In 2000, Wu and Gong [1] introduced the thought of the Henstock integrals of inter-valvalued functions and fuzzy-number-valued functions and obtained a number of their properties. The aim of this paper is to introduce...In 2000, Wu and Gong [1] introduced the thought of the Henstock integrals of inter-valvalued functions and fuzzy-number-valued functions and obtained a number of their properties. The aim of this paper is to introduce the thought of the AP- Henstock integrals of interval-valued functions and fuzzy-number-valued functions which are extensions of [1] and investigate a number of their properties.展开更多
In this paper we introduce the notion of the Henstock-Stieltjes (HS) integrals of interval-valued functions and fuzzy-number-valued functions and discuss some of their properties.
Using score function in a matrix game is very rare. In the proposed paper we have considered a matrix game with pay-off as triangular intuitionistic fuzzy number and a new ranking order has been proposed using value j...Using score function in a matrix game is very rare. In the proposed paper we have considered a matrix game with pay-off as triangular intuitionistic fuzzy number and a new ranking order has been proposed using value judgement index, available definitions and operations. A new concept of score function has been developed to defuzzify the pay-off matrix and solution of the matrix game has been obtained. A numerical example has been given in support of the proposed method.展开更多
The Floyd-Warshall algorithm is frequently used to determine the shortest path between any pair of nodes.It works well for crisp weights,but the problem arises when weights are vague and uncertain.Let us take an examp...The Floyd-Warshall algorithm is frequently used to determine the shortest path between any pair of nodes.It works well for crisp weights,but the problem arises when weights are vague and uncertain.Let us take an example of computer networks,where the chosen path might no longer be appropriate due to rapid changes in network conditions.The optimal path from among all possible courses is chosen in computer networks based on a variety of parameters.In this paper,we design a new variant of the Floyd-Warshall algorithm that identifies an All-Pair Shortest Path(APSP)in an uncertain situation of a network.In the proposed methodology,multiple criteria and theirmutual associationmay involve the selection of any suitable path between any two node points,and the values of these criteria may change due to an uncertain environment.We use trapezoidal picture fuzzy addition,score,and accuracy functions to find APSP.We compute the time complexity of this algorithm and contrast it with the traditional Floyd-Warshall algorithm and fuzzy Floyd-Warshall algorithm.展开更多
Considering the decision maker＇s risk psychological factors and information ambiguity under uncertainty, a novel TOPSIS based on prospect theory （PT） and trapezoidal intuitionistic fuzzy numbers （YrIFNs） for grou...Considering the decision maker＇s risk psychological factors and information ambiguity under uncertainty, a novel TOPSIS based on prospect theory （PT） and trapezoidal intuitionistic fuzzy numbers （YrIFNs） for group decision making is investigated, in which the criteria values and the criteria weights take the form of TrIFNs, and weights of decision makers are unknown. Firstly, distance measures for TrIFNs are used to induce value function under trapezoidal intuitionistic fuzzy environment. Secondly, the concepts of distance measures and trapezoidal intuitionistie fuzzy weighted averaging operator are employed to induce the weights of decision makers and thus the decision makers＇ options can be aggregated. Then the PT-based separation measures and relative closeness coefficient are defined and an algorithm for ranking alternatives under trapezoidal intuitionistic fuzzy environment is proposed. Finally, a numerical example further illustrates the practicality and effectiveness of the proposed TOPSIS method.展开更多
In this paper, a new decision making approach is proposed for the multi-attribute large group emergency decision-making problem that attribute weights are unknown and expert preference information is expressed by gene...In this paper, a new decision making approach is proposed for the multi-attribute large group emergency decision-making problem that attribute weights are unknown and expert preference information is expressed by generalized interval-valued trapezoidal fuzzy numbers （GITFNs）. Firstly, a degree of similarity formula between GITFNs is presented. Secondly, expert preference information on different alternatives is clustered into several aggregations via the fuzzy clustering method. As the clustering proceeds, an index of group preference consistency is introduced to ensure the clustering effect, and then the group preference information on different alternatives is obtained. Thirdly, the TOPSIS method is used to rank the alternatives. Finally, an example is taken to show the feasibility and effectiveness of this approach. These method can ensure the consistency degree of group preference, thus decision efficiency of emergency response activities can be improved.展开更多
The route evaluation is an important basis for airlines to make route decisions. In order to solve the fuzzy multiple attribute route decision problem, route attribute weight was completely unknown, and the route eval...The route evaluation is an important basis for airlines to make route decisions. In order to solve the fuzzy multiple attribute route decision problem, route attribute weight was completely unknown, and the route evaluation fuzzy language information was given, the fuzzy language and preference information were converted into trapezoidal fuzzy numbers. A programming model was constructed by minimizing the total deviation between trapezoidal fuzzy numbers to determining the weight of each attribute in the route decision, By weighting the average of the route attribute value and the weights value, compared the expected value of fuzzy comprehensive evaluation for each route, and ranking alternatives by using the expected value operator of fuzzy variable. Finally, a numerical example was used to illustrate the proposed method. The results show that the method can be used by air-lines to solve multiple attribute route decision problems with unknown weights, and the method is scientific and effective.展开更多
文摘In 2000, Wu and Gong [1] introduced the thought of the Henstock integrals of inter-valvalued functions and fuzzy-number-valued functions and obtained a number of their properties. The aim of this paper is to introduce the thought of the AP- Henstock integrals of interval-valued functions and fuzzy-number-valued functions which are extensions of [1] and investigate a number of their properties.
文摘In this paper we introduce the notion of the Henstock-Stieltjes (HS) integrals of interval-valued functions and fuzzy-number-valued functions and discuss some of their properties.
文摘Using score function in a matrix game is very rare. In the proposed paper we have considered a matrix game with pay-off as triangular intuitionistic fuzzy number and a new ranking order has been proposed using value judgement index, available definitions and operations. A new concept of score function has been developed to defuzzify the pay-off matrix and solution of the matrix game has been obtained. A numerical example has been given in support of the proposed method.
基金extend their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through General Research Project under Grant No.(R.G.P.2/48/43).
文摘The Floyd-Warshall algorithm is frequently used to determine the shortest path between any pair of nodes.It works well for crisp weights,but the problem arises when weights are vague and uncertain.Let us take an example of computer networks,where the chosen path might no longer be appropriate due to rapid changes in network conditions.The optimal path from among all possible courses is chosen in computer networks based on a variety of parameters.In this paper,we design a new variant of the Floyd-Warshall algorithm that identifies an All-Pair Shortest Path(APSP)in an uncertain situation of a network.In the proposed methodology,multiple criteria and theirmutual associationmay involve the selection of any suitable path between any two node points,and the values of these criteria may change due to an uncertain environment.We use trapezoidal picture fuzzy addition,score,and accuracy functions to find APSP.We compute the time complexity of this algorithm and contrast it with the traditional Floyd-Warshall algorithm and fuzzy Floyd-Warshall algorithm.
基金supported by the National Natural Sciences Foundation of China(No.71221061)China Postdoctoral Science Foundation(No.2014M552169)Central South University Business Management Postdoctoral Research Station
文摘Considering the decision maker＇s risk psychological factors and information ambiguity under uncertainty, a novel TOPSIS based on prospect theory （PT） and trapezoidal intuitionistic fuzzy numbers （YrIFNs） for group decision making is investigated, in which the criteria values and the criteria weights take the form of TrIFNs, and weights of decision makers are unknown. Firstly, distance measures for TrIFNs are used to induce value function under trapezoidal intuitionistic fuzzy environment. Secondly, the concepts of distance measures and trapezoidal intuitionistie fuzzy weighted averaging operator are employed to induce the weights of decision makers and thus the decision makers＇ options can be aggregated. Then the PT-based separation measures and relative closeness coefficient are defined and an algorithm for ranking alternatives under trapezoidal intuitionistic fuzzy environment is proposed. Finally, a numerical example further illustrates the practicality and effectiveness of the proposed TOPSIS method.
基金supported by a grant from Natural Science Foundation in China(71171202, 71171201,71210003)the Science Foundation for National Innovation Research Group in China(71221061)Key Project for National Natural Science Foundation in China (71431006)
文摘In this paper, a new decision making approach is proposed for the multi-attribute large group emergency decision-making problem that attribute weights are unknown and expert preference information is expressed by generalized interval-valued trapezoidal fuzzy numbers （GITFNs）. Firstly, a degree of similarity formula between GITFNs is presented. Secondly, expert preference information on different alternatives is clustered into several aggregations via the fuzzy clustering method. As the clustering proceeds, an index of group preference consistency is introduced to ensure the clustering effect, and then the group preference information on different alternatives is obtained. Thirdly, the TOPSIS method is used to rank the alternatives. Finally, an example is taken to show the feasibility and effectiveness of this approach. These method can ensure the consistency degree of group preference, thus decision efficiency of emergency response activities can be improved.
文摘The route evaluation is an important basis for airlines to make route decisions. In order to solve the fuzzy multiple attribute route decision problem, route attribute weight was completely unknown, and the route evaluation fuzzy language information was given, the fuzzy language and preference information were converted into trapezoidal fuzzy numbers. A programming model was constructed by minimizing the total deviation between trapezoidal fuzzy numbers to determining the weight of each attribute in the route decision, By weighting the average of the route attribute value and the weights value, compared the expected value of fuzzy comprehensive evaluation for each route, and ranking alternatives by using the expected value operator of fuzzy variable. Finally, a numerical example was used to illustrate the proposed method. The results show that the method can be used by air-lines to solve multiple attribute route decision problems with unknown weights, and the method is scientific and effective.
