Making Group Decisions within the Framework of a Probabilistic Hesitant Fuzzy Linear Regression Model

Abstract

A fuzzy set extension known as the hesitant fuzzy set (HFS) has increased in popularity for decision making in recent years, especially when experts have had trouble evaluating several alternatives by employing a single value for assessment when working in a fuzzy environment. However, it has a significant problem in its uses, i.e., considerable data loss. The probabilistic hesitant fuzzy set (PHFS) has been proposed to improve the HFS. It provides probability values to the HFS and has the ability to retain more information than the HFS. Previously, fuzzy regression models such as the fuzzy linear regression model (FLRM) and hesitant fuzzy linear regression model were used for decision making; however, these models do not provide information about the distribution. To address this issue, we proposed a probabilistic hesitant fuzzy linear regression model (PHFLRM) that incorporates distribution information to account for multi-criteria decision-making (MCDM) problems. The PHFLRM observes the input–output (IPOP) variables as probabilistic hesitant fuzzy elements (PHFEs) and uses a linear programming model (LPM) to estimate the parameters. A case study is used to illustrate the proposed methodology. Additionally, an MCDM technique called the technique for order preference by similarity to ideal solution (TOPSIS) is employed to compare the PHFLRM findings with those obtained using TOPSIS. Lastly, Spearman’s rank correlation test assesses the statistical significance of two rankings sets.

Fractional Fuzzy Neural System: Fractional Differential-Based Compensation Prediction for Reputation Infringement Cases

“…Meanwhile, simple linear regression can also be used for the retrospective prediction of fines. Therefore, this section will test four different methods: the combination of the fractionalorder fuzzy membership function with the BP neural network (FOFS + BP), the combination of the traditional fuzzy membership function with the BP neural network (FS + BP), the combination of the fractional-order fuzzy membership function with linear regression [28,29] (FOFS + LR), and the combination of the traditional fuzzy membership function with linear regression (FS + LR). The entire dataset is divided into training, validation, and test sets with the following proportions: training dataset 70%, validation dataset 15%, and test dataset 15%.…”

“…The fractional-order fuzzy neural network combines the fractional-order membership function with the BP neural network for the regression prediction of Meanwhile, simple linear regression can also be used for the retrospective predic fines. Therefore, this section will test four different methods: the combination fractional-order fuzzy membership function with the BP neural network (FOFS the combination of the traditional fuzzy membership function with the BP network (FS + BP), the combination of the fractional-order fuzzy membership fu with linear regression [28,29] Detailed MSE and MAE results are presented in the Table 6. Detailed MSE and MAE results are presented in the Table 6.…”

Estimation of parameters for two-stage mixed fuzzy linear regression models

“…When the explanatory variable is a crisp number, there will be a large error between the estimated value and the observed value of the model (2). Therefore, this paper adds the fuzzy adjustment term  δ [24] to model (2). Then the final fuzzy linear regression model is…”

“…In 1982, Tanaka et al [1] established the first fuzzy regression model. With the development, the performance of the improved model has been improved and applied in various fields [2][3][4] , but there are still deficiencies. For example, more observation data will lead to more fuzzy estimation of parameters [5] , and it is very sensitive to outliers [6] .…”

“…There are generally two types of methods for fuzzy regression analysis: (1) Mathematical programming to minimize fuzziness. (2) Using the principle of fuzzy least squares to minimize the error between the observed value and the estimated value. The programming and calculation of the mathematical programming method are simple, while the fuzzy least square method can ensure the minimum degree of fuzziness between the observed value and the estimated value [22] .…”