In order to measure the uncertain information of a type- 2 intuitionistic fuzzy set （T21FS）, an entropy measure of T21FS is presented by using the constructive principles. The proposed entropy measure is also proved...In order to measure the uncertain information of a type- 2 intuitionistic fuzzy set （T21FS）, an entropy measure of T21FS is presented by using the constructive principles. The proposed entropy measure is also proved to satisfy all of the constructive principles. Further, a novel concept of the type-2 triangular in- tuitionistic trapezoidal fuzzy set （T2TITrFS） is developed, and a geometric interpretation of the T2TITrFS is given to comprehend it completely or correctly in a more intuitive way. To deal with a more general uncertain complex system, the constructive principles of an entropy measure of T2TITrFS are therefore proposed on the basis of the axiomatic definition of the type-2 intuitionisic fuzzy entropy measure. This paper elicits a formula of type-2 triangular intuitionistic trapezoidal fuzzy entropy and verifies that it does sa- tisfy the constructive principles. Two examples are given to show the efficiency of the proposed entropy of T2TITrFS in describing the uncertainty of the type-2 intuitionistic fuzzy information and illustrate its application in type-2 triangular intuitionistic trapezodial fuzzy decision making problems.展开更多
The intuitionistic triangular fuzzy set is a generalization of the intuitionistic fuzzy set. In practical applications, we find that the results derived by using the traditional intuitionistic triangular fuzzy aggrega...The intuitionistic triangular fuzzy set is a generalization of the intuitionistic fuzzy set. In practical applications, we find that the results derived by using the traditional intuitionistic triangular fuzzy aggregation operators based on intuitionistic triangular fuzzy sets are sometimes inconsistent with intuition. To overcome this issue, based on the [1/9, 9] scale, we define the concepts of intuitionistic multiplicative triangular fuzzy set and intuitionistic multiplicative triangular fuzzy number, and then we discuss their operational laws and some desirable properties. Based on the operational laws, we develop a series of aggregation operators for intuitionistic multiplicative triangular fuzzy information, and then apply them to propose an approach to multi-attribute decision making under intuitionistic fuzzy environments. Finally, we use a practical example involving the evaluation of investment alternatives of an investment company to demonstrate our aggregation operators and decision making approach.展开更多
An analysis is performed for the three-dimensional stagnation point flow of magnetized tangent hyperbolic fluid over a rotating disk of variable thickness.The viscosity and thermal conductivity of the fluid are presum...An analysis is performed for the three-dimensional stagnation point flow of magnetized tangent hyperbolic fluid over a rotating disk of variable thickness.The viscosity and thermal conductivity of the fluid are presumed to depend on the temperature.Moreover,the impact of various physical parameters i.e.,variable dynamical viscosity,variable thermal conductivity,velocity ratio,thermal stratification,Weissenberg number,Biot number and Eckert number are considered.Here we use the intuitionistic fuzzy set(IFS),which is an extension of fuzzy set,to study the flow and heat transfer analysis.IFS is a better tool for deal with uncertainty and complex modelling.The transformed ODEs are changed into intuitionistic fuzzy differential equations(IFDEs)and then solved by applying(α,β)-cut method,and the notion of triangular intuitionistic fuzzy number(TIFN).The outcomes attained from the solutions of IFDEs are depicted by figures,and results are reliable as calculated with the numerical technique“bvp4c”.The study reports that a rise of 40.68% in local Nusselt number(LNN)is seen when the velocity ratio parameter is raised from 0.1 to 0.4,whereas a rise of 5.26% is noted when the variable thermal conductivity parameter is increased from -0.5 to 0.5.展开更多
The distributed and customized 3D printing can be realized by 3D printing services in a cloud manufacturing environment.As a growing number of 3D printers are becoming accessible on various 3D printing service platfor...The distributed and customized 3D printing can be realized by 3D printing services in a cloud manufacturing environment.As a growing number of 3D printers are becoming accessible on various 3D printing service platforms,there raises the concern over the validation of virtual product designs and their manufacturing procedures for novices as well as users with 3D printing experience before physical products are produced through the cloud platform.This paper presents a 3D model to help users validate their designs and requirements not only in the traditional digital 3D model properties like shape and size,but also in physical material properties and manufacturing properties when producing physical products like surface roughness,print accuracy and part cost.These properties are closely related to the process of 3D printing and materials.In order to establish the 3D model,the paper analyzes the model of the 3D printing process selection in the cloud platform.Triangular intuitionistic fuzzy numbers are applied to generate a set of 3D printers with the same process and material.Based on the 3D printing process selection model,users can establish the 3D model and validate their designs and requirements on physical material properties and manufacturing properties before printing physical products.展开更多
基金supported by the National Natural Science Foundation of China(7137115670971017)the Research Grants Council of the Hong Kong Special Administrative Region,China(City U112111)
文摘In order to measure the uncertain information of a type- 2 intuitionistic fuzzy set （T21FS）, an entropy measure of T21FS is presented by using the constructive principles. The proposed entropy measure is also proved to satisfy all of the constructive principles. Further, a novel concept of the type-2 triangular in- tuitionistic trapezoidal fuzzy set （T2TITrFS） is developed, and a geometric interpretation of the T2TITrFS is given to comprehend it completely or correctly in a more intuitive way. To deal with a more general uncertain complex system, the constructive principles of an entropy measure of T2TITrFS are therefore proposed on the basis of the axiomatic definition of the type-2 intuitionisic fuzzy entropy measure. This paper elicits a formula of type-2 triangular intuitionistic trapezoidal fuzzy entropy and verifies that it does sa- tisfy the constructive principles. Two examples are given to show the efficiency of the proposed entropy of T2TITrFS in describing the uncertainty of the type-2 intuitionistic fuzzy information and illustrate its application in type-2 triangular intuitionistic trapezodial fuzzy decision making problems.
基金supported in part by the National Natural Science Foundation of China(Nos.71071161 and 61273209)
文摘The intuitionistic triangular fuzzy set is a generalization of the intuitionistic fuzzy set. In practical applications, we find that the results derived by using the traditional intuitionistic triangular fuzzy aggregation operators based on intuitionistic triangular fuzzy sets are sometimes inconsistent with intuition. To overcome this issue, based on the [1/9, 9] scale, we define the concepts of intuitionistic multiplicative triangular fuzzy set and intuitionistic multiplicative triangular fuzzy number, and then we discuss their operational laws and some desirable properties. Based on the operational laws, we develop a series of aggregation operators for intuitionistic multiplicative triangular fuzzy information, and then apply them to propose an approach to multi-attribute decision making under intuitionistic fuzzy environments. Finally, we use a practical example involving the evaluation of investment alternatives of an investment company to demonstrate our aggregation operators and decision making approach.
文摘An analysis is performed for the three-dimensional stagnation point flow of magnetized tangent hyperbolic fluid over a rotating disk of variable thickness.The viscosity and thermal conductivity of the fluid are presumed to depend on the temperature.Moreover,the impact of various physical parameters i.e.,variable dynamical viscosity,variable thermal conductivity,velocity ratio,thermal stratification,Weissenberg number,Biot number and Eckert number are considered.Here we use the intuitionistic fuzzy set(IFS),which is an extension of fuzzy set,to study the flow and heat transfer analysis.IFS is a better tool for deal with uncertainty and complex modelling.The transformed ODEs are changed into intuitionistic fuzzy differential equations(IFDEs)and then solved by applying(α,β)-cut method,and the notion of triangular intuitionistic fuzzy number(TIFN).The outcomes attained from the solutions of IFDEs are depicted by figures,and results are reliable as calculated with the numerical technique“bvp4c”.The study reports that a rise of 40.68% in local Nusselt number(LNN)is seen when the velocity ratio parameter is raised from 0.1 to 0.4,whereas a rise of 5.26% is noted when the variable thermal conductivity parameter is increased from -0.5 to 0.5.
基金the National High-Tech Research and Development Plan of China under Grant No.2015AA042101 and Fund of State Key Laboratory of Intelligent Manufacturing System Technology in China.
文摘The distributed and customized 3D printing can be realized by 3D printing services in a cloud manufacturing environment.As a growing number of 3D printers are becoming accessible on various 3D printing service platforms,there raises the concern over the validation of virtual product designs and their manufacturing procedures for novices as well as users with 3D printing experience before physical products are produced through the cloud platform.This paper presents a 3D model to help users validate their designs and requirements not only in the traditional digital 3D model properties like shape and size,but also in physical material properties and manufacturing properties when producing physical products like surface roughness,print accuracy and part cost.These properties are closely related to the process of 3D printing and materials.In order to establish the 3D model,the paper analyzes the model of the 3D printing process selection in the cloud platform.Triangular intuitionistic fuzzy numbers are applied to generate a set of 3D printers with the same process and material.Based on the 3D printing process selection model,users can establish the 3D model and validate their designs and requirements on physical material properties and manufacturing properties before printing physical products.
