Approach to obtaining weights of uncertain ordered weighted geometric averaging operator

The ordered weighted geometric averaging（OWGA） operator is extended to accommodate uncertain conditions where all input arguments take the forms of interval numbers. First, a possibility degree formula for the comparison between interval numbers is introduced. It is proved that the introduced formula is equivalent to the existing formulae, and also some desired properties of the possibility degree is presented. Secondly, the uncertain OWGA operator is investigated in which the associated weighting parameters cannot be specified, but value ranges can be obtained and the associated aggregated values of an uncertain OWGA operator are known. A linear objective-programming model is established; by solving this model, the associated weights vector of an uncertain OWGA operator can be determined, and also the estimated aggregated values of the alternatives can be obtained. Then the alternatives can be ranked by the comparison of the estimated aggregated values using the possibility degree formula. Finally, a numerical example is given to show the feasibility and effectiveness of the developed method.

Group Decision-Making Model of Renal Cancer Surgery Options Using Entropy Fuzzy Element Aczel-Alsina Weighted Aggregation Operators under the Environment of Fuzzy Multi-Sets

Since existing selection methods of surgical treatment schemes of renal cancer patients mainly depend on physicians’clinical experience and judgments,the surgical treatment options of renal cancer patients lack their scientifical and reasonable information expression and group decision-making model for renal cancer patients.Fuzzy multi-sets(FMSs)have a number of properties,which make them suitable for expressing the uncertain information of medical diagnoses and treatments in group decision-making(GDM)problems.To choose the most appropriate surgical treatment scheme for a patient with localized renal cell carcinoma(RCC)(T1 stage kidney tumor),this article needs to develop an effective GDM model based on the fuzzy multivalued evaluation information of the renal cancer patients.First,we propose a conversionmethod of transforming FMSs into entropy fuzzy sets(EFSs)based on the mean and Shannon entropy of a fuzzy sequence in FMS to reasonably simplify the information expression and operations of FMSs and define the score function of an entropy fuzzy element(EFE)for ranking EFEs.Second,we present the Aczel-Alsina t-norm and t-conorm operations of EFEs and the EFE Aczel-Alsina weighted arithmetic averaging(EFEAAWAA)and EFE Aczel-Alsina weighted geometric averaging(EFEAAWGA)operators.Third,we develop a multicriteria GDM model of renal cancer surgery options in the setting of FMSs.Finally,the proposed GDM model is applied to two clinical cases of renal cancer patients to choose the best surgical treatment scheme for a renal cancer patient in the setting of FMSs.The selected results of two clinical cases verify the efficiency and rationality of the proposed GDM model in the setting of FMSs.

Orthopair indeterminate information expression,aggregations and multiattribute decision making method with indeterminate ranges

A neutrosophic number(NN)(d=μ+vI)can flexibly represent the indeterminate information corresponding to values/ranges of the indeterminacy I.Regarding the hybrid concept of intuitionistic fuzzy set(IFS)and NN,this study presents an orthopair indeterminate set(OIS),an orthopair indeterminate element weighted arithmetic averaging(OIEWAA)operator and an orthopair indeterminate element weighted geometric averaging(OIEWGA)operator to simplify and generalise the existing IFS and interval-valued IFS expressions and aggregation forms.Thus,a multiattribute decision making(DM)approach with indeterminate ranges of decision makers is developed based on the OIEWAA and OIEWGA operators and the score and accuracy functions of orthopair indeterminate elements in OIS setting.Finally,the proposed DM approach is applied to a multi-attribute DM example of manufacturing schemes(alternatives)in OIS setting to demonstrate the applicability and flexibility of the proposed DM approach in OIS setting.