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
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
For the conceptual design phase of Unmanned Aerial Vehicles(UAVs),a process for conceptual design and configuration selection of Solar/Hydrogen powered UAVs(S/H-UAVs)is proposed.The design requirements of S/H-UAVs wer...For the conceptual design phase of Unmanned Aerial Vehicles(UAVs),a process for conceptual design and configuration selection of Solar/Hydrogen powered UAVs(S/H-UAVs)is proposed.The design requirements of S/H-UAVs were analyzed firstly.The proposed process used Fuzzy Quality Function Deployment(FQFD)to establish logical and quantitative standards.Moreover,in order to appropriately describe the hesitancy of experts while making decision,it used Q-Rung Dual Hesitant Fuzzy Sets(QRDHFS)to score the correlationships.In addition,a decision-making framework is proposed to perform a logical selection of typical layouts based on defuzzi-fication method and Technique for Order Preference by Similarity to the Ideal Solution(TOPSIS).The present process has been applied for S/H-UAVs.The resulting set of design requirements con-sists of three categories:Mission Requirements(MRs),Engineering Characteristics(ECs)and Tech-nical Indicators(TIs).Four typical layouts of S/H-UAVs were sorted and determined.The performance of four typical layouts were evaluated and the Strut-Braced Wing(SBW)with external hydrogen storage was selected as the best layout for S/H-UAVs.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.
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.
文摘For the conceptual design phase of Unmanned Aerial Vehicles(UAVs),a process for conceptual design and configuration selection of Solar/Hydrogen powered UAVs(S/H-UAVs)is proposed.The design requirements of S/H-UAVs were analyzed firstly.The proposed process used Fuzzy Quality Function Deployment(FQFD)to establish logical and quantitative standards.Moreover,in order to appropriately describe the hesitancy of experts while making decision,it used Q-Rung Dual Hesitant Fuzzy Sets(QRDHFS)to score the correlationships.In addition,a decision-making framework is proposed to perform a logical selection of typical layouts based on defuzzi-fication method and Technique for Order Preference by Similarity to the Ideal Solution(TOPSIS).The present process has been applied for S/H-UAVs.The resulting set of design requirements con-sists of three categories:Mission Requirements(MRs),Engineering Characteristics(ECs)and Tech-nical Indicators(TIs).Four typical layouts of S/H-UAVs were sorted and determined.The performance of four typical layouts were evaluated and the Strut-Braced Wing(SBW)with external hydrogen storage was selected as the best layout for S/H-UAVs.
