The Three-dimensional Fuzzy Sets And Its Application Based On The Interval-valued Level Cut Sets

The three-dimensional fuzzy sets is a special kind of L-fuzzy sets,which is the generalization of interval-valued fuzzy sets and intuitionistic fuzzy sets.The basic theoretical work of the three-dimensional fuzzy sets,such as cut sets,decomposition theorems and representation theorems,has been studied in the literature.This paper continues to study the basic theory of the three-dimensional fuzzy sets and fuzzy decision-making methods on three-dimensional fuzzy sets,and makes the following results:1?We study the interval-valued level cut sets on the three-dimensional fuzzy sets.By defining the interval-valued level cut sets into four-valued fuzzy sets,the definition of 4 different cut sets of the interval-valued level cut sets on the three-dimensional fuzzy sets is given,and the properties of those 4 kinds of interval-valued level cut sets are studied.It is found that the interval-valued level cut sets given in this paper has the properties similar to that of Zadeh fuzzy sets.2?We establish the new decomposition theorems and the new representation theorems on the three-dimensional fuzzy sets.8 kinds of new decomposition theorems and 8 kinds of new representation theorems of the three-dimensional fuzzy sets are established by using the concepts of interval-valued level cut sets and interval-valued level nested sets.These conclusions extend the decomposition theorems and the representation theorems of fuzzy sets.3?We study the relationship between the interval-valued fuzzy points and the three-dimensional fuzzy sets.And we establish the theory of convex three-dimensional fuzzy subsets on the interval-valued fuzzy points.By discussing the properties of 16 kinds of convex three-dimensional fuzzy subsets,it is found that the meaningful convex three-dimensional fuzzy subsets are(?,?)-,(?,? ?q)-,(??q,?)-convex three-dimensional fuzzy subsets.And the 3 kinds of convex three-dimensional fuzzy subsets are generalized to convex three-dimensional fuzzy subsets with thresholds.4?we study fuzzy decision-making problems of the three-dimensional fuzzy sets based on the interval-valued level cut sets.First,the definition of the comparative probability of 2 three-dimensional ordered vectors on[0,1]is given by using the interval-valued level cut sets Then the new fuzzy decision-making method for the three-dimensional fuzzy sets is established by using this possibility.