MTL-algebras arising from partially ordered groups

作者：Vetterlein Thomas^*

来源：Fuzzy Sets and Systems, 2010, 161(3): 433-443.

DOI：10.1016/j.fss.2009.09.008

• Basic semihoop
• MTL-algebra
• Partial algebra associated to a basic semihoop
• Partially ordered group

After dropping the implication-like operation and reversing the order, an MTL-algebra becomes a partially ordered structure (L: <=, circle plus, 0, 1) based on the single addition-like operation circle plus. Furthermore, circle plus may be restricted to a partial, but cancellative addition + without loss of information. We deal in this paper with the case that the resulting partial algebra (L: <=, +, 0, 1) is embeddable into the positive cone of a partially ordered group. It turns out that most of the examples of MTL-algebras known at present can be represented in this way. So the systematisation of a considerable class of MTL-algebras is achieved, and the methods of their construction are brought onto a common line.

• 出版日期2010-2-1