Fuzzy Spatial Similarity Relations And Spatial Data Modeling With Applications In Multidimensional Scale Vector Map Spaces

Autonomy of operations combined with decentralized representation and management of vague spatial objects in spatial databases has given rise to inconsistency and heterogeneity representing spatial objects in multidimensional scale vector map spaces. Many spatial databases deal with objects in space that cannot be adequately described by determinate, crisp spatial concepts because of their intrinsically indeterminate and fuzzy nature. Geographical information systems and spatial database systems are currently unable to cope with such kind of spatial objects in a precise manner. Automated generalization is a necessary tool for the construction of spatial databases that are crucial components in spatial data infrastructure that provides geographical spatial positioning bases for the society in numerous fields like economy, defence, education, transportation, P&D, environment protection, research, telecommunication, etc. Nevertheless, this is still a dream because the generalizations of features of spatial objects in maps are not parameter-free and therefore need human’s interference. One of the major reasons is that automated generalization is a spatial similarity transformation in multidimensional scale vector map spaces which is fuzzy in nature; however, no theory can be found to support such kind of transformations.This dissertation focuses on developing the theory of fuzzy spatial similarity relations in multidimensional scale vector map spaces, aiming at proposing the definitions, models and methods that can be used in selection of parameters to automate generalization algorithms in multidimensional scale vector map spaces. After a systematic review of existing achievements including the definitions of similarity, features of assessing similarity in various fields, classification systems for addressing similarity, and the measurement tools of similarity relations from the fields of mathematics, psychology, information sciences and geography, as well as a number of raster-based models to measure similarity degrees between images, the dissertation achieves the following innovative contributions.First are the realization and the utility of fuzzy set theory and fuzzy logic in similarity transformations for generalization process of spatial objects in multidimensional scale vector map spaces to develop theory of Fuzzy Spatial Similarity Relation for the first time in literature. No such work has been reported in the context of automated generalization for multidimensional scale vector map spaces.Second are the proposed definitions of Fuzzy Spatial Similarity Relations under the paradigms of fuzzy set theory rather than the crisp set theory for the spatial objects in geographic space and in multidimensional scale vector maps, which enhances the capability of modeling spatial objects.Third are the characteristics of proposed Fuzzy Spatial Similarity Relations in automated generalization based on fuzzy relations, and fuzzy logic to strengthen the logical relationship for our theory in geographic space and in multidimensional scale vector maps.Fourth are the ideas of the fuzzy factors, their identification and contribution to fuzziness in representing spatial objects for similarity transformations in geographic spaces and in multidimensional scale vector map spaces.Fifth are the proposed fuzzification procedures to get a complete picture of the degree of membership function that enable us to make a very well aware and optimal decision in the selection of parameter for similarity transformations of spatial objects.Although, the study focuses on fuzzy spatial similarity relations in automated generalization specifically in topographic maps but the application of such a theory exceeds the domain of GIS. Any branch of science and engineering that deals with spatial data that we call spatial objects will benefit from formal understanding of fuzzy spatial similarity relations. It can be utilized in the fields such as, spatial logic, spatial reasoning and thus will extend its benefits in areas such as surveying engineering, medicine, health, genetic engineering, computer aided design, computer aided manufacturing, and robotics which all contribute to the economy of nations ultimately.