On type-2 cyclic associative groupoids and inflationary pseudo general residuated lattices

IF 1.7 4区计算机科学 Q3 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

Journal of Intelligent & Fuzzy Systems Pub Date : 2023-11-01 DOI:10.3233/jifs-232966

Xiaogang An, Mingming Chen

{"title":"On type-2 cyclic associative groupoids and inflationary pseudo general residuated lattices","authors":"Xiaogang An, Mingming Chen","doi":"10.3233/jifs-232966","DOIUrl":null,"url":null,"abstract":"This paper explores the relationship between fuzzy logic algebra and non associative groupoid. As a groupoid which can satisfy type-2 cyclic associative (T2CA) law, T2CA-groupoid is characterized by generalized symmetry. Fuzzy logic algebra is a major direction in the study of fuzzy logic. Residuated lattices are a class of fuzzy logic algebras with widespread applications. The inflationary pseudo general residuated lattice (IPGRL), a generalization of the residuated lattice, does not need to satisfy the associative law and commutative law. Moreover, the greatest element of IPGRL is no longer the identity element. In this paper, the notion of T2CA-IPGRL (IPGRL in T2CA-groupoid) is proposed and its properties are investigated in combination with the study of IPGRL and T2CA-groupoid. In addition, the generalized symmetry and regularity of T2CA-groupoid are investigated based on the characteristics of commutative elements. Meanwhile, the decomposition of T2CA-root of band with T2CA-unipotent radical is studied as well. The result shows that every T2CA-root of band is the disjoint union of T2CA-unipotent radicals.","PeriodicalId":54795,"journal":{"name":"Journal of Intelligent & Fuzzy Systems","volume":"60 12","pages":"0"},"PeriodicalIF":1.7000,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Intelligent & Fuzzy Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3233/jifs-232966","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}

引用次数: 0

Abstract

This paper explores the relationship between fuzzy logic algebra and non associative groupoid. As a groupoid which can satisfy type-2 cyclic associative (T2CA) law, T2CA-groupoid is characterized by generalized symmetry. Fuzzy logic algebra is a major direction in the study of fuzzy logic. Residuated lattices are a class of fuzzy logic algebras with widespread applications. The inflationary pseudo general residuated lattice (IPGRL), a generalization of the residuated lattice, does not need to satisfy the associative law and commutative law. Moreover, the greatest element of IPGRL is no longer the identity element. In this paper, the notion of T2CA-IPGRL (IPGRL in T2CA-groupoid) is proposed and its properties are investigated in combination with the study of IPGRL and T2CA-groupoid. In addition, the generalized symmetry and regularity of T2CA-groupoid are investigated based on the characteristics of commutative elements. Meanwhile, the decomposition of T2CA-root of band with T2CA-unipotent radical is studied as well. The result shows that every T2CA-root of band is the disjoint union of T2CA-unipotent radicals.

查看原文本刊更多论文

关于2型循环关联群和膨胀伪一般剩余格

本文探讨了模糊逻辑代数与非结合群的关系。作为满足型-2循环结合律的群似体，T2CA-群似体具有广义对称性。模糊逻辑代数是模糊逻辑研究的一个重要方向。残格是一类应用广泛的模糊逻辑代数。膨胀伪一般剩余格(IPGRL)是剩余格的一种推广，它不需要满足结合律和交换律。此外，IPGRL最大的元素不再是身份元素。本文提出了T2CA-IPGRL (T2CA-groupoid中的IPGRL)的概念，并结合IPGRL和T2CA-groupoid的研究对其性质进行了探讨。此外，基于交换元的特征，研究了t2ca群拟的广义对称性和正则性。同时，研究了t2ca单能自由基对带根的分解作用。结果表明，每个t2ca根都是t2ca单能自由基的不接合结合。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Journal of Intelligent & Fuzzy Systems 工程技术-计算机：人工智能

CiteScore

3.40

自引率

10.00%

发文量

965

审稿时长

5.1 months

期刊介绍： The purpose of the Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology is to foster advancements of knowledge and help disseminate results concerning recent applications and case studies in the areas of fuzzy logic, intelligent systems, and web-based applications among working professionals and professionals in education and research, covering a broad cross-section of technical disciplines.