL, an expressive fuzzy description logic reasoner, is presented, including some novel concept constructs and queries, and examples of use cases: matchmaking and fuzzy control.
Abstract: In this paper we present fuzzyDL, an expressive fuzzy description logic reasoner.We present its salient features, including some novel concept constructs and queries, and examples of use cases: matchmaking and fuzzy control.
01 Jun 2008
TL;DR: Results from a simulated coupled tank experiment demonstrated that IT2 FLCs that employ the proposed type reduction algorithm share similar robustness properties as FLC's based on the Karnik-Mendel type reducer.
Abstract: This paper introduces an alternative type-reduction method for interval type-2 (IT2) fuzzy logic systems (FLSs), with either continuous or discrete secondary membership function. Unlike the Karnik-Mendel type reducer which is based on the wavy-slice representation of a type-2 fuzzy set, the proposed type reduction algorithm is developed using the vertical-slice representation. One advantage of the approach is the output of the type reducer can be expressed in closed form, thereby providing a tool for the theoretical analysis of IT2 FLSs. The computational complexity of the proposed method is also lower than the uncertainty bounds method and the enhanced Karnik-Mendel method. To assess the feasibility of the proposed type-reducer, it is used to calculate the output of an IT2 fuzzy logic controller (FLCs). Results from a simulated coupled tank experiment demonstrated that IT2 FLCs that employ the proposed type reduction algorithm share similar robustness properties as FLCs based on the Karnik-Mendel type reducer.
TL;DR: A revised method is proposed which can avoid problems of Chu and Tsao's method for ranking fuzzy numbers, and it is easy to rank fuzzy numbers in a way similar to the original method.
Abstract: In 2002, Chu and Tsao proposed a method to rank fuzzy numbers. They employed an area between the centroid and original points to rank fuzzy numbers; however there were some problems with the ranking method. In this paper, we want to indicate these problems of Chu and Tsao's method, and then propose a revised method which can avoid these problems for ranking fuzzy numbers. Since the revised method is based on the Chu and Tsao's method, it is easy to rank fuzzy numbers in a way similar to the original method.
TL;DR: This work uses triangular fuzzy numbers to express the subjective preferences of evaluators and the fuzzy analytical hierarchy process (AHP) method to compute the relative weights for each criterion, and uses non-additive fuzzy integral to obtain the fuzzy synthetic performance of each common criterion.
TL;DR: The integration of fuzzy set theory and wavelet neural networks (WNNs) is proposed to alleviate the problem of effective control of an uncertain system and results in a better performance despite its smaller parameter space.
Abstract: One of the main problems for effective control of an uncertain system is the creation of the proper knowledge base for the control system. In this paper, the integration of fuzzy set theory and wavelet neural networks (WNNs) is proposed to alleviate the problem. The proposed fuzzy WNN is constructed on the base of a set of fuzzy rules. Each rule includes a wavelet function in the consequent part of the rule. The parameter update rules of the system are derived based on the gradient descent method. The structure is tested for the identification and the control of the dynamic plants commonly used in the literature. It is seen that the proposed structure results in a better performance despite its smaller parameter space.
Book•
15 Apr 2008
TL;DR: It is believed that the methods of fuzzy c-means become complete by adding the entropy-based method to the method by Dunn and Bezdek, since one can observe natures of the both methods more deeply by contrasting these two.
Abstract: The main subject of this book is the fuzzy c-means proposed by Dunn and Bezdek and their variations including recent studies A main reason why we concentrate on fuzzy c-means is that most methodology and application studies in fuzzy clustering use fuzzy c-means, and hence fuzzy c-means should be considered to be a major technique of clustering in general, regardless whether one is interested in fuzzy methods or not Unlike most studies in fuzzy c-means, what we emphasize in this book is a family of algorithms using entropy or entropy-regularized methods which are less known, but we consider the entropy-based method to be another useful method of fuzzy c-means Throughout this book one of our intentions is to uncover theoretical and methodological differences between the Dunn and Bezdek traditional method and the entropy-based method We do note claim that the entropy-based method is better than the traditional method, but we believe that the methods of fuzzy c-means become complete by adding the entropy-based method to the method by Dunn and Bezdek, since we can observe natures of the both methods more deeply by contrasting these two
TL;DR: This paper focuses on the generalization of covering-based rough set models via the concept of fuzzy covering, where two pairs of generalized lower and upper fuzzy rough approximation operators are constructed by means of an implicator I and a triangular norm T.
TL;DR: In this article, a multi-objective model for the placement of distributed generation (DG) units in the distribution networks in an uncertain environment is presented. And the true Pareto-optimal solutions are found with a multiobjective genetic algorithm and the final solution is found using a max-min approach.
Abstract: A strategy is presented for the placement of distributed generation (DG) units in the distribution networks in an uncertain environment. Uncertainties in the system are modelled using fuzzy numbers. The proposed approach is based on a multi-objective model in which the objectives are defined as minimisation of monetary cost index (including investment, operation cost of DG units and cost of losses), technical risks (including risks of voltage and loading constraints violation because of load uncertainty) and economic risk due to electricity market price uncertainty. The true Pareto-optimal solutions are found with a multi-objective genetic algorithm and the final solution is found using a max–min approach. An example is presented to demonstrate the effectiveness of the proposed methodology.
TL;DR: It is shown under some suitable conditions that an approximately additive function can be approximated by an additive mapping in a fuzzy sense.
TL;DR: The proposed FANP approach could effectively deal with the uncertain judgment inherent in the decision making process and derive the meaningful priorities explicitly from a complex decision structure in the evaluation of contaminated site remedial countermeasures.
TL;DR: This paper presents a fuzzy optimization method based on the concept of ideal and anti-ideal points to solve multi-criteria decision making problems under fuzzy environments to demonstrate the method's effectiveness.
Abstract: This paper presents a fuzzy optimization method based on the concept of ideal and anti-ideal points to solve multi-criteria decision making problems under fuzzy environments. The quantitative criteria values of each alternative are represented by triangular fuzzy numbers, and its qualitative counterparts and the weight of each criterion are described by linguistic terms, which can also be expressed as triangular fuzzy numbers in the proposed method. With the definition of fuzzy ideal and anti-ideal weight distances, an objective function is constructed to derive the optimal evaluation for each alternative denoted by a fuzzy membership degree. The ranking of alternatives and the best one can be determined directly on the basis of the fuzzy membership degrees without a need to compare fuzzy numbers. The evaluation process is simple and easy to use in practice. A case study of reservoir flood control operation is given to demonstrate the proposed method's effectiveness.
TL;DR: The work of Huang and Shen is extended, and the result enables both interpolation and extrapolation which involve multiple fuzzy rules, with each rule consisting of multiple antecedents.
Abstract: Fuzzy interpolation does not only help to reduce the complexity of fuzzy models, but also makes inference in sparse rule-based systems possible. It has been successfully applied to systems control, but limited work exists for its applications to tasks like prediction and classification. Almost all fuzzy interpolation techniques in the literature make strong assumptions that there are two closest adjacent rules available to the observation, and that such rules must flank the observation for each attribute. Also, some interpolation approaches cannot handle fuzzy sets whose membership functions involve vertical slopes. To avoid such limitations and develop a more practical approach, this paper extends the work of Huang and Shen. The result enables both interpolation and extrapolation which involve multiple fuzzy rules, with each rule consisting of multiple antecedents. Two realistic applications, namely truck backer-upper control and computer activity prediction, are provided in this paper to demonstrate the utility of the extended approach. Experiment-based comparisons to the most commonly used Mamdani fuzzy reasoning mechanism, and to other existing fuzzy interpolation techniques are given to show the significance and potential of this research.
TL;DR: This paper is concerned with the problem of adaptive fuzzy output tracking for a class of perturbed strict-feedback nonlinear systems with time delays and unknown virtual control coefficients, and the adaptive fuzzy tracking controller is designed by using the backstepping technique and Lyapunov-Krasovskii functionals.
TL;DR: A vector similarity measure (VSM) is proposed for IT2 FSs, whose two elements measure the similarity in shape and proximity, respectively, which shows that the VSM gives more reasonable results than all other existing similarity measures for IT1 FSs for the linguistic approximation problem.
TL;DR: A linear goal programming model is constructed to integrate the fuzzy assessment information and to directly compute the collective ranking values of alternatives without the need of information transformation to solve the group decision making (GDM) problems with multi-granularity linguistic assessment information.
TL;DR: A general framework for the study of T-fuzzy rough approximation operators in which both the constructive and axiomatic approaches are used, and a notion of fuzziness is introduced.
TL;DR: A new way of looking at fuzzy intervals is introduced, which enables interval analysis to be directly extended to fuzzy intervals, without resorting to alpha-cuts, in agreement with Zadeh's extension principle.
Abstract: In this paper, we introduce a new way of looking at fuzzy intervals. Instead of considering them as fuzzy sets, we see them as crisp sets of entities we call gradual (real) numbers. They are a gradual extension of real numbers, not of intervals. Such a concept is apparently missing in fuzzy set theory. Gradual numbers basically have the same algebraic properties as real numbers, but they are functions. A fuzzy interval is then viewed as a pair of fuzzy thresholds, which are monotonic gradual real numbers. This view enables interval analysis to be directly extended to fuzzy intervals, without resorting to alpha-cuts, in agreement with Zadeh's extension principle. Several results show that interval analysis methods can be directly adapted to fuzzy interval computation where end- points of intervals are changed into left and right fuzzy bounds. Our approach is illustrated on two known problems: computing fuzzy weighted averages and determining fuzzy floats and latest starting times in activity network scheduling.