# An Approach for a Spatial Data Attribute Similarity Measure Based on Granular Computing Closeness
## 3 Granular Computing Measure  
The fuzzy set based on the set distance can only measure in one dimension; that is, it can only measure the closeness between the two spatial sets, with no way to measure the comprehensive closeness under complex mutual relationships. For example, there are 23 types of land use in an actual land use evaluation. Measuring the similarity coefficient between different land use types by using multi-dimensional economic indexes is a very difficult task. To overcome this deficiency, a multi-dimensional index closeness similarity measure based on granular computing is introduced. Granular computing is a new form of conceptual analysis and its basic idea is to use to solve hierarchical problems in the problem solving process. Granular computing first needs to granulate information, and there are many methods for doing so. This paper uses the atomic formula to granulate information. Let \(IS=(U,A)\) be an information system and \(U\) a universe, where \(a\in A\) represents the attribute in \(A\), and \(v\) is the attribute value of \(a\) on the individual \(x\) on \(U\), \(v=a(x)\). In this case, (\(a\),\(v\)) or \(a_{v}\) is called an atomic formula in granular computing [31]. The land types \(\mathbf{P}\) and \(\mathbf{Q}\) have two measure indexes in Figure 1, R and G, which form the attribute set \(A\). The value of each indicator (i.e., R1 and R2) is the value of the different land units in relation to the index R. (R, R1) or R = R1 is an atomic formula. Thus, through each atomic formula, granular information is obtained, and the calculation of the atomic formula is the information granulation process. Different information granulation approaches can obtain different types of granular information, such as the index R, through the atomic formulas R = R1 and R = R2, the land use area can be granulated into two information granules, [1,4,6,7] and [2,3,5,8,9], while through the atomic formulas G = G1 and G = G2, the land use area can be granulated into two information granules, {1,5,7} and {2,3,4,6,8,9}. Different atomic formulas form different information particles, and how these information particles perform set operations requires some mathematical descriptions and logic rules. Atomic formulas can be described in the form of logical negations, conjunctions and disjunctions. By combining many of the classic logical conjunctions (\(a\),\(v\)) or \(a_{v}\), the formula for the calculation \(\psi\) of the granularity can be obtained. Let \((\varphi,m(\varphi))\) and \((\varphi^{\prime},m(\varphi^{\prime}))\) be two information granules, and the definition of the operation of logical connectives can be calculated using the following forms [31]:  
\[\sim(\varphi,m(\
eg\varphi))=\left(\sim\!\varphi,U-m(\varphi)\right); \tag{2}\] \[(\varphi,m(\varphi))\oplus(\varphi^{\prime},m(\varphi^{\prime}))= \left(\varphi\vee\varphi^{\prime},m(\varphi)\cup m(\varphi^{\prime})\right) \ ; \tag{1}\](3) \((\varphi,m(\varphi))\otimes(\varphi^{\prime},m(\varphi^{\prime}))=(\varphi\lor \varphi^{\prime},m(\varphi)\cap m(\varphi^{\prime}))\) ;  
(4) \((\varphi,m(\varphi))c(\varphi^{\prime},m(\varphi^{\prime}))=(\varphi\to \varphi^{\prime},m(\varphi)\subseteq m(\varphi^{\prime}))\lor m_{*}(\varphi) \subseteq m_{*}(\varphi^{\prime})\wedge m^{*}(\varphi)\subseteq m^{*}( \varphi^{\prime})\) ;  
(5) \((\varphi,m(\varphi))\equiv(\varphi^{\prime},m(\varphi^{\prime}))=(\varphi \leftrightarrow\varphi^{\prime},m(\varphi)\subseteq m(\varphi^{\prime})) \wedge m(\varphi^{\prime})\subseteq m(\varphi)\) \(m(\varphi)\vee((m_{*}(\varphi)\subseteq m_{*}(\varphi^{\prime}))\wedge m^{*}( \varphi^{\prime})\subseteq m^{*}(\varphi)\);  
Feature transformation can be performed on multi-dimensional spatial types through the operation of logical conjunctions.