Intuitionistic hesitant fuzzy set(IHFS)is amixture of two separated notions called intuitionistic fuzzy set(IFS)and hesitant fuzzy set(HFS),as an important technique to cope with uncertain and awkward information in r...Intuitionistic hesitant fuzzy set(IHFS)is amixture of two separated notions called intuitionistic fuzzy set(IFS)and hesitant fuzzy set(HFS),as an important technique to cope with uncertain and awkward information in realistic decision issues.IHFS contains the grades of truth and falsity in the formof the subset of the unit interval.The notion of IHFS was defined by many scholars with different conditions,which contain several weaknesses.Here,keeping in view the problems of already defined IHFSs,we will define IHFS in another way so that it becomes compatible with other existing notions.To examine the interrelationship between any numbers of IHFSs,we combined the notions of power averaging(PA)operators and power geometric(PG)operators with IHFSs to present the idea of intuitionistic hesitant fuzzy PA(IHFPA)operators,intuitionistic hesitant fuzzy PG(IHFPG)operators,intuitionistic hesitant fuzzy power weighted average(IHFPWA)operators,intuitionistic hesitant fuzzy power ordered weighted average(IHFPOWA)operators,intuitionistic hesitant fuzzy power ordered weighted geometric(IHFPOWG)operators,intuitionistic hesitant fuzzy power hybrid average(IHFPHA)operators,intuitionistic hesitant fuzzy power hybrid geometric(IHFPHG)operators and examined as well their fundamental properties.Some special cases of the explored work are also discovered.Additionally,the similarity measures based on IHFSs are presented and their advantages are discussed along examples.Furthermore,we initiated a new approach to multiple attribute decision making(MADM)problem applying suggested operators and a mathematical model is solved to develop an approach and to establish its common sense and adequacy.Advantages,comparative analysis,and graphical representation of the presented work are elaborated to show the reliability and effectiveness of the presented works.展开更多
A novel model termed a bipolar complex fuzzy N-soft set(BCFN-SS)is initiated for tackling information that involves positive and negative aspects,the second dimension,and parameterised grading simultaneously.The theor...A novel model termed a bipolar complex fuzzy N-soft set(BCFN-SS)is initiated for tackling information that involves positive and negative aspects,the second dimension,and parameterised grading simultaneously.The theory of BCFN-SS is the generalisation of two various theories,that is,bipolar complex fuzzy(BCF)and N-SS.The invented model of BCFN-SS helps decision-makers to cope with the genuine-life dilemmas containing BCF information along with parameterised grading at the same time.Further,various algebraic operations,including the usual type of union,intersection,complements,and a few others types,are invented.Certain primary operational laws for BCFNSS are also invented.Moreover,a technique for order preference by similarity to the ideal solution(TOPSIS)approach is devised in the setting of BCFN-SS for managing strategic decision-making(DM)dilemmas containing BCFN-SS information.Keeping in mind the usefulness and benefits of the TOPSIS approach,two various types of TOPSIS approaches in the environment of BCFN-SS are devised and then a numerical example for exposing the usefulness of the devised TOPSIS approach is interpreted.To disclose the prominence and benefits of the devised work,the devised approaches with numerous prevailing work are compared.展开更多
We first propose a series of similarity measures for intuitionistic fuzzy values （IFVs） based on the intuitionistic fuzzy operators （Atanassov 1995）. The parameters in the proposed similarity measures can control ...We first propose a series of similarity measures for intuitionistic fuzzy values （IFVs） based on the intuitionistic fuzzy operators （Atanassov 1995）. The parameters in the proposed similarity measures can control the degree of membership and the degree of non-membership of an IFV, which can reflect the decision maker’s risk preference. Moreover, we can obtain some known similarity measures when some fixed values are assigned to the parameters. Furthermore, we apply the similarity measures to aggregate IFVs and develop some aggregation operators, such as the intuitionistic fuzzy dependent averaging operator and the intuitionistic fuzzy dependent geometric operator, whose prominent characteristic is that the associated weights only depend on the aggregated intuitionistic fuzzy arguments and can relieve the influence of unfair arguments on the aggregated results. Based on these aggregation operators, we develop some group decision making methods, and finally extend our results to interval-valued intuitionistic fuzzy environment.展开更多
由于现有的经典本体映射方法以及相似度计算方法无法处理模糊信息,因此它们都无法计算模糊概念之间的相似度.为此,提出了一种新的基于向量空间模型的模糊概念相似度计算方法 Sim FC-VSM(similarity of fuzzy concept based on vector sp...由于现有的经典本体映射方法以及相似度计算方法无法处理模糊信息,因此它们都无法计算模糊概念之间的相似度.为此,提出了一种新的基于向量空间模型的模糊概念相似度计算方法 Sim FC-VSM(similarity of fuzzy concept based on vector space model).Sim FC-VSM方法首先利用模糊本体中的模糊关系构建向量空间模型;然后将模糊概念表示成此向量空间模型中的向量;最后通过向量运算的方法来计算模糊概念之间的相似度.因此,所提出的方法 Sim FC-VSM可以有效地利用向量空间模型来计算模糊概念之间的相似度.展开更多
基金supported by“Algebra and Applications Research Unit,Division of Computational Science,Faculty of Science,Prince of Songkla University”.
文摘Intuitionistic hesitant fuzzy set(IHFS)is amixture of two separated notions called intuitionistic fuzzy set(IFS)and hesitant fuzzy set(HFS),as an important technique to cope with uncertain and awkward information in realistic decision issues.IHFS contains the grades of truth and falsity in the formof the subset of the unit interval.The notion of IHFS was defined by many scholars with different conditions,which contain several weaknesses.Here,keeping in view the problems of already defined IHFSs,we will define IHFS in another way so that it becomes compatible with other existing notions.To examine the interrelationship between any numbers of IHFSs,we combined the notions of power averaging(PA)operators and power geometric(PG)operators with IHFSs to present the idea of intuitionistic hesitant fuzzy PA(IHFPA)operators,intuitionistic hesitant fuzzy PG(IHFPG)operators,intuitionistic hesitant fuzzy power weighted average(IHFPWA)operators,intuitionistic hesitant fuzzy power ordered weighted average(IHFPOWA)operators,intuitionistic hesitant fuzzy power ordered weighted geometric(IHFPOWG)operators,intuitionistic hesitant fuzzy power hybrid average(IHFPHA)operators,intuitionistic hesitant fuzzy power hybrid geometric(IHFPHG)operators and examined as well their fundamental properties.Some special cases of the explored work are also discovered.Additionally,the similarity measures based on IHFSs are presented and their advantages are discussed along examples.Furthermore,we initiated a new approach to multiple attribute decision making(MADM)problem applying suggested operators and a mathematical model is solved to develop an approach and to establish its common sense and adequacy.Advantages,comparative analysis,and graphical representation of the presented work are elaborated to show the reliability and effectiveness of the presented works.
文摘A novel model termed a bipolar complex fuzzy N-soft set(BCFN-SS)is initiated for tackling information that involves positive and negative aspects,the second dimension,and parameterised grading simultaneously.The theory of BCFN-SS is the generalisation of two various theories,that is,bipolar complex fuzzy(BCF)and N-SS.The invented model of BCFN-SS helps decision-makers to cope with the genuine-life dilemmas containing BCF information along with parameterised grading at the same time.Further,various algebraic operations,including the usual type of union,intersection,complements,and a few others types,are invented.Certain primary operational laws for BCFNSS are also invented.Moreover,a technique for order preference by similarity to the ideal solution(TOPSIS)approach is devised in the setting of BCFN-SS for managing strategic decision-making(DM)dilemmas containing BCFN-SS information.Keeping in mind the usefulness and benefits of the TOPSIS approach,two various types of TOPSIS approaches in the environment of BCFN-SS are devised and then a numerical example for exposing the usefulness of the devised TOPSIS approach is interpreted.To disclose the prominence and benefits of the devised work,the devised approaches with numerous prevailing work are compared.
基金supported in part by the National Science Fund for Distinguished Young Scholars of China (No.70625005)the National Natural Science Foundation of China (No.71071161)the Program Sponsored for Scientific Innovation Research of College Graduate in Jiangsu Province (No.CX10B_059Z)
文摘We first propose a series of similarity measures for intuitionistic fuzzy values （IFVs） based on the intuitionistic fuzzy operators （Atanassov 1995）. The parameters in the proposed similarity measures can control the degree of membership and the degree of non-membership of an IFV, which can reflect the decision maker’s risk preference. Moreover, we can obtain some known similarity measures when some fixed values are assigned to the parameters. Furthermore, we apply the similarity measures to aggregate IFVs and develop some aggregation operators, such as the intuitionistic fuzzy dependent averaging operator and the intuitionistic fuzzy dependent geometric operator, whose prominent characteristic is that the associated weights only depend on the aggregated intuitionistic fuzzy arguments and can relieve the influence of unfair arguments on the aggregated results. Based on these aggregation operators, we develop some group decision making methods, and finally extend our results to interval-valued intuitionistic fuzzy environment.
文摘由于现有的经典本体映射方法以及相似度计算方法无法处理模糊信息,因此它们都无法计算模糊概念之间的相似度.为此,提出了一种新的基于向量空间模型的模糊概念相似度计算方法 Sim FC-VSM(similarity of fuzzy concept based on vector space model).Sim FC-VSM方法首先利用模糊本体中的模糊关系构建向量空间模型;然后将模糊概念表示成此向量空间模型中的向量;最后通过向量运算的方法来计算模糊概念之间的相似度.因此,所提出的方法 Sim FC-VSM可以有效地利用向量空间模型来计算模糊概念之间的相似度.
