Selection of parameters for a fuzzy logic controller

The fuzzy logic controller is reviewed and its parameter are explicitly identified. The problem of initial selection and subsequent adjustment of the parameters are discussed in detail by example.     

Comparison of fuzzy sets on the same decision space

Some methods of making fuzzy decisions include a comparison of fuzzy sets on the same space. Methods have been published which suffer from lack of discrimination between alternatives and occasional conflict with intuitive choice. These methods are reviewed in this paper and then a new approach is described which overcomes their drawbacks. Methods of evaluating the parameter used in decision-making are given which can be varied to incorporate different utility functions.     

Interactive fuzzy linear programming and an application sample at a textile firm

The purpose of this study is to examine Interactive Fuzzy Linear Programming (IFLP) model by using Zimmermann, Werners, Chanas and Verdegay’s approaches that provide best decision-making under fuzzy environments. In this study, it is used the method which can model the fuzzy structure of the real world and which operates with the decision maker interactively, which aims at obtaining the best solution by continuing this interactiveness in the solution process, which includes fuzziness with more realistic approach to the system. It is showed that the importance of fuzziness concept for IFLP problems, how it is applied on real-world problems and its effects.     

Fuzzy σ-algebras and fuzzy measurable functions

In this paper we first give an axiomatic definition of a fuzzy σ-algebra which is a generalisation of the family of fuzzy events considered by L.A. Zadeh [13]. The relationship between classical and fuzzy σ-algebras and between topologies and σ-algebras, in both cases, classical and fuzzy, is established in the notation of commutative diagrams. For fuzzy topologies we refer to the work of R. Lowen [8]. After a comparison between classical measurability of functions and fuzzy measurability defined in this paper we finally introduce the product of fuzzy σ-algebras.     

Directional fuzzy clustering and its application to fuzzy modelling

The paradigm of clustering (unsupervised learning) viewed as a fundamental tool for data analysis has been found useful in fuzzy modelling. While the objective functions guiding the clustering mechanisms are by and large direction-free (namely, they do not distinguish between independent (input) and dependent (output) variables, for most of the models this discrimination becomes of vital importance. The method of directional clustering takes the directionality requirement into account by incorporating the nature of the functional relationships into the objective function guiding the formation of the clusters. The complete clustering algorithm is presented. The role of this method in a two-phase fuzzy identification scheme is also revealed in detail.     

The fuzzy entropy concept and its application

The fuzzy entropy is applied to the seal impression problem to measure the subjective value of information under the condition of uncertainty.Two methods, successive and direct segmentation, are introduced in recognizing the pattern to find out which method is more cost-effective. For the equal entropy, the comparative elements sought in association with the cost information on the successive and direct segmentation methods are 441 and 1024, respectively. Thus, the effectiveness of the former method is 2.32 times higher than that of the latter method, provided that the cost of information is equal.A parametric analysis among the membership function, fuzzy entropy, and threshold level is made and a summary graph shown.     

A quantum mechanical approach to a fuzzy theory

Recently, we proposed a general measurement theory for classical and quantum systems (i.e., “objective fuzzy measurement theory”). In this paper, we propose “subjective fuzzy measurement theory”, which is characterized as the statistical method of the objective fuzzy measurement theory. Our proposal of course has a lot of advantages. For example, we can directly see “membership functions” (= “fuzzy sets”) in this theory. Therefore, we can propose the objective and the subjective methods of membership functions. As one of the consequences, we assert the objective (i.e., individualistic) aspect of Zadeh's theory. Also, as a quantum application, we clarify Heisenberg's uncertainty relation.     

The solution of fuzzy linear systems by non-linear programming: a financial application

Fuzzy linear systems of equations play a major role in various financial applications. In this paper we analyse a particular fuzzy linear system: the derivation of the risk neutral probabilities in a fuzzy binary tree. This system has previously been investigated and different solutions to different forms of the same system have been proposed.     

典型模糊控制器的隶属函数设计及分析

基于一类sum-product模糊推理算子、重心解模糊化法和单点输出的典型模糊控制器的解析结构推导,深入分析了输入隶属函数对模糊控制系统性能的影响,提出了隶属函数的系统化设计方法.并在此基础上,设计了一种具有等差间距因子的三角形隶属函数并推导了其模糊控制器的解析结构,仿真结果证明了该设计的有效性.     

A new method for ranking fuzzy numbers and its application to group decision making

In this paper, a new method for comparing fuzzy numbers based on a fuzzy probabilistic preference relation is introduced. The ranking order of fuzzy numbers with the weighted confidence level is derived from the pairwise comparison matrix based on 0.5-transitivity of the fuzzy probabilistic preference relation. The main difference between the proposed method and existing ones is that the comparison result between two fuzzy numbers is expressed as a fuzzy set instead of a crisp one. As such, the ranking order of n fuzzy numbers provides more information on the uncertainty level of the comparison. Illustrated by comparative examples, the proposed method overcomes certain unreasonable (due to the violation of the inequality properties) and indiscriminative problems exhibited by some existing methods. More importantly, the proposed method is able to provide decision makers with the probability of making errors when a crisp ranking order is obtained. The proposed method is also able to provide a probability-based explanation for conflicts among the comparison results provided by some existing methods using a proper ranking order, which ensures that ties of alternatives can be broken.     

Contribution to application of energy measure of fuzzy sets

The works of De Luca & Termini continued by, for example, Knopfmacher, Loo and Gottwald, are the most important on the topic of determination of measures of fuzzy sets. The matter is to evaluate how fuzzy a fuzzy set is. There are two general concepts of measures of fuzzy set, i.e. entropy and energy measures.We show that the special kind of energy measure is better suited than the entropy kind of measure in many practical situations.Applications of the use of energy measure discussed in detail include decision making, fuzzy process control and prediction in fuzzy systems.     

A fast approach to compute fuzzy values of matrix games with payoffs of triangular fuzzy numbers

The aim of this paper is to develop an effective method for solving matrix games with payoffs of triangular fuzzy numbers (TFNs) which are arbitrary. In this method, it always assures that players’ gain-floor and loss-ceiling have a common TFN-type fuzzy value and hereby any matrix game with payoffs of TFNs has a TFN-type fuzzy value. Based on duality theorem of linear programming (LP) and the representation theorem for fuzzy sets, the mean and the lower and upper limits of the TFN-type fuzzy value are easily computed through solving the derived LP models with data taken from 1-cut set and 0-cut set of fuzzy payoffs. Hereby the TFN-type fuzzy value of any matrix game with payoffs of TFNs can be explicitly obtained. Moreover, we can easily compute the upper and lower bounds of any Alfa-cut set of the TFN-type fuzzy value for any matrix game with payoffs of TFNs and players’ optimal mixed strategies through solving the derived LP models at any specified confidence level Alfa. The proposed method in this paper is demonstrated with a numerical example and compared with other methods to show the validity, applicability and superiority.     

A method of fuzzy preference relation to authorize the worldwide interoperability for microwave access license in Taiwan

This study proposes a preference relation based evaluation framework to help the National Communication Commission (NCC) in Taiwan authorize a worldwide interoperability for microwave access (WiMAX) license under a fuzzy environment where the uncertainty, subjectivity and vagueness are dealt with linguistic variables parameterized by triangular fuzzy numbers. This study applies the fuzzy multi-criteria decision making approach to determine the importance weights of evaluation criteria and consolidate the performance ratings of possible alternatives. Aggregated the evaluators’ opinions toward the criteria and alternatives, the fuzzy preference relation approach is utilized to obtain the non-dominated degree of each alternative for the decision makers to make a final decision. Simultaneously, an empirical case involving sixteen quantitative and fifteen qualitative evaluation criteria, thirteen telecommunication applicants assessed by twelve specialists from various fields of telecommunication industry in Taiwan is solicited to demonstrate the proposed approach.     

A genetic tuning to improve the performance of Fuzzy Rule-Based Classification Systems with Interval-Valued Fuzzy Sets: Degree of ignorance and lateral position

Fuzzy Rule-Based Systems are appropriate tools to deal with classification problems due to their good properties. However, they can suffer a lack of system accuracy as a result of the uncertainty inherent in the definition of the membership functions and the limitation of the homogeneous distribution of the linguistic labels.The aim of the paper is to improve the performance of Fuzzy Rule-Based Classification Systems by means of the Theory of Interval-Valued Fuzzy Sets and a post-processing genetic tuning step. In order to build the Interval-Valued Fuzzy Sets we define a new function called weak ignorance for modeling the uncertainty associated with the definition of the membership functions. Next, we adapt the fuzzy partitions to the problem in an optimal way through a cooperative evolutionary tuning in which we handle both the degree of ignorance and the lateral position (based on the 2-tuples fuzzy linguistic representation) of the linguistic labels.The experimental study is carried out over a large collection of data-sets and it is supported by a statistical analysis. Our results show empirically that the use of our methodology outperforms the initial Fuzzy Rule-Based Classification System. The application of our cooperative tuning enhances the results provided by the use of the isolated tuning approaches and also improves the behavior of the genetic tuning based on the 3-tuples fuzzy linguistic representation.     

Heuristic fuzzy-neuro network and its application to reactive navigation of a mobile robot

A novel pattern recognition approach to reactive navigation of a mobile robot is presented in this paper. A heuristic fuzzy-neuro network is developed for pattern-mapping between quantized ultrasonic sensory data and velocity commands to the robot. The design goal was to enable an autonomous mobile robot to navigate safely and efficiently to a target position in a previously unknown environment. Useful heuristic rules were combined with the fuzzy Kohonen clustering network (FKCN) to build the desired mapping between perception and motion. This method provides much faster response to unexpected events and is less sensitive to sensor misreading than conventional approaches. It allows continuous, fast motion of the mobile robot without any need to stop for obstacles. The effectiveness of the proposed method is demonstrated in a series of practical tests on our experimental mobile robot.     

A new algorithm for generalized Sylvester‐observer equation and its application to state and velocity estimations in vibrating systems

We propose a new algorithm for block‐wise solution of the generalized Sylvester‐observer equation XA?FXE = GC, where the matrices A, E, and C are given, the matrices X, F, and G need to be computed, and matrix E may be singular. The algorithm is based on an orthogonal decomposition of the triplet (A, E, C) into the observer‐Hessenberg‐triangular form. It is a natural generalization of the widely known observer‐Hessenberg algorithm for the Sylvester‐observer equation: XA?FX = GC, which arises in state estimation of a standard first‐order state‐space control system. An application of the proposed algorithm is made to state and velocity estimations of second‐order control systems modeling a wide variety of vibrating structures. For dense un‐structured data, the proposed algorithm is more efficient than the recently proposed SVD‐based algorithm of the authors. Copyright © 2010 John Wiley & Sons, Ltd.     

On a class of functions with equal infima over a domain and its boundary

In this paper, we present a class of functions:f:X such that inf _xX f(x)= , whereX is a nonempty, finitely compact and convex set in a vector space andB _x ={xX: y aff(X){x:[x, y]X={x}. Our main tool is a recent minimax theorem by Ricceri (Ref. 1).