Much information over the Internet is expressed by natural languages. The management of linguistic information involves an operation of comparison and aggregation. Based on the Ordered Weighted Averaging (OWA) operator and modifying indexes of linguistic terms (their indexes are fuzzy numbers on [0,T] ⊆ R+), new linguistic aggregating methods are presented and their properties are discussed. Also, based on a multi-agent system and new linguistic aggregating methods, gathering linguistic information over the Internet is discussed. Moreover, by fixing the threshold α, “soft filtering information” is proposed and better Web pages (or documents) that the user needs are obtained. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 435–453, 2007.

The consistency of a rule base is an essential issue for rule-based intelligent information processing. Due to the uncertainty inevitably included in the rule base, it is necessary to verify the consistency of the rule base while investigating, designing, and applying a rule-based intelligent system. In the framework of the lattice-valued first-order logic system LF(X), which attempts to handle fuzziness and incomparability, this article focuses on how to verify and increase the consistency degree of the rule base in the intelligent information processing system. First, the representations of eight kinds of rule bases in LF(X) as the generalized clause set forms based on these rule bases' nonredundant generalized Skolem standard forms are presented. Then an α-automated reasoning algorithm in LF(X), also used as an automated simplification algorithm, is proposed. Furthermore, the α-consistency and the α-simplification theories of the rule base in LF(X) are formulated, and especially the coherence between these two theories is proved. Therefore, the verification of the α-consistency of the rule base, often an infinity problem that is difficult to solve, can be transformed into a finite and achievable α-simplification problem. Finally, an α-simplification stepwise search algorithm for verifying the consistency of the rule base as well as a kind of filtering algorithm for increasing the consistency level of the rule base are proposed. © 2006 Wiley Periodicals, Inc. Int J Int Syst 21: 399–424, 2006.

This paper focuses on a fuzzy reasoning method based on a generalized If-Then rule. Firstly, the antecedent and the consequent of an If-Then rule are considered and expressed as a component of a kind of binary L-type fuzzy relation on the product of the universes of discourse and the range of definition for a certain fuzzy attribute. Then a generalized extension principle based on this L-type fuzzy relation (FR-GEP) is constructed. Moreover, the paper gives a detailed description of this generalized If-Then rule using 20 well-known common implication operators in the framework of the composition of L-type fuzzy relations. Consequently, an L-type binary fuzzy reasoning method based on this generalized If-Then rule is established according to FR-GEP. © 2002 Wiley Periodicals, Inc.

According to the operation of decomposition (also known as representation theorem) (Negoita CV, Ralescu, DA. Kybernetes 1975;4:169–174) in fuzzy set theory, the whole fuzziness of an object can be characterized by a sequence of local crisp properties of that object. Hence, any fuzzy reasoning could also be implemented by using a similar idea, i.e., a sequence of precise reasoning. More precisely, we could translate a fuzzy relation “If A then B” of the Generalized Modus Ponens Rule (the most common and widely used interpretation of a fuzzy rule, A, B, are fuzzy sets in a universe of discourse X, and of discourse Y, respectively) into a corresponding precise relation between a subset of P(X) and a subset of P(Y), and then extend this corresponding precise relation to two kinds of transformations between all L-type fuzzy subsets of X and those of Y by using Zadeh's extension principle, where L denotes a complete lattice. In this way, we provide an alternative approach to the existing compositional rule of inference, which performs fuzzy reasoning based on the extension principle. The approach does not depend on the choice of fuzzy implication operator nor on the choice of a t-norm. The detailed reasoning methods, applied in particular to the Generalized Modus Ponens and the Generalized Modus Tollens, are established and their properties are further investigated in this paper. © 2001 John Wiley & Sons, Inc.