Two Optimal Aggregation Approaches of Fuzzy Opinions in Group Decision Analysis

The aggregation of fuzzy opinions is an important component of group decision analysis with fuzzy information. This paper proposes two new approaches for the assessment of the weights to be associated with fuzzy opinions. These approaches involve,respectively,the minimization of the sum of squared differences between the individual weighted fuzzy opinion and the weighted mean value of all fuzzy opinions,which is called the weighted minimum variance method (WMVM),and the minimax difference of any two adjacent individual weighted fuzzy opinions,which is called the mean value minimax differences method (MVMDM). The two approaches are developed and numerical examples are presented to illustrate their simplicity and effectiveness in aggregating fuzzy opinions.

Spherical Linear Diophantine Fuzzy Sets with Modeling Uncertainties in MCDM

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.

A New Hesitant Fuzzy Multiple Attribute Decision Making Method with Unknown Weight Information

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.