Etemadi Fuzzy Linear Regression (EFLR)

Modeling and forecasting are among the most powerful and widely-used tools in decision support systems. The Fuzzy Linear Regression (FLR) is the most fundamental method in the fuzzy modeling area in which the uncertain relationship between the target and explanatory variables is estimated and has been frequently used in a broad range of real-world applications efficaciously. The operation logic in this method is to minimize the vagueness of the model, defined as the sum of individual spreads of the fuzzy coefficients. Although this process is coherent and can obtain the narrowest α-cut interval and exceptionally the most accurate results in the training data sets, it can not guarantee to achieve the desired level of generalization. While the quality of made managerial decisions in the modeling-based field is dependent on the generalization ability of the used method. On the other hand, the generalizability of a method is generally dependent on the precision as well as reliability of results, simultaneously. In this paper, a novel methodology is presented for the fuzzy linear regression modeling; in which in contrast to conventional methods, the constructed models' reliability is maximized instead of minimizing the vagueness. In the proposed model, fuzzy parameters are estimated in such a way that the variety of the ambiguity of the model is minimized in different data conditions. In other words, the weighted variance of different ambiguities in each validation data situation is minimized in order to estimate the unknown fuzzy parameters. To comprehensively assess the proposed method's performance, 74 benchmark datasets are regarded from the UCI. Empirical outcomes show that, in 64.86% of case studies, the proposed method has better generalizability, i.e., narrower α-cut interval as well as more accurate results in the interval and point estimation, than classic versions. It is obviously demonstrated the importance of the outcomes' reliability in addition to the precision that is not considered in the traditional FLR modeling processes. Hence, the presented EFLR method can be considered as a suitable alternative in fuzzy modeling fields, especially when more generalization is favorable.

Extended Fully Fuzzy Linear Regression to Analyze a Solid Cantilever Beam Moment

There are several procedures such as possibilistic and least-square methods to estimate regression models. In this study, first, a fully fuzzy regression equation is converted into a fully fuzzy linear framework. By considering a least-square approach, a model is suggested based on matrix equations for solving fully fuzzy regression models. The main advantage of this method over existing ones is that this method considered values based on their specification, and all linear problems can be easily solved. Moreover, a case study for solid mechanics about the quantity of beam momentum is considered. In this example, the inner data are force values, and the output is momentum values.

Hesitant Fuzzy Linear Regression Model for Decision Making

An expert may experience difficulties in decision making when evaluating alternatives through a single assessment value in a hesitant environment. A fuzzy linear regression model (FLRM) is used for decision-making purposes, but this model is entirely unreasonable in the presence of hesitant fuzzy information. In order to overcome this issue, in this paper, we define a hesitant fuzzy linear regression model (HFLRM) to account for multicriteria decision-making (MCDM) problems in a hesitant environment. The HFLRM provides an alternative approach to statistical regression for modelling situations where input–output variables are observed as hesitant fuzzy elements (HFEs). The parameters of HFLRM are symmetric triangular fuzzy numbers (STFNs) estimated through solving the linear programming (LP) model. An application example is presented to measure the effectiveness and significance of our proposed methodology by solving a MCDM problem. Moreover, the results obtained employing HFLRM are compared with the MCDM tool called technique for order preference by similarity to ideal solution (TOPSIS). Finally, Spearman’s rank correlation test is used to measure the significance for two sets of ranking.

Inflation and Marginal Costs in Open Economies: The New Keynesian Hybrid Phillips Curve

The inclusion of the inflation rate in wage determination affects the behavior of economic actors and also positions the expected inflation as one of the main factors in determining inflation. Changes in currency parities in developing countries, which make their production dependent on imports, affect costs and prices. Moreover, changes in labor market structures resulting from free capital flows affect employment and the inflation phenomenon. This paper analyzes the current inflation, expected inflation, and output gap relations with the fuzzy linear regression method in the context of the Turkish economy, which has inflation and effective external dependency. Based on the results obtained using marginal cost instead of the output gap, policy recommendations are provided. The scope of this paper comprises the New Keynesian Hybrid Phillips curve that includes external factors. The relationship between inflation and relevant variables is statistically significant and positive, proving the fuzzy linear regression results as promising. To obtain economic stability and policy precautions, we must examine whether the use of tight monetary policies for coping with inflation leads to unemployment and whether expansionist monetary policies lead to inflation.

Fuzzy linear regression analysis for groundwater response to meteorological drought in the aquifer system of Xanthi plain, NE Greece

This paper studies, through the principles of fuzzy set theory, groundwater response to meteorological drought in the case of an aquifer system located in the plains at the southeast of Xanthi, NE Greece. Meteorological drought is expressed through standardized Reconnaissance Drought Index (RDISt) and Standardized Precipitation Index (SPI), which are calculated for various reference periods. These drought indices are considered as independent variables in multiple fuzzy linear regression based on Tanaka's model, while the observed water table regarding two areas is used as a dependent variable. The fuzzy linear regression of Tanaka is characterized by the inclusion constraints where all the observed data must be included in the produced fuzzy band. Hence, each fuzzy output can get an interval of values where a membership degree corresponds to each of them. A modification of the Tanaka model by adding constraints is proposed in order to avoid irrational behavior. The results show that there was a significant influence of the meteorological drought of the previous hydrological year, while geology plays an important role. Furthermore, the use of RDISt improves the results of fuzzy linear regressions in all cases. Two suitability measures and a measure of comparison between fuzzy numbers are used.

Algorithm 1017

Fuzzy regression provides an alternative to statistical regression when the model is indefinite, the relationships between model parameters are vague, the sample size is low, or the data are hierarchically structured. Such cases allow to consider the choice of a regression model based on the fuzzy set theory. In fuzzyreg, we implement fuzzy linear regression methods that differ in the expectations of observational data types, outlier handling, and parameter estimation method. We provide a wrapper function that prepares data for fitting fuzzy linear models with the respective methods from a syntax established in R for fitting regression models. The function fuzzylm thus provides a novel functionality for R through standardized operations with fuzzy numbers. Additional functions allow for conversion of real-value variables to be fuzzy numbers, printing, summarizing, model plotting, and calculation of model predictions from new data using supporting functions that perform arithmetic operations with triangular fuzzy numbers. Goodness of fit and total error of the fit measures allow model comparisons. The package contains a dataset named bats with measurements of temperatures of hibernating bats and the mean annual surface temperature reflecting the climate at the sampling sites. The predictions from fuzzy linear models fitted to this dataset correspond well to the observed biological phenomenon. Fuzzy linear regression has great potential in predictive modeling where the data structure prevents statistical analysis and the modeled process exhibits inherent fuzziness.