| Combinatorial mathematics plays a great role not only in the field of basic application and software technology,but also in traffic planning,enterprise management and etc.Matroid,as a branch of combinatorial mathematics,is closely related to graph theory and plays an important role in combinatorial optimization.In 1988,R.Goetschel and W.Voxman combined matroids with fuzzy set theory to propose G-V fuzzy matroids.Subsequently,with the efforts of many scholars,G-V fuzzy matroids have been developed rapidly.In this paper,the G-V intuitionistic fuzzy matroid(IFM)is proposed on the basis of G-V fuzzy matroid(FM)and its related properties are researched.The main work is as follows:1.Based on the similarity function h and accuracy function H of intuitionistic fuzzy number(IFN),the operation,intersection and union of intuitionistic fuzzy set(IFS)are defined.The support set,cut set,"h-cardinality" and other comcepts of intuitionistic fuzzy sets are given.2.Based on the intuitionistic fuzzy set and G-V fuzzy matroids,a generalized G-V intuitionistic fuzzy matroids is proposed.The foundamental sequence,the rank function of IFM and closed G-V intuitionistic fuzzy matroids are presented and some related basic properties are researched.3.According to IFM and the concept of the basis of G-V fuzzy matroid,the intuitionistic fuzzy basis(IFB)of IFM is defined and the related properties are studied.The condition of judging IFB of closed G-V intuitionistic fuzzy matroids is given.The tree structure of IFM is studied and its basic properties are discussed.4.According to IFM and the concept of the basis of G-V fuzzy matroid,the intuitionistic fuzzy circuit(IFC)of IFM is defined and the related properties are studied.And the conditions of judging IFC of closed G-V intuitionistic fuzzy matroid are also studied. |
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