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Method of identifying a type 2 membership function and application to decision-making problems

Uemura Y.

Control and Cybernetics

2015

Vol. 44, no. 3

399--406

Tanaka (1991) suggested that the parameters of a linear regression model should be made fuzzy In order to better reﬂect the nature of the system, involving a deﬁnite degree of variability, and created a fuzzy linear regression model. This model can be formulated in the form of a linear programming problem that minimizes the span between the upper and lower limits under the constraints that include all data. In recent years, all the attention in this context has been focused on a fuzzy number that has an indiﬀerent zone. A fuzzy number that we consider here is deﬁned by using a type 2 membership function. This paper addresses the fact that a type 2 membership function has the upper and lower limits and shows that a type 2 membership function can be identiﬁed by expanding a fuzzy linear regression model into a fuzzy linear polynomial regression model. Finally, after a proposed fuzzy polynomial model is identiﬁed, a mathematical model is developed for a fuzzy decision-making method that accounts for an indiﬀerent zone.