Toward a Synergy of a Lattice Implication Algebra with Fuzzy Lattice Reasoning - A Lattice Computing Approach

Abstract

Automated reasoning can be instrumental in real-world applications involving "intelligent" machines such as (semi-)autonomous vehicles as well as robots. From an analytical point of view, reasoning consists of a series of inferences or, equivalently, implications. In turn, an implication is a function which obtains values in a welldefined set. For instance, in classical Boolean logic an implication obtains values in the set {0, 1}, i.e. it is either true (1) or false (0); whereas, in narrow fuzzy logic an implication obtains values in the specific complete mathematical lattice unit-interval, symbolically [0, 1], i.e. it is partially true/false. A lattice implication algebra (LIA)

A Decision Making Approach with Linguistic Weight and Unavoidable Incomparable Ranking

“…Yang Xu et al have extended the binaryresolution to multiary -resolution in lattice-valued propositional logic LP(X) and lattice-valued first-order logic LF(X), obtained a result that multiary -resolution principle in LF(X) can be equivalently transformed into that in LP(X) [27]. Yi Liu and Vassilis Pdf_Folio:1102 G. Kaburlasos et al have introduced a LIA with implication values in a complete lattice of intervals on the real number axis which followed a capacity to optimize [28]. Li Zou proposed a linguisticvalued knowledge representation mode and approximated reasoning approach with linguistic-valued credibility factors [29].…”