Showing papers in "Fuzzy Optimization and Decision Making in 2004"
TL;DR: The ordered weighted averaging operator is extended to a provide a new class of operators called the generalized OWA (GOWA) operators, which add to the OWA operator an additional parameter controlling the power to which the argument values are raised.
Abstract: We extend the ordered weighted averaging (OWA) operator to a provide a new class of operators called the generalized OWA (GOWA) operators. These operators add to the OWA operator an additional parameter controlling the power to which the argument values are raised. We look at some special cases of these operators. One important case corresponds to the generalized mean and another special case is the ordered weighted geometric operator.
566 citations
TL;DR: A theoretic basis has been developed for the application of the interval fuzzy preference relations in group decision making because it is proven that an interval fuzzy preferences relation B and the synthetic intervals fuzzy preference relation A are of acceptable compatibility.
Abstract: This paper defines the concept of compatibility degree of two interval fuzzy preference relations, and gives a compatibility index of two interval fuzzy preference relations. It is proven that an interval fuzzy preference relation B and the synthetic interval fuzzy preference relation of interval fuzzy preference relations A1,A2,…,As are of acceptable compatibility under the condition that the interval fuzzy preference relation B and each of the interval fuzzy preference relations Al,A2,…,As are of acceptable compatibility, and thus a theoretic basis has been developed for the application of the interval fuzzy preference relations in group decision making.
223 citations
TL;DR: This study demonstrates that by considering all the information deriving from the constraints better results in terms of certainty and reliability can be achieved.
Abstract: The selection of a project among a set of possible alternatives is a difficult task decision makers have to face. Difficulties in selecting a project arise because of the different goals involved and because of the large number of attributes to consider. Our approach is based upon a fuzzy extension of the Analytic Hierarchy Process (AHP). This paper focuses on the constraints that have to be considered within fuzzy AHP in order to take in account all the available information. This study demonstrates that by considering all the information deriving from the constraints better results in terms of certainty and reliability can be achieved.
185 citations
TL;DR: A two person zero-sum matrix game with fuzzy goals is shown to be equivalent to a primal-dual pair of fuzzy linear programming problems.
Abstract: A two person zero-sum matrix game with fuzzy goals is shown to be equivalent to a primal-dual pair of fuzzy linear programming problems. Further certain difficulties with similar studies reported in the literature are also discussed.
94 citations
TL;DR: Experimental results show that better results are obtained from composite criteria of confidence and support measures than their individual use, and that genetic algorithm-based rule selection can improve the classification ability of extracted fuzzy rules by searching for good rule combinations.
Abstract: This paper compares heuristic criteria used for extracting a pre-specified number of fuzzy classification rules from numerical data. We examine the performance of each heuristic criterion through computational experiments on well-known test problems. Experimental results show that better results are obtained from composite criteria of confidence and support measures than their individual use. It is also shown that genetic algorithm-based rule selection can improve the classification ability of extracted fuzzy rules by searching for good rule combinations. This observation suggests the importance of taking into account the combinatorial effect of fuzzy rules (i.e., the interaction among them).
69 citations
TL;DR: Based on multicriteria programming problems it should be demonstrated that the dilemma of data processing in case of real programming problems can be handled adequately by modeling them as fuzzy system combined with an interactive problem-solving.
Abstract: Classical mathematical programming models require well-defined coefficients and right hand sides. In order to avoid a non satisfying modeling usually a broad information gathering and processing is necessary. In case of real problems some model parameters can be only roughly estimated. While in case of classical models the vague data is replaced by "average data", fuzzy models offer the opportunity to model subjective imaginations of the decision maker as precisely as a decision maker will be able to describe it. Thus the risk of applying a wrong model of the reality and selecting solutions which do not reflect the real problem can be clearly reduced. The modeling of real problems by means of deterministic and stochastic models requires extensive information processing. On the other hand we know that an optimum solution is finally defined only by few restrictions. Especially in case of larger systems we notice afterwards that most of the information is useless. The dilemma of data processing is due to the fact that first we have to calculate the solution in order to define, whether the information must be well-defined or whether vague data may be sufficient. Based on multicriteria programming problems it should be demonstrated that the dilemma of data processing in case of real programming problems can be handled adequately by modeling them as fuzzy system combined with an interactive problem-solving. Describing the real problem by means of a fuzzy system first of all only the available information or such information which can be achieved easily will be considered. Then we try to develop an optimum solution. With reference to the cost-benefit relation further information can be gathered in order to describe the solution more precisely. Furthermore it should be pointed out that some interactive fuzzy solution algorithms, e.g. FULPAL provide the opportunity to solve mixed integer multicriteria programming models as well.
63 citations
TL;DR: A bi-matrix game with fuzzy goal is shown to be equivalent to a (crisp) non-linear programming problem in which the objective as well as all constraint functions are linear except two constraint functions, which are quadratic.
Abstract: A bi-matrix game with fuzzy goal is shown to be equivalent to a (crisp) non-linear programming problem in which the objective as well as all constraint functions are linear except two constraint functions, which are quadratic. This equivalence is further extended to bi-matrix games with fuzzy pay-offs, as well as to bi-matrix games with fuzzy goals and fuzzy payoffs, whose equilibrium strategies are conceptualized by employing a suitable ranking (defuzzification) function.
56 citations
TL;DR: This paper extends this useful property for fuzzy relation programming problem with max-strict-t-norm composition and presents it as a supplemental note of Guu and Wu's previous work.
Abstract: The fuzzy relation programming problem is a minimization problem with a linear objective function subject to fuzzy relation equations using certain algebraic compositions. Previously, Guu and Wu considered a fuzzy relation programming problem with max-product composition and provided a necessary condition for an optimal solution in terms of the maximum solution derived from the fuzzy relation equations. To be more precise, for an optimal solution, each of its components is either 0 or the corresponding component's value of the maximum solution. In this paper, we extend this useful property for fuzzy relation programming problem with max-strict-t-norm composition and present it as a supplemental note of our previous work.
46 citations
TL;DR: This work focuses on the uncertainty in the right side of constraints which arises, in the context of the radiation therapy problem, from the fact that minimal and maximal radiation tolerances are ranges of values, with preferences within the range whose values are based on research results, empirical findings, and expert knowledge.
Abstract: The semantic and algorithmic differences between fuzzy and possibilistic optimization methods are presented in the context of three methods for solving large fuzzy and possibilistic optimization problems. In particular, an optimization problem in radiation therapy with various orders of complexity, 1,000-55,000 constraints, possessing (i) soft constraints, (ii) fuzzy right-hand side values and (iii) possibilistic right-hand side values, are used to illustrate the semantics and to test the performance of the three fuzzy and possibilistic optimization methods. We focus on the uncertainty in the right side which arises, in the context of the radiation therapy problem, from the fact that minimal/maximal radiation tolerances are target values rather than fixed real numbers. The results indicate that fuzzy/possibilistic optimization is a natural way to model various types of optimization under uncertainty problems and large optimization problems can be solved efficiently.
43 citations
TL;DR: It is shown that there is no duality gap between the primal and dual fuzzy optimization problems under suitable assumptions for fuzzy-valued functions.
Abstract: A solution concept of fuzzy optimization problems, which is essentially similar to the notion of Pareto optimal solution (nondominated solution) in multiobjective programming problems, is introduced by imposing a partial ordering on the set of all fuzzy numbers. We also introduce a concept of fuzzy scalar (inner) product based on the positive and negative parts of fuzzy numbers. Then the fuzzy-valued Lagrangian function and the fuzzy-valued Lagrangian dual function for the fuzzy optimization problem are proposed via the concept of fuzzy scalar product. Under these settings, the weak and strong duality theorems for fuzzy optimization problems can be elicited. We show that there is no duality gap between the primal and dual fuzzy optimization problems under suitable assumptions for fuzzy-valued functions.
35 citations
TL;DR: An aspect of subjective interestingness called “item-relatedness” is introduced, a consequence of relationships that exist between items in a domain, and three mechanisms for extending this measure from a two-item set to an association rule consisting of a set of more than two items.
Abstract: In Knowledge Discovery in Databases (KDD)/Data Mining literature, “interestingness” measures are used to rank rules according to the “interest” a particular rule is expected to evoke. In this paper, we introduce an aspect of subjective interestingness called “item-relatedness”. Relatedness is a consequence of relationships that exist between items in a domain. Association rules containing unrelated or weakly related items are interesting since the co-occurrence of such items is unexpected. ‘Item-Relatedness’ helps in ranking association rules on the basis of one kind of subjective unexpectedness. We identify three types of item-relatedness – captured in the structure of a “fuzzy taxonomy” (an extension of the classical concept hierarchy tree). An “item-relatedness” measure for describing relatedness between two items is developed by combining these three types. Efficacy of this measure is illustrated with the help of a sample taxonomy. We discuss three mechanisms for extending this measure from a two-item set to an association rule consisting of a set of more than two items. These mechanisms utilize the relatedness of item-pairs and other aspects of an association rule, namely its structure, distribution of items and item-pairs. We compare our approach with another method from recent literature.
TL;DR: Various schemes of genetic optimization and gradient-based learning aimed at further refinement of the connections of the neurons are discussed and elaborated on the interpretation aspects of the network and show how this leads to a Boolean or multivalued logic description of the experimental data.
Abstract: This study is concerned with cascade architectures of fuzzy neural networks. These networks exhibit three interesting and practically appealing features: (i) come with sound and transparent logic characteristics by being developed with the aid of AND and OR fuzzy neurons and subsequently logic processors (LPs), (ii) possess significant learning abilities and in this way fall in the realm of neuro-fuzzy architectures, and (iii) exhibit an evident hierarchical structure owing to the cascade of the LPs. We discuss main functional properties of the model and relate them to its form of cascade-type of systems formed as a stack of LPs. The construction of the systems of this form calls for some structural optimization that is realized in the realm of genetic optimization. The structure of the network that deals with a selection of a subset of input variables and their distribution across the individual LPs is optimized with the use of genetic algorithms (GAs). The chromosomes encode the order of the variables as well as include the parameters (connections) of the neurons. We discuss various schemes of genetic optimization (both a two-level and single-level GA) and gradient-based learning aimed at further refinement of the connections of the neurons. We elaborate on the interpretation aspects of the network and show how this leads to a Boolean or multivalued logic description of the experimental data. A number of numeric data sets are discussed with respect to the performance of the constructed networks and their interpretability.
TL;DR: The suggested method was used to build a fuzzy expert system that approximates the functional relationship between physical fitness and some of the measurable physiological parameters by their real measurements and opinion (human-experiences) of a medical expert.
Abstract: This study presents a method of adaptive identification of parameters describing Sugeno fuzzy inference system in presence of bounded disturbances while maintaining the readability and interpretability of the fuzzy model during and after identification. This method do not require any a priori knowledge of a bound on the disturbance and noise and of a bound on the unknown parameters values. The method can be used for the robust and adaptive identification of slowly time varying nonlinear systems using fuzzy inference systems. The suggested method was used to build a fuzzy expert system that approximates the functional relationship between physical fitness and some of the measurable physiological parameters by their real measurements and opinion (human-experiences) of a medical expert.
TL;DR: The proposed robust fuzzy identification scheme has been applied to approximate the physical fitness of patients with a fuzzy expert system and is shown to be capable of capturing the decisions (experiences) of a medical expert.
Abstract: This study considers the robust identification of the parameters describing a Sugeno type fuzzy inference system with uncertain data. The objective is to minimize the worst-case residual error using a numerically efficient algorithm. The Sugeno type fuzzy systems are linear in consequent parameters but nonlinear in antecedent parameters. The robust consequent parameters identification problem can be formulated as second-order cone programming problem. The optimal solution of this second-order cone problem can be interpreted as solution of a Tikhonov regularization problem with a special choice of regularization parameter which is optimal for robustness (Ghaoui and Lebret (1997). SAIM Journal of Matrix Analysis and Applications 18, 1035–1064). The final regularized nonlinear optimization problem allowing simultaneous identification of antecedent and consequent parameters is solved iteratively using a generalized Gauss–Newton like method. To illustrate the approach, several simulation studies on numerical examples including the modelling of a spectral data function (one-dimensional benchmark example) is provided. The proposed robust fuzzy identification scheme has been applied to approximate the physical fitness of patients with a fuzzy expert system. The identified fuzzy expert system is shown to be capable of capturing the decisions (experiences) of a medical expert.
TL;DR: It is shown that, given a possibly optimalextreme point with a higher membership degree, the membership degree of an adjacent extreme point is calculated by solving a linear programming problem and that all possibly optimal vertices are enumerated sequentially by tracing adjacent possibly optimal extreme points from apossibly optimal extreme point with the highest membership degree.
Abstract: In this paper, we treat linear programming problems with fuzzy objective function coefficients. To such a problem, the possibly optimal solution set is defined as a fuzzy set. It is shown that any possibly optimal solution can be represented by a convex combination of possibly optimal vertices. A method to enumerate all possibly optimal vertices with their membership degrees is developed. It is shown that, given a possibly optimal extreme point with a higher membership degree, the membership degree of an adjacent extreme point is calculated by solving a linear programming problem and that all possibly optimal vertices are enumerated sequentially by tracing adjacent possibly optimal extreme points from a possibly optimal extreme point with the highest membership degree.
TL;DR: The sufficient condition for the asymptotic stability is derived with the assumption that the time-delay is unknown by applying Lyapunov–Krasovskii theorem and this condition is converted into the LMI problem.
Abstract: A new discrete-time fuzzy partial state feedback control method for the nonlinear systems with unknown time-delay is proposed. Ma et al. proposed the design method of the fuzzy controller based on the fuzzy observer and Cao and Frank extend this result to be applicable to the case of the nonlinear systems with the time-delay. However, the time-delay is likely to be unknown in practical. In this paper, the sufficient condition for the asymptotic stability is derived with the assumption that the time-delay is unknown by applying Lyapunov–Krasovskii theorem and this condition is converted into the LMI problem.
TL;DR: His epistemic framework offers a comprehensive and surprisingly modern framework to study individual decision making and suggests a bridgeway from the Kantian program into the concept of fuzziness, which may have had its second prolegomenon in the work by Frege, Russell, Wittgenstein, Peirce and Black.
Abstract: “Prolegomenon” means something said in advance of something else. In this study, we posit that part of the work by Arthur Schopenhauer (1788–1860) can be thought of as a prolegomenon to the existing concept of “fuzziness.” His epistemic framework offers a comprehensive and surprisingly modern framework to study individual decision making and suggests a bridgeway from the Kantian program into the concept of fuzziness, which may have had its second prolegomenon in the work by Frege, Russell, Wittgenstein, Peirce and Black. In this context, Zadeh's seminal contribution can be regarded as the logical consequence of the Kant-Schopenhauer representation framework.
TL;DR: The fuzzy perception value of the expectation of the optimal stopped reward is characterized and calculated by a new recursive equation and a numerical example described by triangular fuzzy numbers is given.
Abstract: Stimulated by Zadeh's paper (Journal of Statistical Planning and Inference,2002, 105, 233--264), we will try to consider a perceptive analysis of the optimal stopping problem. In this paper, the fuzzy perception value of the expectation of the optimal stopped reward is characterized and calculated by a new recursive equation. Also, a numerical example described by triangular fuzzy numbers is given.
TL;DR: A genetic algorithm is applied to adjust the automaton parameters for selecting the ones best fit to a particular application, which overcomes the difficulty of using common optimizing techniques like gradient descent.
Abstract: Deformed fuzzy automata are complex structures that can be used for solving approximate string matching problems when input strings are composed by fuzzy symbols. Different string similarity definitions are obtained by the appropriate selection of fuzzy operators and parameters involved in the calculus of the automaton transitions. In this paper, we apply a genetic algorithm to adjust the automaton parameters for selecting the ones best fit to a particular application. This genetic approach overcomes the difficulty of using common optimizing techniques like gradient descent, due to the presence of non-derivable functions in the calculus of the automaton transitions. Experimental results, obtained in a text recognition experience, validate the proposed methodology.