箍和域

IF 3.2 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems Pub Date : 2025-04-08 DOI:10.1016/j.fss.2025.109404

Anatolij Dvurečenskij , Omid Zahiri

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引用次数: 0

摘要

在[31]，[29]，[30]中首次发现了mv -代数与b zout结构域的关系。在本文中，我们以这些研究为基础，将结果扩展到Wajsberg箍。我们首先检查Wajsberg箍作为mv -代数的（弱）过滤器。我们建立了每个Wajsberg箍的表示，作为一个消去环和一个有界可表示的Wajsberg箍的子积。这些结果证明了每个Wajsberg环都可以与bsamzout域R的一个特定子集相关联，即一个具有特殊性质的R的饱和乘法系统。此外，我们还描述了对应于消环和线性Wajsberg环的b zout域。

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Hoops and domains

The relationship between MV-algebras and Bézout domains was first explored in [31], [29], [30]. In this paper, we build upon those studies to extend the results to Wajsberg hoops. We begin by examining Wajsberg hoops as (weak) filters of MV-algebras. We establish a representation for every Wajsberg hoop as a subdirect product of a cancellative hoop and a boundedly representable Wajsberg hoop. These results demonstrate that every Wajsberg hoop can be associated with a specific subset of a Bézout domain R, i.e., a saturated multiplicative system of R with a special property. Furthermore, we characterize Bézout domains corresponding to cancellative hoops and linear Wajsberg hoops.

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来源期刊

Fuzzy Sets and Systems 数学-计算机：理论方法

CiteScore

6.50

自引率

17.90%

发文量

321

审稿时长

6.1 months

期刊介绍： Since its launching in 1978, the journal Fuzzy Sets and Systems has been devoted to the international advancement of the theory and application of fuzzy sets and systems. The theory of fuzzy sets now encompasses a well organized corpus of basic notions including (and not restricted to) aggregation operations, a generalized theory of relations, specific measures of information content, a calculus of fuzzy numbers. Fuzzy sets are also the cornerstone of a non-additive uncertainty theory, namely possibility theory, and of a versatile tool for both linguistic and numerical modeling: fuzzy rule-based systems. Numerous works now combine fuzzy concepts with other scientific disciplines as well as modern technologies. In mathematics fuzzy sets have triggered new research topics in connection with category theory, topology, algebra, analysis. Fuzzy sets are also part of a recent trend in the study of generalized measures and integrals, and are combined with statistical methods. Furthermore, fuzzy sets have strong logical underpinnings in the tradition of many-valued logics.