In this paper, a new kind of L-fuzzy set is introduced which is called Flou-valued fuzzy set to consider the defi-ciency of interval-valued fuzzy set and three-parameters interval-valued fuzzy set in expressing fuzzy information. It puts forward Flou nested set. Using Flou nested set and combined with cut sets as well as decomposition theorems of Flou-valued fuzzy set, the representation theorems are obtained and its effectiveness is vertified by a practical account case.

The method described the fuzzy regions using Flou sets.Then it proposed an overlay analysis model of fuzzy raster map layers based on Flou sets.The model could complete general fuzzy overlay and weighted fuzzy overlay.The fuzzy overlay model could avoid the difficulty in dealing with the relations between fuzzy spatial objects through using fuzzy sets to represent the fuzzy region,and the fuzzy overlay result accord with the cognitive principle of people.The practical case shows that this model can well solve fuzzy overlay analysis between the map layers described as Flou sets.

A method which describes the fuzzy regions using flou sets is proposed aiming at measuring the topological relations between fuzzy regions. It not only accords with the cognitive principle of people, but also is suitable for high-order fuzzy case. Based on the representation model of fuzzy regions, the metric description of topological relations between fuzzy regions is proposed. It is valuable in the fields such as spatial information query and spatial reasoning.

This paper introduced a new kind of L-fuzzy set which is called Flou-valued fuzzy set to consider the deficiencyof interval-valued fuzzy set and three-parameters interval-valued fuzzy set in expressing fuzzy information.The authors put forward eight kinds of cut set on the Flou-valued fuzzy sets.Based on them,the decomposition theorems were obtained and its effectiveness was vertified by a practical account case.