In this article, we define the arithmetic operations of generalized trapezoidal picture fuzzy numbers by vertex method which is assembled on a combination of the (α, γ, β)-cut concept and standard interval analysis...In this article, we define the arithmetic operations of generalized trapezoidal picture fuzzy numbers by vertex method which is assembled on a combination of the (α, γ, β)-cut concept and standard interval analysis. Various related properties are explored. Finally, some computations of picture fuzzy functions over generalized picture fuzzy variables are illustrated by using our proposed technique.展开更多
In this paper, we focus on a new approach based on new generalized hesitant fuzzy hybrid weighted aggregation operators, in which the evaluation information provided by decision makers is expressed in hesitant fuzzy e...In this paper, we focus on a new approach based on new generalized hesitant fuzzy hybrid weighted aggregation operators, in which the evaluation information provided by decision makers is expressed in hesitant fuzzy elements (HFEs) and the information about attribute weights and aggregation-associated vector is unknown. More explicitly, some new generalized hesitant fuzzy hybrid weighted aggregation operators are proposed, such as the new generalized hesitant fuzzy hybrid weighted averaging (NGHFHWA) operator and the new generalized hesitant fuzzy hybrid weighted geometric (NGHFHWG) operator. Some desirable properties and the relationships between them are discussed. Then, a new algorithm for hesitant fuzzy multi-attribute decision making (HF-MADM) problems with unknown weight information is introduced. Further, a practical example is used to illustrate the detailed implementation process of the proposed approach. A sensitivity analysis of the decision results is analyzed with different parameters. Finally, comparative studies are given to verify the advantages of our method.展开更多
This study presents a new approach that advances the algorithm of similarity measures between generalized fuzzy numbers. Following a brief introduction to some properties of the proposed method, a comparative analysis...This study presents a new approach that advances the algorithm of similarity measures between generalized fuzzy numbers. Following a brief introduction to some properties of the proposed method, a comparative analysis based on 36 sets of generalized fuzzy numbers was performed, in which the degree of similarity of the fuzzy numbers was calculated with the proposed method and seven methods established by previous studies in the literature. The results of the analytical comparison show that the proposed similarity outperforms the existing methods by overcoming their drawbacks and yielding accurate outcomes in all calculations of similarity measures under consideration. Finally, in a numerical example that involves recommending cars to customers based on a nine-member linguistic term set, the proposed similarity measure proves to be competent in addressing fuzzy number recommendation problems.展开更多
The definition of the generalized fuzzy set is presented for the first time, and a generalized fuzzy operator is proposed to transform a generalized fuzzy set into a normal fuzzy set. The algorithm theory of the opera...The definition of the generalized fuzzy set is presented for the first time, and a generalized fuzzy operator is proposed to transform a generalized fuzzy set into a normal fuzzy set. The algorithm theory of the operator, as the newest method of the edge detection of a 2-D image, is successfully established. Many experiments haw proved that the algorithm is simpler, more rapid and more precise in location than other edge detection methods. And a schedule of the concrete performance has been given additionally about the edge detection of color images.展开更多
The generalized resolution method presented in ref. [1] is a generalization of Robinson’s resolution principle in the first-order logic, which can be applied to a set of nonclausal formulae, i.e. a set of generalized...The generalized resolution method presented in ref. [1] is a generalization of Robinson’s resolution principle in the first-order logic, which can be applied to a set of nonclausal formulae, i.e. a set of generalized clauses. The method can not only avoid the symbolic redundancy generated from the procedure of transforming a formula into a set of clauses, but also keep the natural description of the problem.展开更多
文摘In this article, we define the arithmetic operations of generalized trapezoidal picture fuzzy numbers by vertex method which is assembled on a combination of the (α, γ, β)-cut concept and standard interval analysis. Various related properties are explored. Finally, some computations of picture fuzzy functions over generalized picture fuzzy variables are illustrated by using our proposed technique.
文摘In this paper, we focus on a new approach based on new generalized hesitant fuzzy hybrid weighted aggregation operators, in which the evaluation information provided by decision makers is expressed in hesitant fuzzy elements (HFEs) and the information about attribute weights and aggregation-associated vector is unknown. More explicitly, some new generalized hesitant fuzzy hybrid weighted aggregation operators are proposed, such as the new generalized hesitant fuzzy hybrid weighted averaging (NGHFHWA) operator and the new generalized hesitant fuzzy hybrid weighted geometric (NGHFHWG) operator. Some desirable properties and the relationships between them are discussed. Then, a new algorithm for hesitant fuzzy multi-attribute decision making (HF-MADM) problems with unknown weight information is introduced. Further, a practical example is used to illustrate the detailed implementation process of the proposed approach. A sensitivity analysis of the decision results is analyzed with different parameters. Finally, comparative studies are given to verify the advantages of our method.
文摘This study presents a new approach that advances the algorithm of similarity measures between generalized fuzzy numbers. Following a brief introduction to some properties of the proposed method, a comparative analysis based on 36 sets of generalized fuzzy numbers was performed, in which the degree of similarity of the fuzzy numbers was calculated with the proposed method and seven methods established by previous studies in the literature. The results of the analytical comparison show that the proposed similarity outperforms the existing methods by overcoming their drawbacks and yielding accurate outcomes in all calculations of similarity measures under consideration. Finally, in a numerical example that involves recommending cars to customers based on a nine-member linguistic term set, the proposed similarity measure proves to be competent in addressing fuzzy number recommendation problems.
基金the National Natural Science Foundation of China Important Research Foundation of Guangdong Province
文摘The definition of the generalized fuzzy set is presented for the first time, and a generalized fuzzy operator is proposed to transform a generalized fuzzy set into a normal fuzzy set. The algorithm theory of the operator, as the newest method of the edge detection of a 2-D image, is successfully established. Many experiments haw proved that the algorithm is simpler, more rapid and more precise in location than other edge detection methods. And a schedule of the concrete performance has been given additionally about the edge detection of color images.
基金the National Natural Science Foundation of China, the National High Technology Development Program and the National "PanDeng" Program
文摘The generalized resolution method presented in ref. [1] is a generalization of Robinson’s resolution principle in the first-order logic, which can be applied to a set of nonclausal formulae, i.e. a set of generalized clauses. The method can not only avoid the symbolic redundancy generated from the procedure of transforming a formula into a set of clauses, but also keep the natural description of the problem.
