Abstract
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.
Highlights
Statistic regression analysis and fuzzy regression analysis are two types of methods underlying different philosophies to assess the functional relationship between the dependent and independent variables and determine the best-fit model for describing the relationship, by exploiting the knowledge from the given input-output data pairs
With the suggestion from Tanaka and Watada [19], a new concept of credibility is introduced to measure the performance of the fuzzy linear regression (FLR) models with different h values in this paper, based on which a systematic approach is formulated to optimize h values for FLR using minimum fuzziness
Each time, two datasets were randomly selected from ten datasets as testing datasets while the rest eight datasets were used to develop FLR models when h value is specified as the optimal value, 0 and 0.5, respectively
Summary
Statistic regression analysis and fuzzy regression analysis are two types of methods underlying different philosophies to assess the functional relationship between the dependent and independent variables and determine the best-fit model for describing the relationship, by exploiting the knowledge from the given input-output data pairs. Moskowitz and Kim [20] studied the relationship among the h value, membership function shape, and the spreads of fuzzy parameters in FLR with symmetric fuzzy numbers, they developed a general approach to assess the proper h parameter values. When the dataset is sufficiently large, h = 0 should be used and is increased along with the decreasing volume of the collected data Both did not suggest how to get an optimal h value for the FLR model when a sample dataset is given. With the suggestion from Tanaka and Watada [19], a new concept of credibility is introduced to measure the performance of the FLR models with different h values in this paper, based on which a systematic approach is formulated to optimize h values for FLR using minimum fuzziness.
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