Possibilistic Regression Models Research Articles

Dual possibilistic regression models of support vector machines and application in power load forecasting

Power load forecasting is an important guarantee of safe, stable, and economic operation of power systems. It is appropriate to use interval data to represent fuzzy information in power load forecasting. The dual possibilistic regression models approximate the observed interval data from the outside and inside directions, respectively, which can estimate the inherent uncertainty existing in the given fuzzy phenomenon well. In this article, efficient dual possibilistic regression models of support vector machines based on solving a group of quadratic programming problems are proposed. And each quadratic programming problem containing fewer optimization variables makes the training speed of the proposed approach fast. Compared with other interval regression approaches based on support vector machines, such as quadratic loss support vector machine approach and two smaller quadratic programming problem support vector machine approach, the proposed approach is more efficient on several artificial datasets and power load dataset.

Fuzzy linear least squares for the identification of possibilistic regression models

The stochastic approach to regression, e.g. the least-squares method, is a commonly used technique in a wide range of disciplines as it offers an intuitive and well-founded solution to the problem of fitting a set of parameters to existing data. Specifically, in the case where the parameters of meta models are identified, the linear least-squares formulation receives wide appreciation among engineers due to its simple yet powerful formulation and solution. Usually, this approach provides a reasonable fit, depending largely on the quality of the model that is employed. However, it has two main drawbacks. From a statistical point of view, the premises justifying its use cannot always be assumed in good faith, and most importantly, the resulting model will almost certainly fail at correctly predicting the output without falling victim to the effect of over-fitting.The presented fuzzy regression algorithm originates from a set of different axioms. For the solution of the linear least-squares problem, it is able to provide the worst-case optimal parameter variation necessary to cover all of the crisp data points while encoding meaningful information in the membership function. This is accomplished by means of a sensible fuzzification procedure of the crisp data points and the application of an exact inverse fuzzy arithmetic for estimating the fuzzy-valued parameters of the model in question.

Investigating the trend of average changes of annual temperatures in Iran

Temperature is one of the key elements of climate formation and its changes can alter the climate structure of each region. To study the trend of temperature changes in Iran, the data from the three variables of average minimum temperature, average maximum temperature and average annual temperature of 43 synoptic stations were obtained from the Iranian Meteorological Organization for a 48-year statistical period (1966–2016). Moreover, in order to detect the trend of average changes of minimum, maximum and annual temperatures, fuzzy possibilistic regression and classical linear regression models were used. The comparison of the results of the slope of the change trend obtained from the two models clearly showed that, in most cases, the fuzzy possibilistic regression shows the slope of the change trend more than the classical linear regression. The statistics of root-mean-square error also showed that the function of classical linear regression was much better than fuzzy possibilistic regression. Therefore, based on the results of classical linear regression, the maximum amount of the average change trend of maximum annual temperatures of Iran is first observed in the west and northwest, and then in the northeastern of Iran. However, the average trend of minimum annual temperatures in Iran has shown more different spatial configurations than the average of maximum annual temperatures in Iran, with the highest rates of change in the east half, especially in the northeast. Finally, based on the classical linear regression model, it was observed that in the whole study period, 1.40 °C has been added to the average of maximum annual temperatures and 1.68 °C to the average of minimum annual temperatures in Iran.

Fuzzy target-environment networks and fuzzy-regression approaches

In systems sciences, the role of the environment is considered as a key factor for a deeper understanding of interconnected complex systems. The framework of target-environment networks allows for an investigation of regulatory systems under various kinds of uncertainty. Parameter-dependent models are applied to predict the future states of the system with respect to uncertain observations. In particular, fuzzy possibilistic regression models have been introduced that are based on crisp measurements. In this study, the concept of fuzzy target-environment networks is further extended towards fuzzy-regression models with fuzzy data sets. Regression models for various shapes of fuzzy coefficients and fuzzy model outputs are presented.

Fuzzy prediction strategies for gene-environment networks – Fuzzy regression analysis for two-modal regulatory systems

Target-environment networks provide a conceptual framework for the analysis and prediction of complex regulatory systems such as genetic networks, eco-finance networks or sensor-target assignments. These evolving networks consist of two major groups of entities that are interacting by unknown relationships. The structure and dynamics of the hidden regulatory system have to be revealed from uncertain measurement data. In this paper, the concept of fuzzy target-environment networks is introduced and various fuzzy possibilistic regression models are presented. The relation between the targets and/or environmental entities of the regulatory network is given in terms of a fuzzy model. The vagueness of the regulatory system results from the (unknown) fuzzy coefficients. For an identification of the fuzzy coefficients’ shape, methods from fuzzy regression are adapted and made applicable to the bi-level situation of target-environment networks and uncertain data. Various shapes of fuzzy coefficients are considered and the control of outliers is discussed. A first numerical example is presented for purposes of illustration. The paper ends with a conclusion and an outlook to future studies.

Tolerance Approach to Possibilistic Nonlinear Regression With Interval Data

We study possibilistic nonlinear regression models with crisp and/or interval data. Herein, the task is to compute tight interval regression parameters such that all observed output data (either crisp or interval) are covered by the range of the nonlinear interval regression function. We propose a method for determination of interval regression parameters based on the tolerance approach developed by the authors for the linear case. We define two classes of nonlinear regression models for which efficient algorithms exist. For other models, we provide some extensions allowing to calculate lower and upper bounds on the widths of the optimal interval regression parameters. We also discuss other approaches to interval regression than the possibilistic one. We illustrate the theory by examples.

Japanese Economic Analysis by Possibilistic Regression Model Building Through Possibility Maximization

A possibilistic regression model illustrates the potential possibilities inherent in the target system by including all data in the model. Tanaka and Guo employ exponential possibility distribution to build a model, while Inuiguchi et al. and Tajima are independently working on coinciding between the center of a possibility distribution and the center of a possibilistic regression model. Typically, samples influence and distort the shape of the model if they are far from the center of data. Yabuuchi and Watada have developed a model for describing the system possibility using the center of a possibilistic fuzzy regression model and an approach that mends the distortion of the model. The objective of this paper is to analyze the Japanese economy using our model, and to show the usefulness of our model by analysis results.

Conservative and aggressive rough SVR modeling

Support vector regression provides an alternative to the neural networks in modeling non-linear real-world patterns. Rough values, with a lower and upper bound, are needed whenever the variables under consideration cannot be represented by a single value. This paper describes two approaches for the modeling of rough values with support vector regression (SVR). One approach, by attempting to ensure that the predicted high value is not greater than the upper bound and that the predicted low value is not less than the lower bound, is conservative in nature. On the contrary, we also propose an aggressive approach seeking a predicted high which is not less than the upper bound and a predicted low which is not greater than the lower bound. The proposal is shown to use ϵ -insensitivity to provide a more flexible version of lower and upper possibilistic regression models. The usefulness of our work is realized by modeling the rough pattern of a stock market index, and can be taken advantage of by conservative and aggressive traders.

Rough support vector regression

This paper describes the relationship between support vector regression (SVR) and rough (or interval) patterns. SVR is the prediction component of the support vector techniques. Rough patterns are based on the notion of rough values, which consist of upper and lower bounds, and are used to effectively represent a range of variable values. Predictions of rough values in a variety of different forms within the context of interval algebra and fuzzy theory are attracting research interest. An extension of SVR, called rough support vector regression (RSVR), is proposed to improve the modeling of rough patterns. In particular, it is argued that the upper and lower bounds should be modeled separately. The proposal is shown to be a more flexible version of lower possibilistic regression model using ϵ -insensitivity. Experimental results on the Dow Jones Industrial Average demonstrate the suggested RSVR modeling technique.

Dual models for possibilistic regression analysis

Upper and lower regression models (dual possibilistic models) are proposed for data analysis with crisp inputs and interval or fuzzy outputs. Based on the given data, the dual possibilistic models can be derived from upper and lower directions, respectively, where the inclusion relationship between these two models holds. Thus, the inherent uncertainty existing in the given phenomenon can be approximated by the dual models. As a core part of possibilistic regression, firstly possibilistic regression for crisp inputs and interval outputs is considered where the basic dual linear models based on linear programming, dual nonlinear models based on linear programming and dual nonlinear models based on quadratic programming are systematically addressed, and similarities between dual possibilistic regression models and rough sets are analyzed in depth. Then, as a natural extension, dual possibilistic regression models for crisp inputs and fuzzy outputs are addressed.

A novel hybrid model for portfolio selection

As we know, the performance of the mean–variance approach depends on the accurate forecast of the return rate. However, the conventional method (e.g. arithmetic mean or regression-based method) usually cannot obtain a satisfied solution especially under the small sample situation. In this paper, the proposed method which incorporates the grey and possibilistic regression models formulates the novel portfolio selection model. In order to solve the multi-objective quadric programming problem, multi-objective evolution algorithms (MOEA) is employed. A numerical example is also illustrated to show the procedures of the proposed method. On the basis of the numerical results, we can conclude that the proposed method can provide the more flexible and accurate results.

The garbage volume analysis to consider CO2 emission reduction using households survey data

Recently, The garbage problem has become aggravated. This Problem includes that the capacity of waste treatment plants is not only insufficient, but also the global warming is caused by carbon dioxide emission. This research investigates the garbage volume and CO2 emission reduction in Nagano city using households survey data. A life cycle inventory analysis is employed to represent the relation between the CO2 emission and household expenditures. At the same time, the forecasting model of the garbage volume is also estimated by using a possibilistic regression model. And using these models, as restrains on CO2 emission, the garbage volume is estimated.

可能性回帰分析の応用研究 : 日本の広告費の予測(<特集論文>人文・社会科学へのファジィ理論の応用)

経済変動のような社会現象には数多くのあいまい性が含まれている。そのため、計量的予測にはファジィ集合論に基づいたファジィ関数を用いることが有効と考えられる。この論文では可能性回帰分析を日本の広告費の予測に応用した事例について述べている。広告費の定義は時代とともに徐々に変化している。もとより広告の概念があいまいだからであり、コミュニケーションの手段やあり方が技術的にも社会的にも変化しているからである。このような状況から発生するデータを分析するには、統計的分布に従う分析法よりも可能性測度に基づく分析法の方が有効ではないかと考える。データが発生する環境条件が一様でないとか、データそのものがあいまいだからである。実際の分析方法としては、日本の広告費や四媒体広告費の時系列データを用いて、回帰係数がファジィである場合、データがファジィである場合、実験計画法を取り入れた手法について分析を行った。