The Research Of Decision Modeling Theory And Approach Based On Fuzzy Multi-granulations

In modern decision-making theory and practice,as a common psychological phenomena and personality trait,indecisiveness often makes decisionmaking individuals or organizations unable to make a timely decision,and further affects the smooth conduction of the whole decision-making process.The research on indecisiveness is still on the initial stage,and its definition regards descriptive manners as principle that lacks the definite intension.In order to overcome theoretical defects of indecisiveness,as an effective tool for describing indecisiveness quantitatively,through processing hesitation and fuzziness in uncertain information simultaneously,hesitant fuzzy sets provide brandnew ideas for studying decision-making problems under the background of indecisiveness.In recent years,the rapid development of information science fields provides decision-makers with many theoretical models for researching decision-making problems based on hesitant fuzzy information in depth.Among them,as a new data analysis model,the multigranulation rough set theory not only inherits advantages of feature selections and rule acquisitions in the rough set theory well,enhances the rough set theory's computational efficiency when handling multi-source data and high-dimensional data,but also offers optimistic and pessimistic information fusion strategies under the uncertain environment that can be better utilized in realistic decision-making procedures.In order to conduct hesitant fuzzy information systems analysis by means of the multigranulation rough set theory,this study introduces hesitation and fuzziness in information to multigranulation rough sets that widens its application range.Specifically,with reference to existing rough set theories and decision-making methods,this study selects four typical hesitant fuzzy forms that embrace hesitant fuzzy sets,dual hesitant fuzzy sets,interval-valued hesitant fuzzy sets,hesitant fuzzy linguistic term sets,respectively,and explores multigranulation rough sets-based theoretical models and decision-making approaches under the corresponding hesitant fuzzy environment successively.The main works and innovation points can be summed up as follows:(1)We propose the concept of hesitant fuzzy multigranulation rough sets,and enrich theoretical results of hesitant fuzzy multigranulation rough sets from viewpoints of properties and uncertainty measures.In light of the advantages of multigranulation rough sets over two universes model when representing,fusing and analyzing information under the uncertain environment,we generalize the decision-making information system to two universes,and propose hesitant fuzzy multigranulation rough sets-based decision-making strategies.This part of the study provides a reasonable uncertain decision-making method for hesitant fuzzy information systems analysis.Meanwhile,it enlarges the theory and application fields of the classical multigranulation rough set theory.(2)We propose the concept of dual hesitant fuzzy multigranulation rough sets,and explore properties and uncertainty measures approaches of dual hesitant fuzzy multigranulation rough sets.According to decision-making theories under uncertainty in the classical operational research,we establish dual hesitant fuzzy multigranulation rough sets-based decision-making strategies.This part of the study provides a theoretical basis for decision-makers in decisionmaking under uncertainty when facing choices of multiple possible natural states.Meanwhile,it considers different situations when expert opinions' are divided in group decision-making.(3)We propose the concept of interval-valued hesitant fuzzy multigranulation rough sets,and further discuss properties and uncertainty measures methods of interval-valued hesitant fuzzy multigranulation rough sets.In terms of the idea of the prospect theory,we set up interval-valued hesitant fuzzy multigranulation rough sets-based decision-making strategies.This part of the study considers the uncertainty under complicated decision-making environment and the risk attitudes owned by decision-makers impact on the decision-making results,it provides a theoretical basis for decision-makers to proceed group decision-making analysis based on interval-valued hesitant fuzzy data under the irrational state.(4)We propose the concept of hesitant fuzzy linguistic multigranulation rough sets,and continue to enrich theoretical results of hesitant fuzzy linguistic multigranulation rough sets from viewpoints of properties and uncertainty measures.With reference to the idea of three-way decisions,we further put forward hesitant fuzzy linguistic multigranulation decision-theoretic rough sets model,and set up hesitant fuzzy linguistic multigranulation decision-theoretic rough sets-based decision-making strategies.This part of the study considers erroneous decision-making opinions impact on the whole decision-making procedure under the complicated decision-making conditions,keeping the expected decision-making risk to a minimum,it provides a theoretical basis for multigranulation rough sets-based uncertain decision-making,and it also extends the application scope of decision-theoretic rough sets to the hesitant fuzzy linguistic environment.This paper takes multigranulation rough sets for the research object,combines hesitation and fuzziness in uncertain expressions with the multigranulation rough set theory,gives multigranulation rough set theoretical models under the corresponding hesitant fuzzy environments,and focuses on decisionmaking approaches based on various proposed hesitant fuzzy multigranulation rough set models.The work of this paper expands theoretical and practical scopes of multigranulation rough sets,and provides new perspectives for multigranulation rough sets-based decision-making analysis.