On probabilistic linguistic term set operations

Abstract

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.