{'fraction_non_alphanumeric': 0.014588859416445624, 'fraction_numerical': 0.0, 'mean_word_length': 4.94488188976378, '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}}
Near rough and near exact sets in topological spaces

The basic concepts of some near open, near rough, near exact and near fuzzy sets are introduced and sufficiently illustrated. The topology induced by binary relations is used to generalize the basic rough set concepts. We introduce the near exactness and near roughness by applying the near concepts to make more accuracy for definability of sets. We give a new definition for a membership function to find near interior, near boundary and near exterior points. Moreover, proved results, examples and counter examples are provided. The topological structure which suggested in this paper opens up the way for applying rich amount of topological facts and methods in the process of granular computing.