具有连续和阿基米德基础 T-norms 和 T-conorms 的 Uni-nullnorm 在任意 Uninorm 上的可分配性

IF 0.9 3区数学 Q2 MATHEMATICS

Mathematica Slovaca Pub Date : 2023-12-01 DOI:10.1515/ms-2023-0110

D. Jocic, I. Štajner-Papuga

{"title":"具有连续和阿基米德基础 T-norms 和 T-conorms 的 Uni-nullnorm 在任意 Uninorm 上的可分配性","authors":"D. Jocic, I. Štajner-Papuga","doi":"10.1515/ms-2023-0110","DOIUrl":null,"url":null,"abstract":"ABSTRACT The issue of distributivity of aggregation operators is crucial for many different areas such as fuzzy sets and fuzzy logic, pseudo-analysis and measure theory, and particulary in the decision making theory. The problem of distributivity of an operator form a special class of uni-nullnorms over a general uninorm is being addressed through this paper. The class in question consists of uni-nullnorms with continuous and Archimedean underlying t-norms and t-conorms, and the results presented here are a natural continuation and extension of some previous works with an emphasis on a much wider class of uninorms as inner operators.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"151 ","pages":"1527 - 1544"},"PeriodicalIF":0.9000,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Distributivity of a Uni-nullnorm with Continuous and Archimedean Underlying T-norms and T-conorms Over an Arbitrary Uninorm\",\"authors\":\"D. Jocic, I. Štajner-Papuga\",\"doi\":\"10.1515/ms-2023-0110\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"ABSTRACT The issue of distributivity of aggregation operators is crucial for many different areas such as fuzzy sets and fuzzy logic, pseudo-analysis and measure theory, and particulary in the decision making theory. The problem of distributivity of an operator form a special class of uni-nullnorms over a general uninorm is being addressed through this paper. The class in question consists of uni-nullnorms with continuous and Archimedean underlying t-norms and t-conorms, and the results presented here are a natural continuation and extension of some previous works with an emphasis on a much wider class of uninorms as inner operators.\",\"PeriodicalId\":18282,\"journal\":{\"name\":\"Mathematica Slovaca\",\"volume\":\"151 \",\"pages\":\"1527 - 1544\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2023-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematica Slovaca\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1515/ms-2023-0110\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematica Slovaca","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/ms-2023-0110","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

摘要集合算子的分布性问题对许多不同领域都至关重要，如模糊集和模糊逻辑、伪分析和度量理论，尤其是在决策理论中。本文研究的是一般非矩形上的一类特殊单无矩形算子的分布性问题。这一类算子包括具有连续和阿基米德基础 t-norms 和 t-conorms 的 uni-nullnorms，本文提出的结果是以前一些工作的自然延续和扩展，重点是作为内算子的更广泛的 uninorms 类。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Distributivity of a Uni-nullnorm with Continuous and Archimedean Underlying T-norms and T-conorms Over an Arbitrary Uninorm

ABSTRACT The issue of distributivity of aggregation operators is crucial for many different areas such as fuzzy sets and fuzzy logic, pseudo-analysis and measure theory, and particulary in the decision making theory. The problem of distributivity of an operator form a special class of uni-nullnorms over a general uninorm is being addressed through this paper. The class in question consists of uni-nullnorms with continuous and Archimedean underlying t-norms and t-conorms, and the results presented here are a natural continuation and extension of some previous works with an emphasis on a much wider class of uninorms as inner operators.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Mathematica Slovaca 数学-数学

CiteScore

2.10

自引率

6.20%

发文量

审稿时长

6-12 weeks

期刊介绍： Mathematica Slovaca, the oldest and best mathematical journal in Slovakia, was founded in 1951 at the Mathematical Institute of the Slovak Academy of Science, Bratislava. It covers practically all mathematical areas. As a respectful international mathematical journal, it publishes only highly nontrivial original articles with complete proofs by assuring a high quality reviewing process. Its reputation was approved by many outstanding mathematicians who already contributed to Math. Slovaca. It makes bridges among mathematics, physics, soft computing, cryptography, biology, economy, measuring, etc.　 The Journal publishes original articles with complete proofs. Besides short notes the journal publishes also surveys as well as some issues are focusing on a theme of current interest.