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) assumes implication values in a general complete mathematical lattice toward enhancing the representation of ambiguity in reasoning. This work introduces a LIA with implication values in a complete lattice of intervals on the real number axis. Since real numbers stem from real-world measurements, this work sets a ground for real-world applications of a LIA. We show that the aforementioned lattice of intervals includes all
the enabling mathematical tools for fuzzy lattice reasoning (FLR). It follows a capacity to optimize, in principle, LIA-reasoning based on FLR as described in this work.


Y. Liu, V.G. Kaburlasos, A.G. Hatzimichailidis, Y. Xu, Toward a Synergy of a Lattice Implication Algebra with Fuzzy Lattice Reasoning – A Lattice Computing Approach. In: Handbook of Fuzzy Sets Comparison – Theory, Algorithms and Applications, George A. Papakostas, Anestis G. Hatzimichailidis, Vassilis G. Kaburlasos (eds.), GCSR vol. 6, pp. 23-42, 2016.

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