{'fraction_non_alphanumeric': 0.024375, 'fraction_numerical': 0.003125, 'mean_word_length': 5.643153526970955, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Fuzzy Intersection and Difference Model for Topological Relations

Topological relations have played important roles in spatial query, analysis and reasoning in Geographic Information Systems (GIS) and spatial databases. The topological relations between crisp and fuzzy spatial objects based upon the 9- intersections topological model have been identified. However the formalization of the topological relations between fuzzy regions needs more investigation. The paper provides a theoretical framework for modelling topological relations between fuzzy regions based upon a new fuzzy topological model called the Fuzzy Intersection and Difference (FID) Model. A novel topological model is formalized based on Fuzzy Topological Space (FTS). In order to derive all fuzzy topological relations between two fuzzy spatial objects, the fuzzy spatial object (A) is decomposed in four components: the Interior, the Interior's Boundary, the Object's Boundary, and the Exterior's Boundary of A. By use of this definition of fuzzy spatial object, new 4*4-Intersection and Fuzzy Intersection and Difference (FID) models are proposed as a qualitative model for the identification of all topological relations between two simple fuzzy regions. These two new models are compared with other fuzzy models studied in the literature. Examples are provided to illustrate the use of these two models presented in this paper with results which can be applied for modeling GIS and geospatial databases. Keywords— Fuzzy Intersection and Difference Model, 4*4- Intersection Matrix, Fuzzy Objects, Topological Relations, GIS