A Linguistic Truth-Valued Uncertainty Reasoning Model Based on Lattice-Valued Logic Shuwei Chen, Yang Xu, and Jun Ma Department of Mathematics, Southwest Jiaotong University, Chengdu 610031, Sichuan, P.R. China chensw915@163.com Abstract. The subject of this work is to establish a mathematical framework that provide the basis and tool for uncertainty reasoning based on linguistic information. This paper focuses on a flexible and realistic approach, i.e., the use of linguistic terms, specially, the symbolic approach acts by direct computation on linguistic terms. An algebra model with linguistic terms, which is based on a logical algebraic struc- ture, i.e., lattice implication algebra, is applied to represent imprecise information and deals with both comparable and incomparable linguistic terms (i.e., non-ordered linguistic terms). Within this framework, some inferential rules are analyzed and extended to deal with these kinds of lattice-valued linguistic information. 1 Introduction One of the fundamental goals of artificial intelligence (AI) is to build artificially computer- based systems which make computer simulate, extend and expand hu- man’s intelligence and empower computers to perform tasks which are routinely performed by human beings. Due to the fact that human intelligence actions are always involved with uncertainty information processing, one important task of AI is to study how to make the computer simulate human being to deal with uncertainty information. Among major ways in which human being deal with uncertainty information, the uncertainty reasoning becomes an essential mecha- nism in AI. In real uncertainty reasoning problem, most information, which are always propositions with truth-values, can be very qualitative in nature, i.e., described in natural language. Usually, in a quantitative setting the information is expressed by means of numerical values. However, when we work in a qualitative setting, that is, with vague or imprecise knowledge, this cannot be estimated with an exact numerical value. Then, it may be more realistic to use linguistic truth- values instead of numerical values. Since 1990, there have been some important conclusions on inference with linguistic terms. In 1990, Ho [3] constructed a distributive lattice-Hedge alge- bra, which can be used to deal with linguistic terms. He [4] gave a measure function between two linguistic terms, and obtained the fuzzy inference theory and method, which based on linguistic term Hedge algebra. In 1996, Zadeh [17] L. Wang and Y. Jin (Eds.): FSKD 2005, LNAI 3613, pp. 276–284, 2005. c  Springer-Verlag Berlin Heidelberg 2005