People use natural languages to think, to reason, to deduce conclusions, and to make decisions. Fuzzy set theory introduced by L. A. Zadeh has been intensively developed and founded a computational foundation for modeling human reasoning processes. The contribution of this theory both in the theoretical and the applied aspects is well recognized. However, the traditional fuzzy set theory cannot handle linguistic terms directly. In our approach, we have constructed algebraic structures to model linguistic domains, and developed a method of linguistic reasoning, which directly manipulates linguistic terms. In particular, our approach can be applied to fuzzy control problems.In many applications of expert systems or fuzzy control, there exist numerous fuzzy reasoning methods. Intuitively, the effectiveness of each method depends on how well this method satisfies the following criterion: the similarity degree between the conclusion (the output) of the method and the consequence of an if-then sentence (in the given fuzzy model) should be the "same" as that between the input of the method and the antecedent of this if-then sentence. To formalize this idea, we introduce a "measure function" to measure the similarity between linguistic terms in a domain of any linguistic variable and to build approximate reasoning methods. The resulting comparison between our method and some other methods shows that our method is simpler and more effective.

The paper introduces fuzzy linguistic logic programming, which is a combination of fuzzy logic programming, introduced by P. Vojtáš, and hedge algebras in order to facilitate the representation and reasoning on human knowledge expressed in natural languages. In fuzzy linguistic logic programming, truth values are linguistic ones, e.g., VeryTrue, VeryProbablyTrue, and LittleFalse, taken from a hedge algebra of a linguistic truth variable, and linguistic hedges (modifiers) can be used as unary connectives in formulae. This is motivated by the fact that humans reason mostly in terms of linguistic terms rather than in terms of numbers, and linguistic hedges are often used in natural languages to express different levels of emphasis. The paper presents: (i) the language of fuzzy linguistic logic programming; (ii) a declarative semantics in terms of Herbrand interpretations and models; (iii) a procedural semantics which directly manipulates linguistic terms to compute a lower bound to the truth value of a query, and proves its soundness; (iv ) a fixpoint semantics of logic programs, and based on it, proves the completeness of the procedural semantics; (v ) several applications of fuzzy linguistic logic programming; and (vi ) an idea of implementing a system to execute fuzzy linguistic logic programs.

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There are various types of multi-attribute decision-making (MADM) problems in our daily lives and decision-making problems under uncertain environments with vague and imprecise information involved. Therefore, linguistic multi-attribute decision-making problems are an important type studied extensively. Besides, it is easier for decision-makers to use linguistic terms to evaluate/choose among alternatives in real life. Based on the theoretical foundation of the Hedge algebra and linguistic many-valued logic, this study aims to address multi-attribute decision-making problems by linguistic valued qualitative aggregation and reasoning method. In this paper, we construct a finite monotonous Hedge algebra for modeling the linguistic information related to MADM problems and use linguistic many-valued logic for deducing the outcome of decision making. Our method computes directly on linguistic terms without numerical approximation. This method takes advantage of linguistic information processing and shows the benefit of Hedge algebra.