scholarly journals A Systematic Approach to OptimizinghValue for Fuzzy Linear Regression with Symmetric Triangular Fuzzy Numbers

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Xilong Liu ◽  
Yizeng Chen
Keyword(s):  
Linear Regression ◽  
Systematic Approach ◽  
Fuzzy Numbers ◽  
Programming Model ◽  
Numerical Study ◽  
Triangular Fuzzy Numbers ◽  
Fuzzy Linear Regression ◽  
The Real ◽  
Optimal Value ◽  
Sample Data

A systematic approach is proposed to optimizehvalue for fuzzy linear regression (FLR) analysis using minimum fuzziness criteria with symmetric triangular fuzzy numbers (TFNs). Firstly, a new concept of credibility is defined to evaluate the performance of FLR models with differenthvalues when a set of sample data pairs is given. Secondly, based on the defined concept of credibility, a programming model is formulated to optimize the value ofh. Finally, both the numerical study and the real application show that the approach proposed in this paper is effective and efficient; that is, optimal value forhcan be determined definitely with respect to a set of given sample data pairs.

scholarly journals Multivariate Matrix for Fuzzy Linear Regression Model to Analyse The Taxation in Malaysia

2018 ◽  
Vol 7 (4.33) ◽  
pp. 78
Author(s):  
Noor Hidayah Mohamed Isa ◽  
Mahmod Othman ◽  
Samsul Ariffin Abdul Karim
Keyword(s):  
Linear Regression ◽  
World Bank ◽  
Fuzzy Numbers ◽  
Tax Revenue ◽  
Triangular Fuzzy Numbers ◽  
Fuzzy Linear Regression ◽  
Independent Variables ◽  
Fuzzy Linear Regression Model ◽  
Merchandise Trade ◽  
The Relationship

A multivariate matrix is proposed to find the best factor for fuzzy linear regression (FLR) with symmetric triangular fuzzy numbers (TFNs). The goal of this paper is to select the best factor influence tax revenue among four variables. Eighteen years’ data of the variables from IndexMundi and World Bank Data. It is found that the model is successfully explained between independent variables and response variable. It is notices that  sixty-six percent of the variance of tax revenue is explained by Gross Domestic Product, Inflation, Unemployment and Merchandise Trade. The introduction of multivariate matrix for fuzzy linear regression in taxation is a first attempt to analyses the relationship the tax revenue with the independent variables.  

MONTE CARLO METHODS IN FUZZY NON-LINEAR REGRESSION

2008 ◽  
Vol 04 (02) ◽  
pp. 123-141 ◽  
Author(s):  
AREEG ABDALLA ◽  
JAMES BUCKLEY
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Linear Regression ◽  
Fuzzy Numbers ◽  
Random Number ◽  
Random Number Generator ◽  
Search Space ◽  
Triangular Fuzzy Numbers ◽  
Non Linear ◽  
Regression Problems

We apply our new fuzzy Monte Carlo method to certain fuzzy non-linear regression problems to estimate the best solution. The best solution is a vector of triangular fuzzy numbers, for the fuzzy coefficients in the model, which minimizes an error measure. We use a quasi-random number generator to produce random sequences of these fuzzy vectors which uniformly fill the search space. We consider example problems to show that this Monte Carlo method obtains solutions comparable to those obtained by an evolutionary algorithm.

scholarly journals A fuzzy multi-objective linear programming with interval-typed triangular fuzzy numbers

2019 ◽  
Vol 17 (1) ◽  
pp. 607-626 ◽  
Author(s):  
Chunquan Li
Keyword(s):  
Linear Programming ◽  
Fuzzy Numbers ◽  
Programming Model ◽  
Optimal Solution ◽  
Objective Functions ◽  
Triangular Fuzzy Numbers ◽  
Matlab Toolbox ◽  
Multi Objective ◽  
Cut Set ◽  
The Stability

Abstract A multi-objective linear programming problem (ITF-MOLP) is presented in this paper, in which coefficients of both the objective functions and constraints are interval-typed triangular fuzzy numbers. An algorithm of the ITF-MOLP is provided by introducing the cut set of interval-typed triangular fuzzy numbers and the dominance possibility criterion. In particular, for a given level, the ITF-MOLP is converted to the maximization of the sum of membership degrees of each objective in ITF-MOLP, whose membership degrees are established based on the deviation from optimal solutions of individual objectives, and the constraints are transformed to normal inequalities by utilizing the dominance possibility criterion when compared with two interval-typed triangular fuzzy numbers. Then the equivalent linear programming model is obtained which could be solved by Matlab toolbox. Finally several examples are provided to illuminate the proposed method by comparing with the existing methods and sensitive analysis demonstrates the stability of the optimal solution.

Method for Fuzzy Multi-Attribute Decision-Making with Fuzzy Reciprocal Preference Relation on Alternatives under Partical Weight Information

2011 ◽  
Vol 58-60 ◽  
pp. 869-874
Author(s):  
Hong An Zhou
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Programming Model ◽  
Preference Relation ◽  
Triangular Fuzzy Numbers ◽  
Attribute Weights ◽  
Translation Function ◽  
Goal Programming Model ◽  
Subjective Preference ◽  
Multi Attribute Decision Making

The fuzzy multi-attribute decision-making (FMADM) problems, in which the information about attribute weights is partly known, the attribute values take the form of triangular fuzzy numbers, and the decision maker (DM) has fuzzy reciprocal preference relation on alternatives, are investigated. Firstly, some concepts, such as the multiply between two triangular fuzzy numbers, the projection of triangular fuzzy numbers vectors, etc, are given. Secondly, in order to reflect to the DM’s subjective preference information on alternatives, we make the objective decision information uniform by using a translation function and establish a goal programming model, and then the attribute weights is obtained by solving the model, thus the weighted attribute values of all alternatives are gained. The concept of fuzzy positive ideal solution (FPIS) of alternatives is introduced, and the alternatives are ranked by using the projection of the weighted attribute values of every alternative on FPIS. The method not only can sufficiently utilize the objective information and meet the DM’s subjective preferences on alternatives as much as possible, but also it is characterized by simple operation and easy to implement on a computer. Finally, a practical example is illustrated to show the feasibility and availability of the developed method.

scholarly journals Quadratic Programming Method for Cooperative Games with Coalition Values Expressed by Triangular Fuzzy Numbers and Its Application in the Profit Distribution of Logistics Coalition

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Jia-Cai Liu ◽  
Yuan-Fei Zhu ◽  
Wen-Jian Zhao
Keyword(s):  
Quadratic Programming ◽  
Fuzzy Set ◽  
Cooperative Games ◽  
Fuzzy Numbers ◽  
Programming Model ◽  
Least Square ◽  
Triangular Fuzzy Numbers ◽  
Profit Distribution ◽  
Cut Set ◽  
Quadratic Programming Method

A quadratic programming model is constructed for solving the fuzzy cooperative games with coalition values expressed by triangular fuzzy numbers, which will be abbreviated to TFN-typed cooperative games from now on. Based on the concept of α-cut set and the representation theorem for the fuzzy set, the least square distance solution for solving TFN-typed cooperative games is proposed. The least square distance solution successfully avoids the subtraction operation of TFNs, which may inevitably lead to the amplification of uncertainty and the distortion of decision information. A calculating example related to the profit distribution of logistics coalition is illustrated to show the advantages, validity, and applicability of the proposed method. Besides, the least square distance solution for solving TFN-typed cooperative games satisfies many important properties of cooperative games, such as uniqueness, additivity, symmetry, and uniqueness.

scholarly journals Boscovich Fuzzy Regression Line

Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 685
Author(s):  
Pavel Škrabánek ◽  
Jaroslav Marek ◽  
Alena Pozdílková
Keyword(s):  
Fuzzy Numbers ◽  
Linear Time ◽  
Regression Line ◽  
Fuzzy Regression ◽  
Linear Regression Method ◽  
Triangular Fuzzy Numbers ◽  
Fuzzy Linear Regression ◽  
Regression Methods ◽  
Dependent Variables ◽  
Real Value

We introduce a new fuzzy linear regression method. The method is capable of approximating fuzzy relationships between an independent and a dependent variable. The independent and dependent variables are expected to be a real value and triangular fuzzy numbers, respectively. We demonstrate on twenty datasets that the method is reliable, and it is less sensitive to outliers, compare with possibilistic-based fuzzy regression methods. Unlike other commonly used fuzzy regression methods, the presented method is simple for implementation and it has linear time-complexity. The method guarantees non-negativity of model parameter spreads.

RIDGE REGRESSION PROCEDURES FOR FUZZY MODELS USING TRIANGULAR FUZZY NUMBERS

2004 ◽  
Vol 12 (02) ◽  
pp. 145-159 ◽  
Author(s):  
DUG HUN HONG ◽  
CHANGHA HWANG
Keyword(s):  
Nonlinear Regression ◽  
Ridge Regression ◽  
Fuzzy Numbers ◽  
Linear Models ◽  
Estimation Method ◽  
Feature Space ◽  
Triangular Fuzzy Numbers ◽  
Fuzzy Linear Regression ◽  
Data Set ◽  
Nonlinear Regression Models

This paper presents a new method of estimating fuzzy multivariable linear and nonlinear regression models using triangular fuzzy numbers. This estimation method is obtained by implementing a dual version of the ridge regression procedure for linear models. It allows us to perform fuzzy nonlinear regression by constructing a fuzzy linear regression in a high dimensional feature space for the data set with crisp inputs and fuzzy output. Experimental results are then presented, which indicate the performance of this algorithm.

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