Building a type-2 fuzzy regression model based on credibility theory and its application on arbitrage pricing theory

2016 ◽  
Vol 11 (6) ◽  
pp. 720-729 ◽  
Author(s):  
Yicheng Wei ◽  
Junzo Watada
Keyword(s):  
Regression Model ◽  
Fuzzy Regression ◽  
Credibility Theory ◽  
Arbitrage Pricing Theory ◽  
Arbitrage Pricing ◽  
Model Based ◽  
Fuzzy Regression Model ◽  
Pricing Theory

Introducing a trapezoidal interval type-2 fuzzy regression model

2021 ◽  
pp. 1-23
Author(s):  
Mikaeel Mokhtari ◽  
Tofigh Allahviranloo ◽  
Mohammad Hassan Behzadi ◽  
Farhad Hoseinzadeh Lotfi
Keyword(s):  
Regression Model ◽  
Goodness Of Fit ◽  
Fuzzy Numbers ◽  
Fuzzy Regression ◽  
Regression Coefficients ◽  
Uncertain Environments ◽  
Model Based ◽  
Fuzzy Regression Model ◽  
Interval Type

The uncertainty is an important attribute about data that can arise from different sources including randomness and fuzziness, therefore in uncertain environments, especially, in modeling, planning, decision-making, and control under uncertainty, most data available contain some degree of fuzziness, randomness, or both, and at the same time, some of this data may be anomalous (outliers). In this regard, the new fuzzy regression approaches by creating a functional relationship between response and explanatory variables can provide efficient tools to explanation, prediction and possibly control of randomness, fuzziness, and outliers in the data obtained from uncertain environments. In the present study, we propose a new two-stage fuzzy linear regression model based on a new interval type-2 (IT2) fuzzy least absolute deviation (FLAD) method so that regression coefficients and dependent variables are trapezoidal IT2 fuzzy numbers and independent variables are crisp. In the first stage, to estimate the IT2 fuzzy regression coefficients and provide an initial model (by original dataset), we introduce two new distance measures for comparison of IT2 fuzzy numbers and propose a novel framework for solving fuzzy mathematical programming problems. In the second stage, we introduce a new procedure to determine the mild and extreme fuzzy outlier cutoffs and apply them to remove the outliers, and then provide the final model based on a clean dataset. Furthermore, to evaluate the performance of the proposed methodology, we introduce and employ suitable goodness of fit indices. Finally, to illustrate the theoretical results of the proposed method and explain how it can be used to derive the regression model with IT2 trapezoidal fuzzy data, as well as compare the performance of the proposed model with some well-known models using training data designed by Tanaka et al. [55], we provide two numerical examples.

scholarly journals Valuation of Government Bonds: the Exchange Rate Is an Important Aspect

2017 ◽  
Vol 65 (6) ◽  
pp. 1911-1916
Author(s):  
Blanka Francová
Keyword(s):  
Regression Model ◽  
Interest Rates ◽  
Arbitrage Pricing Theory ◽  
Arbitrage Pricing ◽  
Data Set ◽  
Government Bonds ◽  
Exchange Risk ◽  
Pricing Theory ◽  
Multi Linear Regression ◽  
The Relationship

Interest rates are currently very low in the countries. In these countries bonds are issued with low or negative yields. In this paper, I empirically investigate the factors that affect the price of bonds. I follow international arbitrage pricing theory to determine the relationship between factors and the price of bonds. The international arbitrage pricing theory applies a multi‑linear regression model. The regression model is used for emerging markets and developing markets separately. I have a unique data set of 46 countries. The main data are the monthly returns on government bonds in the period 2010–2015. Exchange risk influences the bond prices. Currency movements can bring further yield for investors.

scholarly journals Quadrilateral Interval Type-2 Fuzzy Regression Analysis for Data Outlier Detection

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Pingping Gao ◽  
Yabin Gao
Keyword(s):  
Regression Analysis ◽  
Regression Model ◽  
Outlier Detection ◽  
Euclidean Distance ◽  
Fuzzy Numbers ◽  
Fuzzy Regression ◽  
Fuzzy Regression Analysis ◽  
Fuzzy Regression Model ◽  
Interval Type

This paper presents a fuzzy regression analysis method based on a general quadrilateral interval type-2 fuzzy numbers, regarding the data outlier detection. The Euclidean distance for the general quadrilateral interval type-2 fuzzy numbers is provided. In the sense of Euclidean distance, some parameter estimation laws of the type-2 fuzzy linear regression model are designed. Then, the data outlier detection-oriented parameter estimation method is proposed using the data deletion-based type-2 fuzzy regression model. Moreover, based on the fuzzy regression model, by using the root mean squared error method, an impact evaluation rule is designed for detecting data outlier. An example is finally provided to validate the presented methods.

Nephropathy forecasting in diabetic patients using a GA-based type-2 fuzzy regression model

2017 ◽  
Vol 37 (2) ◽  
pp. 281-289 ◽  
Author(s):  
Narges Shafaei Bajestani ◽  
Ali Vahidian Kamyad ◽  
Ensieh Nasli Esfahani ◽  
Assef Zare
Keyword(s):  
Regression Model ◽  
Fuzzy Regression ◽  
Diabetic Patients ◽  
Fuzzy Regression Model

Building a Type-2 Fuzzy Qualitative Regression Model

2012 ◽  
Vol 16 (4) ◽  
pp. 527-532 ◽  
Author(s):  
Yicheng Wei ◽  
◽  
Junzo Watada
Keyword(s):  
Regression Model ◽  
Fuzzy Set ◽  
Point Of View ◽  
Fuzzy Regression ◽  
Theoretical Point ◽  
Heuristic Solution ◽  
Fuzzy Regression Model ◽  
Real Value

Type-1 fuzzy regression model is constructed with type-1 fuzzy coefficients dealing with real value inputs and outputs. From the fuzzy set-theoretical point of view, uncertainty also exists when associated with qualitative data (membership degrees). This paper intends to build a qualitative regression model to measure uncertainty by applying the type-2 fuzzy set as the model’s coefficients. We are thus able to quantitatively describe the relationship between qualitative object variables and qualitative values of multivariate attributes (membership degree or type-1 fuzzy set), which are given by subjective recognition and judgment. We will build a basic qualitative model first and then improve it capable of ranging inputs. We will also give a heuristic solution in the end.

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