Dug Hun Hong

Multicriteria fuzzy decision-making problems based on vague set theory

Abstract Chen et al. (Fuzzy Sets and Systems 67 (1994) (163–172)) present some techniques for handling multicriteria fuzzy decision-making problems based on vague set theory. They provide some functions to measure the degree of suitability of each alternative with respect to a set of criteria presented by vague values. However, in some cases, these functions do not give sufficient information about alternatives. In this paper, we provide new functions to measure the degree of accuracy in the grades of membership of each alternative with respect to a set of criteria represented by vague values. The proposed functions give additional information about alternatives. The techniques proposed in this paper can provide more useful way than those of Chen to efficiently help the decision-maker to make his decision.

Short-term load forecasting for the holidays using fuzzy linear regression method

Average load forecasting errors for the holidays are much higher than those for weekdays. So far, many studies on the short-term load forecasting have been made to improve the prediction accuracy using various methods such as deterministic, stochastic, artificial neural net (ANN) and neural network-fuzzy methods. In order to reduce the load forecasting error of the 24 hourly loads for the holidays, the concept of fuzzy regression analysis is employed in the short-term load forecasting problem. According to the historical load data, the same type of holiday showed a similar trend of load profile as in previous years. The fuzzy linear regression model is made from the load data of the previous three years and the coefficients of the model are found by solving the mixed linear programming problem. The proposed algorithm shows good accuracy, and the average maximum percentage error is 3.57% in the load forecasting of the holidays for the years of 1996-1997.

A note on similarity measures between vague sets and between elements

Recently, Chen (Fuzzy Sets and Systems 74 (2) (1995) 217-223; IEEE Trans. Syst. Man and Cybern., 27 (1) (1997) 153-158) proposed a set of methods for measuring the degree of similarity between vague sets and between elements, and presented some examples to illustrate the application of the said measures in handling behavior analysis problems. In this paper, we showed by examples that the similarity measures proposed by Chen do not fit well in some cases, and proposed a set of modified measures. Comparing the similarity degree of each measure, the modified similarity measures turned out to be more reasonable in more general cases than the previous one.

Support vector fuzzy regression machines

Support vector machine (SVM) has been very successful in pattern recognition and function estimation problems. In this paper, we introduce the use of SVM for multivariate fuzzy linear and nonlinear regression models. Using the basic idea underlying SVM for multivariate fuzzy regressions gives computational efficiency of getting solutions.

Correlation of intuitionistic fuzzy sets in probability spaces

In this paper, we study the concepts of correlation and correlation coefficient of intuitionistic fuzzy sets in probability spaces. In the case of finite spaces, these results give the results of Gerstenkorn and Manko: (1991) and in the case of infinite spaces, also give the correct forms of Yus (1993) results.

A note on correlation of interval-valued intuitionistic fuzzy sets

In this note, we generalize the concepts of correlation and correlation coefficient of interval-valued intuitionistic fuzzy sets in a general probability space and generalize the results of Bustince and Burillo (1995) with remarkably simple proofs. We also introduce three more decomposition theorems of the correlation of interval-valued intuitionistic fuzzy sets in terms of the correlation of interval-valued fuzzy sets and the entropy of the intuitionistic fuzzy sets.

Some algebraic properties and a distance measure for interval-valued fuzzy numbers

In this paper, we generalize results of Wang and Li [Fuzzy Sets and Systems 98 (1998) 331] on interval-valued fuzzy numbers and extend their operations with simple proofs. We also consider some algebraic properties and a distance measure for interval-valued fuzzy numbers.

Support vector interval regression machine for crisp input and output data

Support vector regression (SVR) has been very successful in function estimation problems for crisp data. In this paper, we propose a robust method to evaluate interval regression models for crisp input and output data combining the possibility estimation formulation integrating the property of central tendency with the principle of standard SVR. The proposed method is robust in the sense that outliers do not affect the resulting interval regression. Furthermore, the proposed method is model-free method, since we do not have to assume the underlying model function for interval nonlinear regression model with crisp input and output. In particular, this method performs better and is conceptually simpler than support vector interval regression networks (SVIRNs) which utilize two radial basis function networks to identify the upper and lower sides of data interval. Five examples are provided to show the validity and applicability of the proposed method.

Fuzzy system reliability analysis by the use of T Ω (the weakest t-norm) on fuzzy number arithmetic operations

Abstract In general, the sup-min convolution has been used for fuzzy arithmetic to analyze fuzzy system reliability, where the reliability of each system component is represented by fuzzy numbers. It is well known that T ω -based addition preserves the shape of L - R type fuzzy numbers. In this paper, we show T ω -based multiplication also preserves the shape of L - R type fuzzy numbers. We then apply T ω -based arithmetic operations to fuzzy system reliability analysis. In fact, we show that we can simplify fuzzy arithmetic operations and even get the exact solutions for L - R type fuzzy system reliability, while others [Singer, Fuzzy Sets Syst. 34 (1990) 145; Cheng and Mon, Fuzzy Sets Syst. 56 (1993) 29; Chen, Fuzzy Sets Syst. 64 (1994) 31] have got the approximate solutions using sup-min convolution for evaluating fuzzy system reliability.

Interval regression analysis using quadratic loss support vector machine

Support vector machines (SVMs) have been very successful in pattern recognition and function estimation problems for crisp data. This paper proposes a new method to evaluate interval linear and nonlinear regression models combining the possibility and necessity estimation formulation with the principle of quadratic loss SVM. This version of SVM utilizes quadratic loss function, unlike the traditional SVM. For data sets with crisp inputs and interval outputs, the possibility and necessity models have been recently utilized, which are based on quadratic programming approach giving more diverse spread coefficients than a linear programming one. The quadratic loss SVM also uses quadratic programming approach whose another advantage in interval regression analysis is to be able to integrate both the property of central tendency in least squares and the possibilistic property in fuzzy regression. However, this is not a computationally expensive way. The quadratic loss SVM allows us to perform interval nonlinear regression analysis by constructing an interval linear regression function in a high dimensional feature space. The proposed algorithm is a very attractive approach to modeling nonlinear interval data, and is model-free method in the sense that we do not have to assume the underlying model function for interval nonlinear regression model with crisp inputs and interval output. Experimental results are then presented which indicate the performance of this algorithm.