The existing concepts of picture fuzzy sets(PFS),spherical fuzzy sets(SFSs),T-spherical fuzzy sets(T-SFSs)and neutrosophic sets(NSs)have numerous applications in decision-making problems,but they have various strict l...The existing concepts of picture fuzzy sets(PFS),spherical fuzzy sets(SFSs),T-spherical fuzzy sets(T-SFSs)and neutrosophic sets(NSs)have numerous applications in decision-making problems,but they have various strict limitations for their satisfaction,dissatisfaction,abstain or refusal grades.To relax these strict constraints,we introduce the concept of spherical linearDiophantine fuzzy sets(SLDFSs)with the inclusion of reference or control parameters.A SLDFSwith parameterizations process is very helpful formodeling uncertainties in themulti-criteria decisionmaking(MCDM)process.SLDFSs can classify a physical systemwith the help of reference parameters.We discuss various real-life applications of SLDFSs towards digital image processing,network systems,vote casting,electrical engineering,medication,and selection of optimal choice.We show some drawbacks of operations of picture fuzzy sets and their corresponding aggregation operators.Some new operations on picture fuzzy sets are also introduced.Some fundamental operations on SLDFSs and different types of score functions of spherical linear Diophantine fuzzy numbers(SLDFNs)are proposed.New aggregation operators named spherical linear Diophantine fuzzy weighted geometric aggregation(SLDFWGA)and spherical linear Diophantine fuzzy weighted average aggregation(SLDFWAA)operators are developed for a robust MCDM approach.An application of the proposed methodology with SLDF information is illustrated.The comparison analysis of the final ranking is also given to demonstrate the validity,feasibility,and efficiency of the proposed MCDM approach.展开更多
In this paper, we focus on a new approach based on new generalized hesitant fuzzy hybrid weighted aggregation operators, in which the evaluation information provided by decision makers is expressed in hesitant fuzzy e...In this paper, we focus on a new approach based on new generalized hesitant fuzzy hybrid weighted aggregation operators, in which the evaluation information provided by decision makers is expressed in hesitant fuzzy elements (HFEs) and the information about attribute weights and aggregation-associated vector is unknown. More explicitly, some new generalized hesitant fuzzy hybrid weighted aggregation operators are proposed, such as the new generalized hesitant fuzzy hybrid weighted averaging (NGHFHWA) operator and the new generalized hesitant fuzzy hybrid weighted geometric (NGHFHWG) operator. Some desirable properties and the relationships between them are discussed. Then, a new algorithm for hesitant fuzzy multi-attribute decision making (HF-MADM) problems with unknown weight information is introduced. Further, a practical example is used to illustrate the detailed implementation process of the proposed approach. A sensitivity analysis of the decision results is analyzed with different parameters. Finally, comparative studies are given to verify the advantages of our method.展开更多
The score function and aggregation operator provide the theoretical basis for intuitionistic fuzzy multiple attribute decision making(MADM),where the role of the score function is to compare and rank the intuitionisti...The score function and aggregation operator provide the theoretical basis for intuitionistic fuzzy multiple attribute decision making(MADM),where the role of the score function is to compare and rank the intuitionistic fuzzy numbers(IFNs),and the role of the aggregation operator is to integrate the evaluation information.In view of that,this paper proposes a new score function and aggregation operator,and a new intuitionistic fuzzy MADM method.It first constructs a parametric piecewise score function and discusses the influence of hesitancy degree and the parameterλon it.Moreover,some properties of the constructed score function are discussed,including the monotonicity,maximum,minimum,and range.Then,it introduces a intuitionistic fuzzy modified Einstein aggregation(IFMEWA)operator and proves monotonicity,idempotency and boundedness of IFMEWA operator.Finally,combined with the constructed score function and IFMEWA operator,it proposes a new intuitionistic fuzzy MADM method.展开更多
文摘The existing concepts of picture fuzzy sets(PFS),spherical fuzzy sets(SFSs),T-spherical fuzzy sets(T-SFSs)and neutrosophic sets(NSs)have numerous applications in decision-making problems,but they have various strict limitations for their satisfaction,dissatisfaction,abstain or refusal grades.To relax these strict constraints,we introduce the concept of spherical linearDiophantine fuzzy sets(SLDFSs)with the inclusion of reference or control parameters.A SLDFSwith parameterizations process is very helpful formodeling uncertainties in themulti-criteria decisionmaking(MCDM)process.SLDFSs can classify a physical systemwith the help of reference parameters.We discuss various real-life applications of SLDFSs towards digital image processing,network systems,vote casting,electrical engineering,medication,and selection of optimal choice.We show some drawbacks of operations of picture fuzzy sets and their corresponding aggregation operators.Some new operations on picture fuzzy sets are also introduced.Some fundamental operations on SLDFSs and different types of score functions of spherical linear Diophantine fuzzy numbers(SLDFNs)are proposed.New aggregation operators named spherical linear Diophantine fuzzy weighted geometric aggregation(SLDFWGA)and spherical linear Diophantine fuzzy weighted average aggregation(SLDFWAA)operators are developed for a robust MCDM approach.An application of the proposed methodology with SLDF information is illustrated.The comparison analysis of the final ranking is also given to demonstrate the validity,feasibility,and efficiency of the proposed MCDM approach.
文摘In this paper, we focus on a new approach based on new generalized hesitant fuzzy hybrid weighted aggregation operators, in which the evaluation information provided by decision makers is expressed in hesitant fuzzy elements (HFEs) and the information about attribute weights and aggregation-associated vector is unknown. More explicitly, some new generalized hesitant fuzzy hybrid weighted aggregation operators are proposed, such as the new generalized hesitant fuzzy hybrid weighted averaging (NGHFHWA) operator and the new generalized hesitant fuzzy hybrid weighted geometric (NGHFHWG) operator. Some desirable properties and the relationships between them are discussed. Then, a new algorithm for hesitant fuzzy multi-attribute decision making (HF-MADM) problems with unknown weight information is introduced. Further, a practical example is used to illustrate the detailed implementation process of the proposed approach. A sensitivity analysis of the decision results is analyzed with different parameters. Finally, comparative studies are given to verify the advantages of our method.
基金supported by the National Natural Science Foundation of China[grant number 11401494]the Postdoctoral Science Foundation of China[grant number 2016M592682]+2 种基金the Sichuan Science and Technology Program[grant number 2022YFQ0012]the Young Scholars Development Fund of Southwest Petroleum University[grant number 202199010062]the Scientific Research Starting Project of Southwest Petroleum University[grant number 2021QHZ020].
文摘The score function and aggregation operator provide the theoretical basis for intuitionistic fuzzy multiple attribute decision making(MADM),where the role of the score function is to compare and rank the intuitionistic fuzzy numbers(IFNs),and the role of the aggregation operator is to integrate the evaluation information.In view of that,this paper proposes a new score function and aggregation operator,and a new intuitionistic fuzzy MADM method.It first constructs a parametric piecewise score function and discusses the influence of hesitancy degree and the parameterλon it.Moreover,some properties of the constructed score function are discussed,including the monotonicity,maximum,minimum,and range.Then,it introduces a intuitionistic fuzzy modified Einstein aggregation(IFMEWA)operator and proves monotonicity,idempotency and boundedness of IFMEWA operator.Finally,combined with the constructed score function and IFMEWA operator,it proposes a new intuitionistic fuzzy MADM method.
