{'fraction_non_alphanumeric': 0.01881331403762663, 'fraction_numerical': 0.0, 'mean_word_length': 5.017391304347826, '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}}
Multiset Approach to Algebraic Structures

This chapter explores the various algebraic structures that exist in the fuzzy set environment in a multiset context. The authors have also established analogs of groups, rings, and ideals of sets in multiset environment. The conditions under which a multiset that is derived from a group becomes a multiset group (shortly mset group) and that derived from a ring to become a multiset ring (shortly mset ring) have been mentioned. The distinguishing between multiset subring and multiset ideals has been discussed on in the chapter. The authors have also delved into properties such as intersection and union of mset groups, mset rings, and ideals.