Fuzzy Regression Models Using the Least-Squares Method Based on the Concept of Distance

Abstract

Fuzzy regression models are developed to construct the relationship between explanatory variables and responses in a fuzzy environment. In order to increase the explanatory performance of the model, the least-squares method is applied to determine the numeric coefficients based on the concept of distance. Unlike most existing approaches, the numeric coefficients in the proposed model can have negative values. The proposed model minimizes total estimation error in terms of the sum of the average squared distance between the observed and estimated responses based on a few α-cuts. The proposed approach is not limited to triangular fuzzy numbers; it can be used to carry out a large number of fuzzy observations efficiently because the model is based on traditional statistical methods. Comparisons with existing methods show that based on the total estimation error using the mean squared error and Kim and Bishu's criterion, the explanatory performance of the proposed model is satisfactory.

Fuzzy Regression Model Based on Fuzzy Distance Measure

“…It can be seem from Figure 2 that the estimated values of several models are almost the same, and in the right of Table 2 showed Table 3 from Chen [13]. Journal of Data Analysis and Information Processing Table 5 lists the estimation errors from the earlier models based on the two criteria, ε and SSE.…”

Regression Analysis of a Kind of Trapezoidal Fuzzy Numbers Based on a Shape Preserving Operator

“…Now, we get the final sample in data Table 3. We still use (14) to construct fuzzy regression model, obtain the estimated output and use Error Index, Similarity Measure, Distance Criterion to evaluate deviation. Besides, the results in Table 4, we also illustrate the results through Figure 1.…”

“…The specific steps are similar to Example 2. After obtaining the proper sample data in Table 5, we still use (14) to construct fuzzy regression model, obtain the estimated output and use Error Index, Similarity Measure, Distance Criterion to evaluate deviation shown in Table 6. Table 6, we can find that the sum of i E of our proposed model is smaller than that of the reference models, and the sum of i S and i R of our proposed model is larger than that of the reference models, that means our proposed model has lower deviations than the reference models, but bad shape estimation.…”

“…Moreover, several variants of this approach [12] [13] [14] [15] [16] have been used in fuzzy linear regression.…”

Gray Relational Evaluation Model with Preferences Based on Characteristics-AHP

“…Along with the development of social economy,researcher gradually pay attention to cost-benefit synthetical evaluation.At present,there are many methods of synthetical evaluation,such as analytic hierarchy process(AHP) [1,2],fuzzy comprehensive evaluation [3,4],data envelopment analysis(DEA) [5,6],gray system theory [7][8][9][10] and so on.Among them, gray system theory take small sample and poor data of part of the information known,partial information unknown indeterminacy system as research object,mostly go through section known information's generation and development.extract valuable information,implement correct description and effective control of operational system behavior,evolution law,appear more advantage than other synthetical evaluation.Especially study and develop in a deep-goingway of gray system theory,gray relational analysis(GRA) is used on more fields of synthetical evalution.…”