Multi-Granularity Rough Intuitionistic Fuzzy Cut Sets Theory And Its Application

Intuitionistic fuzzy sets is a expansion of fuzzy sets,which includes two functions: membership and non-membership and intuitionistic fuzzy sets can describe fuzziness and uncertainty message better that in our daily life.With the research development of intuitionistic fuzzy sets,it has been widely used in many fields.The cut set as an important theory in intuitionistic fuzzy sets,playing an significant role in fuzzy algebra,fuzzy reasoning and some other fields.Rough set theory is a mathematical theory which can analysis and deal with uncertainty,inconsistency,incomplete information effective.And multi-granularity rough sets is a concept that proposed from the perspective of granular computing,it makes up the lack of the rough sets that approximate represented by an equivalence classes which determinedby an equivalence relation,multi-granularity rough sets extended two models of optimism and pessimism multi-granularity rough set.Currently it is a hot research about the combination of intuitionistic fuzzy sets and multi-granularity rough sets and applied them to practical application.But existing multi-granularity rough intuitionistic fuzzy sets theory is not perfect enoughand there are also few research on the representation of multi-granularity rough intuitionistic fuzzy sets that set out from the cut sets of intuitionistic fuzzy sets.On the basis of existing theory in this paper,research futher on the combination of intuitionistic fuzzy sets and multi-granularity rough sets and applied to practical application,provides a theoretical basis to enrich and improve the multi-granularity rough intuitionistic fuzzy sets theory.Main research work in this paper including following aspects:(1)For the representation problem of multi-granularity rough intuitionistic fuzzy sets,construct the optimism and pessimism multi-granularity rough intuitionistic fuzzy sets models according to the decomposition theorems and the cut sets theory of intuitionistic fuzzy sets,and define the upper and lower approximation sets on the optimism and pessimism multi-granularity rough intuitionistic fuzzy sets,furthermore,prove some properties of multi-granularity rough intuitionistic fuzzy sets.(2)Proposea new similarity formula of intuitionistic fuzzy sets.Combined with the multi-granularity rough intuitionistic fuzzy sets model,created a solving process of the upper and lower approximation of multi-granularity intuitionistic fuzzy rough sets that based on similarity.(3)Apply these theories to practical application.Design a wheat growth evaluation system and a land planting distribution system,use the solution process in these systems,analyze and discusse the validity of the optimism and pessimism multi-granularity rough intuitionistic fuzzy model through examples.Through the research of combined intuitionistic fuzzy sets with multi-granularity rough sets to construct optimism and pessimism multi-granularity rough intuitionistic fuzzy model,enrich and perfect the multi-granularity intuitionistic fuzzy rough sets theories,provide theoretical basis for future research work and use the model to the actual application.