# An Approach for a Spatial Data Attribute Similarity Measure Based on Granular Computing Closeness
## 1 Introduction  
Spatial similarity is an important theoretical issue of Geographic Information System ( GIS ), and it is necessary to conduct in-depth research [1]. Spatial problems can be explained by similar spatial phenomena, and the knowledge obtained from the research examples can be used to understand other phenomena, as well as to help explain certain scene phenomena [2; 3]. Before the advent of computer graphics, the understanding of the law of spatial similarity was a mostly intuitive and subjective judgement. It did not achieve precision, quantification and formulation, and there was no strict mathematical model for the understanding of similar laws [4]. Similarity provides a basis for judging how to classify objects, form concepts, solve problems and integrate ideas [5]. Spatial similarity belongs to a type of spatial relationship that is juxtaposed with topological relations, directional relations, distance relationships and related relationships [6]. Due to the development of computer technology, scholars have carried out various research efforts in recent years on the basic theory and application of spatial data similarity. Because many similarity measure methods cannot measure the relationship between apertured polygons, scholars have proposed a method based on a positional map to describe the distribution of complex geometric shapes [7]. Scholars have developed and tested a spatial geometric consistency algorithm based on two spatial surface objects in the Euclidean plane for the continuous function of increasing the consistency of the position, orientation, size and shape of the spatial object [8]. A geometric similarity measure method for complex solid objects with surface holes was introduced to describe local and global features by constructing a multi-level bending radius complex function [9]. The abovementioned method is used to analyse spatial similarity in the geometry of spatial targets, and there is much similar literature regarding similar geometric shapes [10; 11; 12]. Spatial similarity, in addition to geometric similarities, is similar in structure to spatial objects (groups). It is often used to study the spatial distributions and layouts of geographic phenomena, as wellas to study the internal structures of geographic entities in geoscience research. The similarities of such structures are the basis for classification. Using the vegetation temperature condition index, scholars have applied structural similarity to analyse the spatial characteristics of the vegetation temperature condition index time series in plain areas and considered that structural factors are the main factors affecting the change [13]. The community structure and spatial distribution of macrobenthos in the Bering Sea shelf area were studied by scholars [14]. The scholars used the nearest-neighbour method to describe the K-function and box dimension of the spatial distributions of species and the spatial similarities, and verified the method with an experimental region [15]. To explore the insufficiency of habitat structure for the quantification of bird biodiversity, the researchers proposed a structural similarity method to determine the relationship between vertical and horizontal habitat structure indexes and bird biodiversity patterns and calculated the richness of all birds and of three specific bird species for each route of the habitat [16]. There are many papers on the distribution law of spatial entities using spatial structure similarity [17; 18]. Due to the similarities between spatial entities in spatial relationships, spatial data based on spatial locations may also have similar feature attributes, and there is presently little theoretical or applied research on the similarity of feature attributes for spatial entities. Similarity is an uncertainty problem, and its measurement methods are mainly based on fuzzy sets [19], rough sets [20] and granular computing [21].