As a generalization of fuzzy set,hesitant probabilistic fuzzy set and pythagorean triangular fuzzy set have their own unique advantages in describing decision information.As modern socioeconomic decision-making proble...As a generalization of fuzzy set,hesitant probabilistic fuzzy set and pythagorean triangular fuzzy set have their own unique advantages in describing decision information.As modern socioeconomic decision-making problems are becoming more and more complex,it also becomes more and more difficult to appropriately depict decision makers’cognitive information in decision-making process.In order to describe the decision information more comprehensively,we define a pythagorean probabilistic hesitant triangular fuzzy set(PPHTFS)by combining the pythagorean triangular fuzzy set and the probabilistic hesitant fuzzy set.Firstly,the basic operation and scoring function of the pythagorean probabilistic hesitant triangular fuzzy element(PPHTFE)are proposed,and the comparison rule of two PPHTFEs is given.Then,some pythagorean probabilistic hesitant triangular fuzzy aggregation operators are developed,and their properties are also studied.Finally,a multi-attribute decision-making(MADM)model is constructed based on the proposed operators under the pythagorean probabilistic hesitant triangular fuzzy information,and an illustration example is given to demonstrate the practicability and validity of the proposed decision-making method.展开更多
In real life,incomplete information,inaccurate data,and the preferences of decision-makers during qualitative judgment would impact the process of decision-making.As a technical instrument that can successfully handle...In real life,incomplete information,inaccurate data,and the preferences of decision-makers during qualitative judgment would impact the process of decision-making.As a technical instrument that can successfully handle uncertain information,Fermatean fuzzy sets have recently been used to solve the multi-attribute decision-making(MADM)problems.This paper proposes a Fermatean hesitant fuzzy information aggregation method to address the problem of fusion where the membership,non-membership,and priority are considered simultaneously.Combining the Fermatean hesitant fuzzy sets with Heronian Mean operators,this paper proposes the Fermatean hesitant fuzzy Heronian mean(FHFHM)operator and the Fermatean hesitant fuzzyweighted Heronian mean(FHFWHM)operator.Then,considering the priority relationship between attributes is often easier to obtain than the weight of attributes,this paper defines a new Fermatean hesitant fuzzy prioritized Heronian mean operator(FHFPHM),and discusses its elegant properties such as idempotency,boundedness and monotonicity in detail.Later,for problems with unknown weights and the Fermatean hesitant fuzzy information,aMADM approach based on prioritized attributes is proposed,which can effectively depict the correlation between attributes and avoid the influence of subjective factors on the results.Finally,a numerical example of multi-sensor electronic surveillance is applied to verify the feasibility and validity of the method proposed in this paper.展开更多
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...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.展开更多
The Maclaurin symmetric mean(MSM)operator exhibits a desirable characteristic by effectively capturing the correlations among multiple input parameters,and it serves as an extension of certain existing aggregation ope...The Maclaurin symmetric mean(MSM)operator exhibits a desirable characteristic by effectively capturing the correlations among multiple input parameters,and it serves as an extension of certain existing aggregation operators through adjustments to the parameter k.The hesitant q-rung orthopair set(Hq-ROFSs)can serve as an extension of the existing orthopair fuzzy sets,which provides decision makers more freedom in describing their true opinions.The objective of this paper is to present an MSM operator to aggregate hesitant q-rung orthopair numbers and solve the multiple attribute decision making(MADM)problems in which the attribute values take the form of hesitant q-rung orthopair fuzzy sets(H-qROFSs).Firstly,the definition of H-qROFSs and some operational laws of H-qROFSs are proposed.Then we develop a family of hesitant q-rung orthopair fuzzy maclaurin symmetric mean aggregation operators,such as the hesitant q-rung orthopair fuzzy maclaurin symmetric mean(Hq-ROFMSM)operator,the hesitant q-rung orthopair fuzzy weighted maclaurin symmetric mean(Hq-ROFWMSM)operator,the hesitant q-rung orthopair fuzzy dual maclaurin symmetric mean(Hq-ROFDMSM)operator,the hesitant q-rung orthopair fuzzy weighted dual maclaurin symmetric mean(Hq-ROFWDMSM)operator.And the properties and special cases of these proposed operators are studied.Furthermore,an approach based on the Hq-ROFWMSM operator is proposed for multiple attribute decision making problems under hesitant q-rung orthopair fuzzy environment.Finally,a numerical example and comparative analysis is given to illustrate the application of the proposed approach.展开更多
基金supported by the Key Research and Development Project of Hunan Province(2019SK2331)the Natural Science Foundation of Hunan Province(2019JJ40099,2019JJ40100,2020JJ4339)+2 种基金the Key Scientific Research Project of Hunan Education Department(18A317,19A202)the Scientific Research Fund of Hunan Provincial Education Department(20B272)the Innovation Foundation for Postgraduate of Hunan Institute of Science and Technology(YCX2020A34).
文摘As a generalization of fuzzy set,hesitant probabilistic fuzzy set and pythagorean triangular fuzzy set have their own unique advantages in describing decision information.As modern socioeconomic decision-making problems are becoming more and more complex,it also becomes more and more difficult to appropriately depict decision makers’cognitive information in decision-making process.In order to describe the decision information more comprehensively,we define a pythagorean probabilistic hesitant triangular fuzzy set(PPHTFS)by combining the pythagorean triangular fuzzy set and the probabilistic hesitant fuzzy set.Firstly,the basic operation and scoring function of the pythagorean probabilistic hesitant triangular fuzzy element(PPHTFE)are proposed,and the comparison rule of two PPHTFEs is given.Then,some pythagorean probabilistic hesitant triangular fuzzy aggregation operators are developed,and their properties are also studied.Finally,a multi-attribute decision-making(MADM)model is constructed based on the proposed operators under the pythagorean probabilistic hesitant triangular fuzzy information,and an illustration example is given to demonstrate the practicability and validity of the proposed decision-making method.
文摘In real life,incomplete information,inaccurate data,and the preferences of decision-makers during qualitative judgment would impact the process of decision-making.As a technical instrument that can successfully handle uncertain information,Fermatean fuzzy sets have recently been used to solve the multi-attribute decision-making(MADM)problems.This paper proposes a Fermatean hesitant fuzzy information aggregation method to address the problem of fusion where the membership,non-membership,and priority are considered simultaneously.Combining the Fermatean hesitant fuzzy sets with Heronian Mean operators,this paper proposes the Fermatean hesitant fuzzy Heronian mean(FHFHM)operator and the Fermatean hesitant fuzzyweighted Heronian mean(FHFWHM)operator.Then,considering the priority relationship between attributes is often easier to obtain than the weight of attributes,this paper defines a new Fermatean hesitant fuzzy prioritized Heronian mean operator(FHFPHM),and discusses its elegant properties such as idempotency,boundedness and monotonicity in detail.Later,for problems with unknown weights and the Fermatean hesitant fuzzy information,aMADM approach based on prioritized attributes is proposed,which can effectively depict the correlation between attributes and avoid the influence of subjective factors on the results.Finally,a numerical example of multi-sensor electronic surveillance is applied to verify the feasibility and validity of the method proposed in this paper.
基金supported by the National Natural Science Foundation of China(71771140)Project of Cultural Masters and“the Four Kinds of a Batch”Talents,the Special Funds of Taishan Scholars Project of Shandong Province(ts201511045)the Major Bidding Projects of National Social Science Fund of China(19ZDA080)。
文摘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.
基金Supported by the Key Project of Humanities and Social Research Science Institute of Chongqing Municipal Education Commission(22SKGH432,22SKGH428)2023 Chongqing Education Commission Humanities and Social Sciences Research General Project(23SKGH353)Science and Technology Research Project of Chongqing Education Commission(KJQN202101524)。
文摘The Maclaurin symmetric mean(MSM)operator exhibits a desirable characteristic by effectively capturing the correlations among multiple input parameters,and it serves as an extension of certain existing aggregation operators through adjustments to the parameter k.The hesitant q-rung orthopair set(Hq-ROFSs)can serve as an extension of the existing orthopair fuzzy sets,which provides decision makers more freedom in describing their true opinions.The objective of this paper is to present an MSM operator to aggregate hesitant q-rung orthopair numbers and solve the multiple attribute decision making(MADM)problems in which the attribute values take the form of hesitant q-rung orthopair fuzzy sets(H-qROFSs).Firstly,the definition of H-qROFSs and some operational laws of H-qROFSs are proposed.Then we develop a family of hesitant q-rung orthopair fuzzy maclaurin symmetric mean aggregation operators,such as the hesitant q-rung orthopair fuzzy maclaurin symmetric mean(Hq-ROFMSM)operator,the hesitant q-rung orthopair fuzzy weighted maclaurin symmetric mean(Hq-ROFWMSM)operator,the hesitant q-rung orthopair fuzzy dual maclaurin symmetric mean(Hq-ROFDMSM)operator,the hesitant q-rung orthopair fuzzy weighted dual maclaurin symmetric mean(Hq-ROFWDMSM)operator.And the properties and special cases of these proposed operators are studied.Furthermore,an approach based on the Hq-ROFWMSM operator is proposed for multiple attribute decision making problems under hesitant q-rung orthopair fuzzy environment.Finally,a numerical example and comparative analysis is given to illustrate the application of the proposed approach.
