The Application Of Fuzzy Integrals In Linguistic Quantifiers And Fuzzy Queries

Fuzzy integral theory is an important branch of fuzzy mathematics. A wealth of theoretical results has been obtained since the birth of fuzzy integral theory. Moreover, fuzzy integrals can be widely used in many areas, such as cluster analysis, information fusion etc. Recently, on the basis of fuzzy measures and Sugeno integrals, Professor Mingsheng Ying introduced a new framework for dealing with linguistic quantifiers. Specifically, he represented linguistic quantifiers by fuzzy measures and used Sugeno's integrals for the evaluation. It's well known that quantified propositions are frequently used by humans in their reasoning processes. In addition, quantified propositions can be widely applied in the process of fuzzy, imprecise information, such as data querying, data summarization etc. Based on Ying's model for linguistic quantification, fuzzy integrals can be used to solve the issues of fuzzy queries with linguistic quantifiers and data summarization.Based on the integral semantic theory of linguistic quantifiers, we discuss the application of fuzzy integrals in fuzzy queries with quantifers and linguistic suammrization. The achievements of this article mainly included:(1) Using the approach based on Sugeno integrals to evaluating the truth value of quantified statements with weights, we improve the fuzzy query method based on Zadeh's fuzzy cardinality theory. The query results obtained by this improved method are more reasonable. Compared with the existing query method, this query approach is more flexible. Thus, it's a useful complement to existing query methods. In addition, using Delpi 7.0 and SQL Server we design a program for an actual query problem to verify the effectiveness of the query method.(2) With regard to fuzzy queries in fuzzy databases, we introduce the existing semantic distance between fuzzy data and evaluate the semantic distances of each record to the query condition with linguistic quantifiers. Accordingly, we present a new approach to handling the fuzzy query problems with linguistic quantifiers in fuzzy databases. Afterwards we give the specific realization of an example of actual query. Furthermore, the query results obtained is nice and consistent with people's subjective instincts.(3) We apply interval-valued Choquet integrals to linguistic summaries. The degree of truth of a given linguistic summary is represented by an interval number. We use the interval-valued Choquet integrals with respect to interval-valued measures to evaluate the interval-valued truths of data summaries, and acquire the essence of large amouts of data in the concise form of linguistic summaries. Finally, with examples we show the effetiveness of the linguistic summary method based on interval-valued Choquet integrals.