On probabilistic linguistic term set operations

作者：Songsong Dai, Jianwei Zheng · 发表于：Journal of Intelligent & Fuzzy Systems · 年份：2023 · DOI：10.3233/jifs-223747 · 被引用次数：2 · 研究领域：Rough Sets and Fuzzy Logic、Natural Language Processing Techniques、Multi-Criteria Decision Making

In a recent work (Wang et al. 2020), a partial order ⪯, a join operation ⊔ and a meet operation ⊓ of probabilistic linguistic term sets (PLTSs) were introduced and it was proved that L1 ⊓ L2 ⪯ L1 ⪯ L1 ⊔ L2 and L1 ⊓ L2 ⪯ L2 ⪯ L1 ⊔ L2. In this paper, we demonstrate that its join and meet operations are not satisfy the above requirement. To satisfy this requirement, we modify its join and meet operations. Moreover, we define a negation operation of PLTSs based on the partial order ⪯. The combinations of the proposed negation, the modified join and meet operations yield a bounded, distributive lattice over PLTSs. Meanwhile, we also define a new join operation and a new meet operation which, together with the negation operation, yield a bounded De Morgan over PLTSs.