The system of linear equations plays a vital role in real life problems such as optimization, economics, and engineering. The parameters of the system of linear equations are modeled by taking the experimental or obse...The system of linear equations plays a vital role in real life problems such as optimization, economics, and engineering. The parameters of the system of linear equations are modeled by taking the experimental or observation data. So the parameters of the system actually contain uncertainty rather than the crisp one. The uncertainties may be considered in term of interval or fuzzy numbers. In this paper, a detailed study of three solution techniques namely Classical Method, Extension Principle method and α-cuts and interval Arithmetic Method to solve the system of fuzzy linear equations has been done. Appropriate applications are given to illustrate each technique. Then we discuss the comparison of the different methods numerically and graphically.展开更多
In this paper,a method is proposed to deal with factors affecting the fuzzy time series forecasting.A new fuzzification process is used by considering all the fuzzy sets with nonzero membership values corresponding to...In this paper,a method is proposed to deal with factors affecting the fuzzy time series forecasting.A new fuzzification process is used by considering all the fuzzy sets with nonzero membership values corresponding to the data points.A strong alpha-cut based method is presented to select appropriate fuzzy logical relationships that carry importance in analyzing the trend of time series.Further,a unique defuzzification approach based on weights is proposed to get crisp variation.This obtained variation is finally converted to the forecasted value.The presented method is tested on the benchmark enrolment dataset of Alabama University and seven datasets of the Taiwan Capitalization Weighted Stock Index.On comparing the results,it is observed that the presented method performs better than the existing methods.Also,the statistical measures indicate the good forecasting results of the presented method.展开更多
In this article, we define the arithmetic operations of generalized trapezoidal picture fuzzy numbers by vertex method which is assembled on a combination of the (α, γ, β)-cut concept and standard interval analysis...In this article, we define the arithmetic operations of generalized trapezoidal picture fuzzy numbers by vertex method which is assembled on a combination of the (α, γ, β)-cut concept and standard interval analysis. Various related properties are explored. Finally, some computations of picture fuzzy functions over generalized picture fuzzy variables are illustrated by using our proposed technique.展开更多
The conventional data envelopment analysis （DEA） measures the relative efficiencies of a set of decision making units with exact values of inputs and outputs. In real-world prob- lems, however, inputs and outputs ty...The conventional data envelopment analysis （DEA） measures the relative efficiencies of a set of decision making units with exact values of inputs and outputs. In real-world prob- lems, however, inputs and outputs typically have some levels of fuzziness. To analyze a decision making unit （DMU） with fuzzy input/output data, previous studies provided the fuzzy DEA model and proposed an associated evaluating approach. Nonetheless, numerous deficiencies must still be improved, including the α- cut approaches, types of fuzzy numbers, and ranking techniques. Moreover, a fuzzy sample DMU still cannot be evaluated for the Fuzzy DEA model. Therefore, this paper proposes a fuzzy DEA model based on sample decision making unit （FSDEA）. Five eval- uation approaches and the related algorithm and ranking methods are provided to test the fuzzy sample DMU of the FSDEA model. A numerical experiment is used to demonstrate and compare the results with those obtained using alternative approaches.展开更多
文摘The system of linear equations plays a vital role in real life problems such as optimization, economics, and engineering. The parameters of the system of linear equations are modeled by taking the experimental or observation data. So the parameters of the system actually contain uncertainty rather than the crisp one. The uncertainties may be considered in term of interval or fuzzy numbers. In this paper, a detailed study of three solution techniques namely Classical Method, Extension Principle method and α-cuts and interval Arithmetic Method to solve the system of fuzzy linear equations has been done. Appropriate applications are given to illustrate each technique. Then we discuss the comparison of the different methods numerically and graphically.
文摘In this paper,a method is proposed to deal with factors affecting the fuzzy time series forecasting.A new fuzzification process is used by considering all the fuzzy sets with nonzero membership values corresponding to the data points.A strong alpha-cut based method is presented to select appropriate fuzzy logical relationships that carry importance in analyzing the trend of time series.Further,a unique defuzzification approach based on weights is proposed to get crisp variation.This obtained variation is finally converted to the forecasted value.The presented method is tested on the benchmark enrolment dataset of Alabama University and seven datasets of the Taiwan Capitalization Weighted Stock Index.On comparing the results,it is observed that the presented method performs better than the existing methods.Also,the statistical measures indicate the good forecasting results of the presented method.
文摘In this article, we define the arithmetic operations of generalized trapezoidal picture fuzzy numbers by vertex method which is assembled on a combination of the (α, γ, β)-cut concept and standard interval analysis. Various related properties are explored. Finally, some computations of picture fuzzy functions over generalized picture fuzzy variables are illustrated by using our proposed technique.
基金supported by the National Natural Science Foundation of China (70961005)211 Project for Postgraduate Student Program of Inner Mongolia University+1 种基金National Natural Science Foundation of Inner Mongolia (2010Zd342011MS1002)
文摘The conventional data envelopment analysis （DEA） measures the relative efficiencies of a set of decision making units with exact values of inputs and outputs. In real-world prob- lems, however, inputs and outputs typically have some levels of fuzziness. To analyze a decision making unit （DMU） with fuzzy input/output data, previous studies provided the fuzzy DEA model and proposed an associated evaluating approach. Nonetheless, numerous deficiencies must still be improved, including the α- cut approaches, types of fuzzy numbers, and ranking techniques. Moreover, a fuzzy sample DMU still cannot be evaluated for the Fuzzy DEA model. Therefore, this paper proposes a fuzzy DEA model based on sample decision making unit （FSDEA）. Five eval- uation approaches and the related algorithm and ranking methods are provided to test the fuzzy sample DMU of the FSDEA model. A numerical experiment is used to demonstrate and compare the results with those obtained using alternative approaches.
