Geometric properties of interval type-II fuzzy regions

Abstract

Fuzzy geographical phenomena widely exist in the real world, and many modeling and measurement methods for such phenomena have been reported. The most common models and methods are based on type-I fuzzy sets; therefore, they cannot measure the uncertainty of the membership value or describe complicated fuzzy geographical phenomena. Several researchers have used high-order fuzzy theory to avoid the limitations of traditional methods; however, only a few successful models and methods in that domain exist. A fuzzy region model based on interval type-II fuzzy sets is proposed in this paper, considering the uncertainty due to error and to scale effects. Two concepts are proposed to describe the spatial geometric properties of interval type-II fuzzy geographical regions: the geometric summary property and the geometric detailed property, which can reflect different aspects of spatial attributes. Next, some geometric attributes, the area, perimeter, height, width, and extrinsic diameter, of interval type-II fuzzy regions are discussed. The theories and methods proposed in this paper can objectively describe complicated and vague geographical phenomena and thus are meaningful for the development of fuzzy geographical information science.