The Structure Of Linguistic Truth-Valued Lattice Implication Algebra

A lattice-valued logical algebra -lattice implication algebra (LIA) and its corresponding logic and reasoning systems have been extensively investigated in the last few years. There have been also some research works with an attempt to establish the linguistic truth valued logical algebra for decision making purpose, including the linguistic truth valued logical algebra based on LIA. In this paper, in order to characterize the feature of linguistic truth-valued algebra based on LIA, firstly the product-irreducible and sum-irreducible elements of LIA are introduced and their properties are discussed,. Then some decomposition theorems in linguistic truth-valued LIA are given, these results will place a support for the further investigation of linguistic truth-valued algebra structure and modeling.