Multi-granularity Intuitionistic Fuzzy Rough Sets Over Two Universes Based On Two Probabilistic Strategies

Rough sets introduce extended elements(such as probability,multi-granularity,two universes,intuitionistic fuzziness)to make models,they are beneficial to uncertainty analysis.At present,multi-granularity intuitionistic fuzzy rough sets over two universes comprehensively consider “intuitionistic fuzzy,multi-granularity,two universes”,they have validity and generalization.However,for these models,their fuzzy forms are complicated,and their semantics are weak,and their application in group decision making is less.To solve these problems,two probabilistic strategies are adopted to build multi-granularity intuitionistic fuzzy rough sets over two universes.Specifically,four improved models are constructed by using four logical integration methods of probability,and two new models are constructed by means of probability mean three-way.Furthermore,the three-way group decision making is carried out to enhance the applicability of the models.The research contents mainly include the following two aspects.(1)Based on intuitionistic fuzzy relation,multi-granularity probabilistic rough sets are studied in two universes.Firstly,the intuitionistic fuzzy relations and two-universe background are utilized to model multi-granularity probabilistic rough sets,and four improved models regarding “positive optimism”,“positive pessimism”,“inverse optimism” and “inverse pessimism” are established to acquire their integrated algorithms.Furthermore,mathematical properties of models lower and upper approximations are studied.Based on these,examples are used to calculate and analyze the models to verify their validity and properties correctness.Secondly,the expected risk and group decision algorithms are updated and obtained,and three-way group decision making schemes are provided.Finally,through comparative analysis with existing models and single-granularity models,it is revealed that the four models carry the systematicness and improvability,the obtained properties have the expansibility,and the three-way group decision-making schemes are provided.They effectively guide the application of uncertainty analysis and knowledge discovery.(2)The probability measure is used to carry out mean statistics,and the multi-granularity intuitionistic fuzzy rough sets models are established based on the three-way decisions.Firstly,in the two-universe,multi-granularity,intuitionistic-fuzzy environment,conditional probability measures and their arithmetic mean are determined,the three-measure interception and three-region modeling are implemented by using three-way decisions,two models of “positive model” and “inverse model” are obtained.Furthermore,the optimization algorithms of regions are designed,and the related region properties are studied.Therefore,examples are used to verify the models validity and properties correctness.Secondly,the expected risk and related group decision algorithms are obtained based on arithmetic average,and three-way group decision making is carried out.Finally,compared with the single granularity models,the existing related models and the four improved models,the results show that the two models carry the effective integration and improvability,the obtained properties have the expansion applicability,and the proposed three-way group decision-making schemes avoid the faroutness,so they together promote the processing ability and application space of uncertainty.In this thesis,the relevant research improves the existing multi-granularity intuitionistic fuzzy rough sets over two universes.To be specific,two-universe multi-granularity probability rough sets based on intuitionistic fuzzy relations and multi-granularity intuitionistic fuzzy rough sets over two-universe based on three ways of probability mean are proposed.They respectively adopt two different strategies for systematic and comprehensive modeling,i.e.,four logic integration strategies of probability and mean statistics of probability integration are adopted,and then the method of three-branch division is adopted.The relevant results enrich the theoretical research of multi-granularity intuitionistic fuzzy rough sets over two universes,and provide three-way group decision making schemes,so they have uncertainty application prospects.