A Three-way Decisions Model Based On Linguistic Information

In modern decision theory,three-way decisions theory which based on decision-theoretic rough sets(DTRS)can be more powerful than two-way decisions theory by introducing a third option named a non-commitment option into consideration.As a new extension of classical fuzzy sets,spherical fuzzy sets(SFS)can carry more information due to the fact that it considers both the positive membership,neutral membership and negative membership of an element.Three-way decisions model will become invalid when it comes to fuzzy concept and non-numeric information.Thus,it is necessary to study three-way decisions model under linguistic spherical fuzzy environment.Furthermore,we propose the three-way decisions model based on linguistic spherical fuzzy multi-granulation decision-theoretic rough sets(LSFMGDTRS)on two universes both absorbing the merits of multi-granulation rough sets(MGRS)of handling multi-source information and borrowing the idea of rough sets over two universes.To be specifically,the main contribution and innovation of our thesis can be as follows.Firstly,we propose linguistic spherical fuzzy sets(LSFS)based on linguistic terms theory which extends spherical sets from quantitative environment to qualitative environment.First of all,we introduce the basic concept and the definition of LSFS.Furthermore,the basic operation rules as well as some interesting properties of both SFS and spherical fuzzy element are studied.Then we provide a general method of comparing two spherical fuzzy elements based on the score function and accuracy function we proposed.Secondly,we propose linguistic spherical fuzzy multi-granulation rough sets(LSFMGRS)over two universes under linguistic spherical fuzzy environment.We define the linguistic spherical fuzzy relation over two universes at first and propose the LSFMGRS based on it.Then we propose three types of LSFMGRS namely the optimistic,pessimistic and variable precision type of LSFMGRS based on the linguistic spherical fuzzy relation over two universes we defined,respectively.Additionally,combining the idea of three-way decisions,we propose the LSFMGDTRS over two universes and deduce the corresponding decision rules.Firstly,three types of linguistic spherical fuzzy multi-granulation probabilistic rough sets(LSFMGPRS)are constructed based on the conditional probability we defined.Furthermore,we take the linguistic loss functions into consideration and propose the three-way decisions model based on LSFMGDTRS over two universes.Then,the consistency and effectiveness of our model are tested through a medical diagnose problem.