E.S. Lee

Ranking of fuzzy sets based on the concept of existence

Abstract Various approaches have been proposed for the comparison or ranking of fuzzy sets. However, due to the complexity of the problem, a general method which can be used for any situation still does not exist. This paper formalizes the concept of existence for the ranking of fuzzy sets. Many of the existing fuzzy ranking methods are shown to be some application of this concept. An improved fuzzy ranking method is then introduced, based on this concept. This newly introduced method is expanded for treating both normal and nonnormal, convex and nonconvex fuzzy sets. Emphasis is placed on the use of the subjectivity of the decision maker, such as the optimistic or the pessimistic view points. An improved procedure for obtaining linguistic conclusions is also developed. Finally, some numerical examples are given to illustrate the approach.

Latticized linear programming and fuzzy relation inequalities

Abstract A logical linear programming problem, the latticized linear programming, is proposed based on fuzzy lattice and fuzzy relation inequalities. The proposed problem is essentially an optimization problem which should be useful under certain logical “if…, then…” situations. To illustrate the proposed approach, numerical examples are solved.

Fuzzy linear regression with spreads unrestricted in sign

Abstract By the use of actual examples, it is shown that when the two trends, namely the fuzzy spread trend and the center line, or modal, trend, are in conflict or inconsistent, the results of the fuzzy linear regression (FLR) model based on the approach of Tanaka and coworkers frequently misinterprets the data. To avoid this misinterpretation, a modification of the FLR procedure, by allowing the spreads of the parameter to be unrestricted in sign, is proposed. It is shown that by the use of this unrestricted fuzzy linear regression (UFLR) model, correct prediction of the trends are obtained.

Neuro-fuzzy and genetic algorithm in multiple response optimization

Abstract Optimization of a multiple output system, whose function is only approximately known and is represented in tabular form, is modeled and optimized by the combined use of a neuro-fuzzy network and optimization techniques which do not require the explicit representation of the function. Neuro-fuzzy network is useful for learning the approximate original tabular system. However, the results obtained by the neuro-fuzzy network are represented implicitly in the network. The MANFIS neuro-fuzzy network, which is an extension of the ANFIS network, is used to model the multiple output system and a genetic algorithm is used to optimize the resulting multiple objective decision making problem. A chemical process whose function is represented approximately in tabular form is solved to illustrate the approach.

Applying fuzzy adaptive network to fuzzy regression analysis

Abstract A fuzzy inference system based on the Sugeno inference model is first formulated for fuzzy regression analysis. This system is then represented by a fuzzy adaptive network. This approach combines the power of representation of fuzzy inference system with the ability of learning of the neural network. Numerical examples are trained and solved to illustrate the approach. The results are compared with other approaches.

Variable universe stable adaptive fuzzy control of a nonlinear system

Abstract A kind of stable adaptive fuzzy control of a nonlinear system is implemented based on the variable universe method proposed first in [1]. First of all, the basic structure of variable universe adaptive fuzzy controllers is briefly introduced. Then the contraction-expansion factor which is a key tool of the variable universe method is defined by means of the integral regulation idea, and then a kind of adaptive fuzzy controller is designed by using such a contraction-expansion factor. The simulation on the first-order nonlinear system is done, and as a result, its simulation effect is quite good in comparison with the corresponding result in [2,3]. Second, it is proved that the variable universe adaptive fuzzy control is asymptotically stable by use of Liapunov theory. The simulation on a second-order nonlinear system shows that its simulation effect is also quite good in comparison with the corresponding result in [2]. Besides, a useful tool, called symbolic factor, is proposed, which may be of universal significance. It can greatly reduce the setting time and enhance the robustness of the system.

Fuzzy approaches to multicriteria de Novo programs

Abstract Multicriteria de Novo programming is a promising tool for optimal system design. However, there exist no algorithms for solving a general multicriteria de Novo program. Only special cases have been discussed. This paper proposes a two-step fuzzy approach based on the ideal and negative ideal solutions. It is shown that this approach is very efficient and is applicable to the general multicriteria de Novo programming. The fuzzy version of this problem is also formulated and analyzed. Numerical examples are given to illustrate the approaches.

The estimation of normalized fuzzy weights

Abstract The estimation of a normalized set of positive fuzzy weights constitutes the most important aspects in the fuzzy multiple attribute decision making process. A systematic treatment of this problem is carried out in this paper. The concept of fuzzy normalization is first defined and the meaning of consistency in a fuzzy environment is discussed. Based on these definitions and discussions, the various approaches in the literature are examined and several improvements or new approaches are proposed. Numerical examples are used to evaluate and to compare the various existing and the newly proposed approaches.

Fuzzy decision networks and deconvolution

Abstract Three kinds of networks, namely, fuzzy minimal spanning tree, fuzzy PERT, and fuzzy shortest path, are analyzed by the use of a recently developed fuzzy ranking method to handle the various fuzzy quantities. To overcome the problem of double-inclusion of the amounts of uncertainties involved in the fuzzy quantities when extended subtraction is used for problems such as fuzzy PERT, fuzzy deconvolution is used. Since we are only interested in the ranking and aggregation of the results, the existence or nonexistence of the results from deconvolution does not influence the resulting analysis. A technique based on the ranking method is developed to handle negative spreads in the resulting fuzzy quantities. With the use of this fuzzy ranking method, the structure of the network is maintained and conventional algorithms can be applied with appropriate modifications. Emphasis is placed on the use of the subjective decision makers opinion in the proposed fuzzy network analysis approach. Numerical examples are given to illustrate the approach.

Fuzzy multiple attributes and multiple hierarchical decision making

Abstract A procedure is proposed to solve the multiple attributes and multiple hierarchical system under fuzzy environment. The approach is based on: 1. (1) fuzzy representation; 2. (2) hierarchical performance evaluation structure, 3. (3) gradient eigenvector method for rating the fuzzy criteria weighting, and 4. (4) using the max-min paired elimination method for aggregation. To illustrate the approach, an example on the evaluation of teaching performance in higher education is solved.