| Abstrakt: |
Recently, the concept of overlap functions on complete lattices has been introduced by extending the truth values set from the unit closed interval to complete lattices. On the other hand, the residual implications induced from commonly used aggregation functions (see, e.g., t-norms, pseudo-t-norms, uninorms, semi-uninorms and pseudo-uninorms), as a natural research topic of these commonly used aggregation functions in the case of lattice values, play a vital role in many-valued logic. In this paper, we consider the residual implications derived from the so-called C L -overlap functions on complete lattices which are the weak form of overlap functions on complete lattices. To be precise, firstly, we give the notion of R O -implications which are residual implications induced from the C L -overlap functions on complete lattices and give some basic properties of them. Secondly, we focus on the conditions under which R O -implications can satisfy the certain algebraic properties possessed by implications on complete lattices. Finally, we give a one-to-one correspondence between different families of certain implications on complete lattices and the family of C L -overlap functions on complete lattices. [ABSTRACT FROM AUTHOR] |
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