Multi-Attribute Decision-Making Method With Fuzzy Covering-Based Rough Set

Decision-making is one of the most important part of human productive activity,and nowadays,it is usually necessary to consider several aspects of the problem in a balanced way when making decisions,due to the increasing complexity and diversity of decisions faced by production practices.Some decision-making issues can be condensed into multi-attribute decision-making(MADM)issue and the solution of MADM often need to analyze in multiple attributes and multiple perspectives,and then selecting the optimal solution by information integration.With the development of science and technology,in practical problem,the pending data trends to more and more complex and it is also common that data is not available due to missing in data collection,storage and transmission.Therefore,fuzzy covering-based rough set,which is one of the most important generalizations of rough set to handle fuzzy incomplete and indistinguishable data in fuzzy environment,can be introduced to deal with complicated decision-making problem.In this thesis,we introduce neighborhood operators into fuzzy environment by overlap function,and also define some neighborhood-related fuzzy covering-based rough set models based on above operators to deal with fuzzy MADM.Moreover,we generalize fuzzy β-covering into Fermatean fuzzy and interval-valued Fermatean fuzzy environment,and establish corresponding decision-making methods.The specific research content is as follows:(1)We define some fuzzy neighborhood operators and their properties are also investigated.Firstly,by means of overlap function and its residual implicator,we define four basic fuzzy neighborhood operators and induce six derived coverings from the original fuzzy covering.Furthermore,by combining basic fuzzy neighborhood operators with derived coverings,we define other twenty-four neighborhood operators and group them via equivalence relation.And then,the partial order relation among neighborhood operators are also discussed.(2)We propose some neighborhood-related fuzzy covering-based rough set models to handle a medical nanomaterial selection issue.Firstly,we construct two series of fuzzy rough set models by -norm-basesd fuzzy neighborhood operators and overlap function-based fuzzy neighborhood operators,respectively.And their related properties are also studied.And then,we introduce a novel TOPSIS methodology for MADM without weights.Finally,a medical nanomaterial selection issue is solved by new method,and the validity and rationality of the new method are verified via comparing with nine classical methods.(3)We generalize fuzzy β-covering rough set model into Fermatean fuzzy and intervalvalued Fermatean fuzzy environment.Firstly,we define Fermatean fuzzy β-neighborhood and interval-valued Fermatean fuzzy β-neighborhood,respectively.And then,we also contruct Fermatean fuzzy approximation space and interval-valued Fermatean fuzzy approximation space,and define the corresponding rough set models,respectively.Furthermore,in the light of the notion of complementary neighborhood,Fermatean fuzzy complementary β-neighborhood and interval-valued Fermatean fuzzy complementary β-neighborhood are defined.In addition,we establish two novel TOPSIS methods for Fermatean fuzzy and interval-valued Fermatean fuzzy environment,respectively.The decision-making processes of two methods are shown with the help of two examples.Finally,we verify the effectiveness of models by comparing with existing methodologies and give the selection principle of precision parameter β.