With the rapid growth of urbanization,smart city development has become a strategic priority worldwide,requiring complex and uncertain decision-making processes.In this context,advanced decision-support tools are esse...With the rapid growth of urbanization,smart city development has become a strategic priority worldwide,requiring complex and uncertain decision-making processes.In this context,advanced decision-support tools are essential to evaluate and prioritize competing initiatives effectively.To support effective prioritization of smart city initiatives under uncertainty,this study introduces a robust decision-making framework based on the t-arbicular fuzzy(t-AF)set—a recent extension of the t-spherical fuzzy set that incorporates an additional parameter,the radius r,to enhance the representation of uncertainty.Dombi-based operational laws are formulated within this context,leading to the development of four power aggregation operators that integrate a support degree to reflect inter-attribute relationships.The structural and theoretical foundations of the operators are rigorously demonstrated.Further,the proposed operators are embedded into an extended weighted aggregated sum product assessment(WASPAS)method to create a comprehensive multi-criteria decision-making model.The practical utility of the proposed approach is demonstrated through a case study involving the evaluation of seven smart city initiatives against eight critical criteria.Comparative analysis against establishedmodels reveals that the proposed approach offers superior ranking consistency,enhanced discrimination power among alternatives,and improved handling of uncertainty—ultimately supporting more reliable and interpretable decision-making outcomes.展开更多
Although fuzzy set concepts have evolved,neutrosophic sets are attractingmore attention due to the greater power of the structure of neutrosophic sets.The ability to account for components that are true,false or neith...Although fuzzy set concepts have evolved,neutrosophic sets are attractingmore attention due to the greater power of the structure of neutrosophic sets.The ability to account for components that are true,false or neither true nor false is useful in the resolution of real-life problems.However,simultaneous variations render neutrosophic sets unsuitable in specific circumstances.To enable the management of these sorts of issues,we combine the principle of multi-valued neutrosophic uncertain linguistic sets and complex fuzzy sets to develop the principle of multivalued complex neutrosophic uncertain linguistic sets.Multi-valued complex neutrosophic uncertain linguistic sets can contain grades of truth,abstinence,and falsity,and uncertain linguistic terms,which are expressed as complex numbers whose real and imaginary parts are limited to the unit interval.Some important Dombi laws are elaborated along with Bonferroni mean operators,which offer a flexible general structure with modifiable factors.Bonferroni means aggregation operators perform a significant role in conveying the magnitude level of options and characteristics.To determine relationships among any number of attributes,we develop multi-valued complex neutrosophic uncertain linguistic Dombi-normalized weighted Bonferroni mean operators and discuss their important properties with some special cases.By using these laws,we can deploy themulti-attribute decisionmaking(MADM)technique using the novel principle of multi-valued complex neutrosophic uncertain linguistic sets.To determine the power and flexibility of the elaborated approach,we resolve some numerical examples based on the proposed operator.Finally,the work is validated with the help of comparative analysis,a discussion of its advantages,and geometric expressions of the elaborated theories.展开更多
作为模糊集扩展之一的T球形模糊集,由于引入了参数q,使其能够在更大范围内处理不确定信息。相比以往的语言术语集,双层语言术语集在表达决策者意见时,具有优越性。文章在考虑决策者犹豫心理的情况下,提出概率双层语言T球形模糊集的新概...作为模糊集扩展之一的T球形模糊集,由于引入了参数q,使其能够在更大范围内处理不确定信息。相比以往的语言术语集,双层语言术语集在表达决策者意见时,具有优越性。文章在考虑决策者犹豫心理的情况下,提出概率双层语言T球形模糊集的新概念,定义其基本运算、Hamming距离以及排序规则。基于Dombi运算规则,构建加权平均算子,并对其性质进行研究。结合信任度和Shapley值确定决策者的综合权重,利用IDOCRIW方法得到属性的客观权重。进而,提出基于概率双层语言T球形模糊集的多属性决策方法。最后将所提决策框架应用于一个实际案例,并通过对比分析,验证所提方法的有效性。As one of the extensions of fuzzy sets, T-spherical fuzzy sets can deal with uncertain information in a wider range due to the introduction of parameter q. Compared with the previous language term sets, the double hierarchy linguistic term set has advantages in expressing the opinions of decision-makers. Therefore, considering the hesitation of decision makers, the paper proposes a new concept of probabilistic double hierarchy linguistic T-spherical fuzzy sets and defines its basic operation, Hamming distance and ranking rules. Based on the Dombi operation rules, the weighted average operator is proposed, and its properties are investigated. The comprehensive weight of the decision maker is determined by combining the trust degree and the Shapley value, and the objective weight of the attribute is obtained by using the IDOCRIW method. Furthermore, a multi-attribute decision-making method based on probabilistic double hierarchy linguistic T-spherical fuzzy sets is investigated. Finally, the proposed decision-making framework is applied to a practical case, and the effectiveness of the proposed method is verified by comparative analysis.展开更多
Purpose-The main goal of this paper is to present a synthetic multiple criteria group decision-making(MCGDM)methodology for assessing the enterprise digital maturity with linear Diophantine fuzzy(LDF)setting.Design/me...Purpose-The main goal of this paper is to present a synthetic multiple criteria group decision-making(MCGDM)methodology for assessing the enterprise digital maturity with linear Diophantine fuzzy(LDF)setting.Design/methodology/approach-This paper utilizes the presented LDF generalized Dombi operator to aggregate assessment information of experts.The developed combined weight model through merging the rank sum(RS)model and symmetry point of criterion(SPC)method is used to ascertain the comprehensive importance of criterion.The evaluation based on distance from average solution(EDAS)approach based upon regret theory(RT)is presented to achieve the sorting of candidate enterprises.Findings-Firstly,the proposed method has strong stability.Secondly,the proposed method takes into consideration the psychological behavior of experts during the decision-making process which further enhances the rationality of the decision results.Finally,the proposed method integrates expert and criterion weight determination models which provides a practical evaluation framework for assessing the digital maturity of enterprises.The research outcomes confirm that the proposed approach fails to resolve the decision problems with unknown weight information flexibly,but also reflect the psychological behavior of expert in decision process.The presented weight approach also provides a rational algorithm to ascertain the weight more accurate.Originality/value-A composite LDF group decision-making approach is presented by aggregating the proposed generalized Dombi operator,combined weight model and the EDAS model,which make the outcome more reasonable.Sensitivity analysis and comparison study are conducted to reflect the superiority of the proposed approach.展开更多
文摘With the rapid growth of urbanization,smart city development has become a strategic priority worldwide,requiring complex and uncertain decision-making processes.In this context,advanced decision-support tools are essential to evaluate and prioritize competing initiatives effectively.To support effective prioritization of smart city initiatives under uncertainty,this study introduces a robust decision-making framework based on the t-arbicular fuzzy(t-AF)set—a recent extension of the t-spherical fuzzy set that incorporates an additional parameter,the radius r,to enhance the representation of uncertainty.Dombi-based operational laws are formulated within this context,leading to the development of four power aggregation operators that integrate a support degree to reflect inter-attribute relationships.The structural and theoretical foundations of the operators are rigorously demonstrated.Further,the proposed operators are embedded into an extended weighted aggregated sum product assessment(WASPAS)method to create a comprehensive multi-criteria decision-making model.The practical utility of the proposed approach is demonstrated through a case study involving the evaluation of seven smart city initiatives against eight critical criteria.Comparative analysis against establishedmodels reveals that the proposed approach offers superior ranking consistency,enhanced discrimination power among alternatives,and improved handling of uncertainty—ultimately supporting more reliable and interpretable decision-making outcomes.
文摘Although fuzzy set concepts have evolved,neutrosophic sets are attractingmore attention due to the greater power of the structure of neutrosophic sets.The ability to account for components that are true,false or neither true nor false is useful in the resolution of real-life problems.However,simultaneous variations render neutrosophic sets unsuitable in specific circumstances.To enable the management of these sorts of issues,we combine the principle of multi-valued neutrosophic uncertain linguistic sets and complex fuzzy sets to develop the principle of multivalued complex neutrosophic uncertain linguistic sets.Multi-valued complex neutrosophic uncertain linguistic sets can contain grades of truth,abstinence,and falsity,and uncertain linguistic terms,which are expressed as complex numbers whose real and imaginary parts are limited to the unit interval.Some important Dombi laws are elaborated along with Bonferroni mean operators,which offer a flexible general structure with modifiable factors.Bonferroni means aggregation operators perform a significant role in conveying the magnitude level of options and characteristics.To determine relationships among any number of attributes,we develop multi-valued complex neutrosophic uncertain linguistic Dombi-normalized weighted Bonferroni mean operators and discuss their important properties with some special cases.By using these laws,we can deploy themulti-attribute decisionmaking(MADM)technique using the novel principle of multi-valued complex neutrosophic uncertain linguistic sets.To determine the power and flexibility of the elaborated approach,we resolve some numerical examples based on the proposed operator.Finally,the work is validated with the help of comparative analysis,a discussion of its advantages,and geometric expressions of the elaborated theories.
文摘作为模糊集扩展之一的T球形模糊集,由于引入了参数q,使其能够在更大范围内处理不确定信息。相比以往的语言术语集,双层语言术语集在表达决策者意见时,具有优越性。文章在考虑决策者犹豫心理的情况下,提出概率双层语言T球形模糊集的新概念,定义其基本运算、Hamming距离以及排序规则。基于Dombi运算规则,构建加权平均算子,并对其性质进行研究。结合信任度和Shapley值确定决策者的综合权重,利用IDOCRIW方法得到属性的客观权重。进而,提出基于概率双层语言T球形模糊集的多属性决策方法。最后将所提决策框架应用于一个实际案例,并通过对比分析,验证所提方法的有效性。As one of the extensions of fuzzy sets, T-spherical fuzzy sets can deal with uncertain information in a wider range due to the introduction of parameter q. Compared with the previous language term sets, the double hierarchy linguistic term set has advantages in expressing the opinions of decision-makers. Therefore, considering the hesitation of decision makers, the paper proposes a new concept of probabilistic double hierarchy linguistic T-spherical fuzzy sets and defines its basic operation, Hamming distance and ranking rules. Based on the Dombi operation rules, the weighted average operator is proposed, and its properties are investigated. The comprehensive weight of the decision maker is determined by combining the trust degree and the Shapley value, and the objective weight of the attribute is obtained by using the IDOCRIW method. Furthermore, a multi-attribute decision-making method based on probabilistic double hierarchy linguistic T-spherical fuzzy sets is investigated. Finally, the proposed decision-making framework is applied to a practical case, and the effectiveness of the proposed method is verified by comparative analysis.
基金funded by National Social Science Foundation of China under Grant 22CGL015。
文摘Purpose-The main goal of this paper is to present a synthetic multiple criteria group decision-making(MCGDM)methodology for assessing the enterprise digital maturity with linear Diophantine fuzzy(LDF)setting.Design/methodology/approach-This paper utilizes the presented LDF generalized Dombi operator to aggregate assessment information of experts.The developed combined weight model through merging the rank sum(RS)model and symmetry point of criterion(SPC)method is used to ascertain the comprehensive importance of criterion.The evaluation based on distance from average solution(EDAS)approach based upon regret theory(RT)is presented to achieve the sorting of candidate enterprises.Findings-Firstly,the proposed method has strong stability.Secondly,the proposed method takes into consideration the psychological behavior of experts during the decision-making process which further enhances the rationality of the decision results.Finally,the proposed method integrates expert and criterion weight determination models which provides a practical evaluation framework for assessing the digital maturity of enterprises.The research outcomes confirm that the proposed approach fails to resolve the decision problems with unknown weight information flexibly,but also reflect the psychological behavior of expert in decision process.The presented weight approach also provides a rational algorithm to ascertain the weight more accurate.Originality/value-A composite LDF group decision-making approach is presented by aggregating the proposed generalized Dombi operator,combined weight model and the EDAS model,which make the outcome more reasonable.Sensitivity analysis and comparison study are conducted to reflect the superiority of the proposed approach.
