Pythagorean fuzzy prioritized aggregation operators with priority degrees for multi-criteria decision-making

Purpose-The authors develop some prioritized operators named Pythagorean fuzzy prioritized averaging operator with priority degrees and Pythagorean fuzzy prioritized geometric operator with priority degrees.The properties of the existing method are routinely compared to those of other current approaches,emphasizing the superiority of the presented work over currently used methods.Furthermore,the impact of priority degrees on the aggregate outcome is thoroughly examined.Further,based on these operators,a decision-making approach is presented under the Pythagorean fuzzy set environment.An illustrative example related to the selection of the best alternative is considered to demonstrate the efficiency of the proposed approach.Design/methodology/approach-In real-world situations,Pythagorean fuzzy numbers are exceptionally useful for representing ambiguous data.The authors look at multi-criteria decision-making issues in which the parameters have a prioritization relationship.The idea of a priority degree is introduced.The aggregation operators are formed by awarding non-negative real numbers known as priority degrees among strict priority levels.Consequently,the authors develop some prioritized operators named Pythagorean fuzzy prioritized averaging operator with priority degrees and Pythagorean fuzzy prioritized geometric operator with priority degrees.Findings-The authors develop some prioritized operators named Pythagorean fuzzy prioritized averaging operator with priority degrees and Pythagorean fuzzy prioritized geometric operator with priority degrees.The properties of the existing method are routinely compared to those of other current approaches,emphasizing the superiority of the presented work over currently used methods.Furthermore,the impact of priority degrees on the aggregate outcome is thoroughly examined.Further,based on these operators,a decision-making approach is presented under the Pythagorean fuzzy set environment.An illustrative example related to the selection of the best alternative is considered to demonstrate the efficiency of the proposed approach.Originality/value-The aggregation operators are formed by awarding non-negative real numbers known as priority degrees among strict priority levels.Consequently,the authors develop some prioritized operators named Pythagorean fuzzy prioritized averaging operator with priority degrees and Pythagorean fuzzy prioritized geometric operator with priority degrees.The properties of the existing method are routinely compared to those of other current approaches,emphasizing the superiority of the presented work over currently used methods.Furthermore,the impact of priority degrees on the aggregate outcome is thoroughly examined.

A Novel Green Supplier Selection Method Based on the Interval Type-2 Fuzzy Prioritized Choquet Bonferroni Means

In view of the environment competencies,selecting the optimal green supplier is one of the crucial issues for enterprises,and multi-criteria decision-making(MCDM)methodologies can more easily solve this green supplier selection(GSS)problem.In addition,prioritized aggregation(PA)operator can focus on the prioritization relationship over the criteria,Choquet integral(CI)operator can fully take account of the importance of criteria and the interactions among them,and Bonferroni mean(BM)operator can capture the interrelationships of criteria.However,most existing researches cannot simultaneously consider the interactions,interrelationships and prioritizations over the criteria,which are involved in the GSS process.Moreover,the interval type-2 fuzzy set(IT2FS)is a more effective tool to represent the fuzziness.Therefore,based on the advantages of PA,CI,BM and IT2FS,in this paper,the interval type-2 fuzzy prioritized Choquet normalized weighted BM operators with fuzzy measure and generalized prioritized measure are proposed,and some properties are discussed.Then,a novel MCDM approach for GSS based upon the presented operators is developed,and detailed decision steps are given.Finally,the applicability and practicability of the proposed methodology are demonstrated by its application in the shared-bike GSS and by comparisons with other methods.The advantages of the proposed method are that it can consider interactions,interrelationships and prioritizations over the criteria simultaneously.