The class of multiple attribute decision making (MADM) problems is studied, where the attribute values are intuitionistic fuzzy numbers, and the information about attribute weights is completely unknown. A score fun...The class of multiple attribute decision making (MADM) problems is studied, where the attribute values are intuitionistic fuzzy numbers, and the information about attribute weights is completely unknown. A score function is first used to calculate the score of each attribute value and a score matrix is constructed, and then it is transformed into a normalized score matrix. Based on the normalized score matrix, an entropy-based procedure is proposed to derive attribute weights. Furthermore, the additive weighted averaging operator is utilized to fuse all the normalized scores into the overall scores of alternatives, by which the ranking of all the given alternatives is obtained. This paper is concluded by extending the above results to interval-valued intuitionistic fuzzy set theory, and an illustrative example is also provided.展开更多
From the viewpoint of entropy, this paper investigates a hybrid multiple attribute decision making problem with precision number, interval number and fuzzy number. It defines a new concept: project entropy and the de...From the viewpoint of entropy, this paper investigates a hybrid multiple attribute decision making problem with precision number, interval number and fuzzy number. It defines a new concept: project entropy and the decision is taken according to the values. The validity and scientific nature of the given is proven.展开更多
Because of the uncertainty and subjectivity of decision makers in the complex decision-making environment,the evaluation information of alternatives given by decision makers is often fuzzy and uncertain.As a generaliz...Because of the uncertainty and subjectivity of decision makers in the complex decision-making environment,the evaluation information of alternatives given by decision makers is often fuzzy and uncertain.As a generalization of intuitionistic fuzzy set(IFSs)and Pythagoras fuzzy set(PFSs),q-rung orthopair fuzzy set(q-ROFS)is more suitable for expressing fuzzy and uncertain information.But,in actual multiple attribute decision making(MADM)problems,the weights of DMs and attributes are always completely unknown or partly known,to date,the maximizing deviation method is a good tool to deal with such issues.Thus,combine the q-ROFS and conventional maximizing deviation method,we will study the maximizing deviation method under q-ROFSs and q-RIVOFSs in this paper.Firstly,we briefly introduce the basic concept of q-rung orthopair fuzzy sets(q-ROFSs)and q-rung interval-valued orthopair fuzzy sets(q-RIVOFSs).Then,combine the maximizing deviation method with q-rung orthopair fuzzy information,we establish two new decision making models.On this basis,the proposed models are applied to MADM problems with q-rung orthopair fuzzy information.Compared with existing methods,the effectiveness and superiority of the new model are analyzed.This method can effectively solve the MADM problem whose decision information is represented by q-rung orthopair fuzzy numbers(q-ROFNs)and whose attributes are incomplete.展开更多
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
In an ambiguous decision domain, the evaluation values of alternatives against attributes would be interval numbers because of the inherent, uncertain property of the problems. By using a number of linear programming ...In an ambiguous decision domain, the evaluation values of alternatives against attributes would be interval numbers because of the inherent, uncertain property of the problems. By using a number of linear programming models, Bryson and Mobolurin propose an approach to compute attribute weights and overall values of the alternatives in the form of interval numbers. The intervals of the overall values of alternatives are then transformed into points or crisp values for comparisons among the alternatives. However, the attribute weights are different because of the use of linear programming models in Bryson and Mobolurin's approach. Thus, the alternatives are not comparable because different attribute weights are employed to calculate the overall values of the alternatives. A new approach is proposed to overcome the drawbacks of Bryson and Mobolurin's approach. By transforming the decision matrix with intervals into the one with crisp values, a new linear programming model is proposed, to calculate the attribute weights for conducting alternative ranking.展开更多
With respect to the multiple attribute decision making problems with linguistic preference relations on alternatives in the form of incomplete linguistic judgment matrix, a method is proposed to analyze the decision p...With respect to the multiple attribute decision making problems with linguistic preference relations on alternatives in the form of incomplete linguistic judgment matrix, a method is proposed to analyze the decision problem. The incomplete linguistic judgment matrix is transformed into incomplete fuzzy judgment matrix and an optimization model is developed on the basis of incomplete fuzzy judgment matrix provided by the decision maker and the decision matrix to determine attribute weights by Lagrange multiplier method. Then the overall values of all alternatives are calculated to rank them. A numerical example is given to illustrate the feasibility and practicality of the proposed method.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
Industrial risk and the diversification of risk types both increase with industrial development. Many uncertain factors and high risk are inherent in the implementation of new green manufacturing methods. Because of t...Industrial risk and the diversification of risk types both increase with industrial development. Many uncertain factors and high risk are inherent in the implementation of new green manufacturing methods. Because of the shortage of successful examples and complete and certain knowledge, decision-making methods using probabilities to represent risk, which need many examples, cannot be used to evaluate risk in the implementation of green manufacturing projects. Therefore, a fuzzy multiple attribute decision-making (FMADM) method was developed with a three-level hierarchical decision-making model to evaluate the aggregate risk for green manufacturing projects. A case study shows that the hierarchical decision-making model of the aggregate risk and the FMADM method effectively reflect the characteristics of the risk in green manufacturing projects.展开更多
This paper presents a fuzzy multiple attribute decision-making (FMADM) method in which the attribute weights and decision matrix elements (attribute values) are fuzzy variables. Fuzzy arithmetic and the expected v...This paper presents a fuzzy multiple attribute decision-making (FMADM) method in which the attribute weights and decision matrix elements (attribute values) are fuzzy variables. Fuzzy arithmetic and the expected value operator of fuzzy variables are used to develop the expected value method to solve the FMADM problem. A numerical example is given to demonstrate the feasibility and effectiveness of the method.展开更多
As an generalization of hesitant fuzzy set, interval-valued hesitant fuzzy set and dual hesitant fuzzy set, interval-valued dual hesitant fuzzy set has been proposed and applied in multiple attribute decision making. ...As an generalization of hesitant fuzzy set, interval-valued hesitant fuzzy set and dual hesitant fuzzy set, interval-valued dual hesitant fuzzy set has been proposed and applied in multiple attribute decision making. Hamacher t-norm and t-conorm is an generalization of algebraic and Einstein t-norms and t-conorms. In order to combine interval-valued dual hesitant fuzzy aggregation operators with Hamacher t-norm and t-conorm. We first introduced some new Hamacher operation rules for interval-valued dual hesitant fuzzy elements. Then, several interval-valued dual hesitant fuzzy Hamacher aggregation operators are presented, some desirable properties and their special cases are studied. Further, a new multiple attribute decision making method with these operators is given,and an numerical example is provided to demonstrate that the developed approach is both valid and practical.展开更多
In this paper,we investigate the multiple attribute decision making(MADM)problems in which the attribute values take the form of hesitant trapezoid fuzzy information.Firstly,inspired by the idea of hesitant fuzzy sets...In this paper,we investigate the multiple attribute decision making(MADM)problems in which the attribute values take the form of hesitant trapezoid fuzzy information.Firstly,inspired by the idea of hesitant fuzzy sets and trapezoid fuzzy numbers,the definition of hesitant trapezoid fuzzy set and some operational laws of hesitant trapezoid fuzzy elements are proposed.Then some hesitant trapezoid fuzzy aggregation operators based on Hamacher operation are developed,such as the hesitant trapezoid fuzzy Hamacher weighted average(HTr FHWA)operator,the hesitant trapezoid fuzzy Hamacher weighted geometric(HTr FHWG)operator,the hesitant trapezoid fuzzy Hamacher Choquet average(HTr FHCA),the hesitant trapezoid fuzzy Hamacher Choquet geometric(HTr FHCG),etc.Furthermore,an approach based on the hesitant trapezoid fuzzy Hamacher weighted average(HTr FHWA)operator and the hesitant trapezoid fuzzy Hamacher weighted geometric(HTr FHWG)operator is proposed for MADM problems under hesitant trapezoid fuzzy environment.Finally,a numerical example for supplier selection is given to illustrate the application of the proposed approach.展开更多
An effective maintenance schedule can largely improve productivity and reduce maintenance costs for enterprises. Many factors, such as resource, production, cost and crew, should be considered when we make maintenance...An effective maintenance schedule can largely improve productivity and reduce maintenance costs for enterprises. Many factors, such as resource, production, cost and crew, should be considered when we make maintenance plans. However, it is difficult to meet all requests of the production targets in practical engineering.The multiple attribute decision making for equipment maintenance is proposed in this paper, and the multiple objectives decision making method is utilized to solve the problem in the maintenance process. In the particular environment and resources, a case is studied to illustrate the model and methods. The model gives the optimal maintenance plan with the analytic hierarchy process method in accordance with the particular criteria. It has been proved that this model and decision methods are scientific and operable.展开更多
The multiple attribute decision making problems are studied, in which the information about attribute weights is partly known and the attribute values take the form of intuitionistic fuzzy numbers. The operational law...The multiple attribute decision making problems are studied, in which the information about attribute weights is partly known and the attribute values take the form of intuitionistic fuzzy numbers. The operational laws of intuitionistic fuzzy numbers are introduced, and the score function and accuracy function are presented to compare the intuitionistic fuzzy numbers. The intuitionistic fuzzy ordered weighted averaging (IFOWA) operator which is an extension of the well-known ordered weighted averaging (OWA) operator is investigated to aggregate the intuitionistic fuzzy information. In order to determine the weights of intuitionistic fuzzy ordered weighted averaging operator, a linear goal programming procedure is proposed for learning the weights from data. Finally, an example is illustrated to verify the effectiveness and practicability of the developed method.展开更多
基金supported by the National Science Fund for Distinguished Young Scholars of China(70625005).
文摘The class of multiple attribute decision making (MADM) problems is studied, where the attribute values are intuitionistic fuzzy numbers, and the information about attribute weights is completely unknown. A score function is first used to calculate the score of each attribute value and a score matrix is constructed, and then it is transformed into a normalized score matrix. Based on the normalized score matrix, an entropy-based procedure is proposed to derive attribute weights. Furthermore, the additive weighted averaging operator is utilized to fuse all the normalized scores into the overall scores of alternatives, by which the ranking of all the given alternatives is obtained. This paper is concluded by extending the above results to interval-valued intuitionistic fuzzy set theory, and an illustrative example is also provided.
文摘From the viewpoint of entropy, this paper investigates a hybrid multiple attribute decision making problem with precision number, interval number and fuzzy number. It defines a new concept: project entropy and the decision is taken according to the values. The validity and scientific nature of the given is proven.
基金supported by the National Natural Science Foundation of China under Grant No.71571128the Humanities and Social Sciences Foundation of Ministry of Education of the People’s Republic of China(No.17XJA630003).
文摘Because of the uncertainty and subjectivity of decision makers in the complex decision-making environment,the evaluation information of alternatives given by decision makers is often fuzzy and uncertain.As a generalization of intuitionistic fuzzy set(IFSs)and Pythagoras fuzzy set(PFSs),q-rung orthopair fuzzy set(q-ROFS)is more suitable for expressing fuzzy and uncertain information.But,in actual multiple attribute decision making(MADM)problems,the weights of DMs and attributes are always completely unknown or partly known,to date,the maximizing deviation method is a good tool to deal with such issues.Thus,combine the q-ROFS and conventional maximizing deviation method,we will study the maximizing deviation method under q-ROFSs and q-RIVOFSs in this paper.Firstly,we briefly introduce the basic concept of q-rung orthopair fuzzy sets(q-ROFSs)and q-rung interval-valued orthopair fuzzy sets(q-RIVOFSs).Then,combine the maximizing deviation method with q-rung orthopair fuzzy information,we establish two new decision making models.On this basis,the proposed models are applied to MADM problems with q-rung orthopair fuzzy information.Compared with existing methods,the effectiveness and superiority of the new model are analyzed.This method can effectively solve the MADM problem whose decision information is represented by q-rung orthopair fuzzy numbers(q-ROFNs)and whose attributes are incomplete.
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.
基金the National Natural Science Foundation of China (70571041).
文摘In an ambiguous decision domain, the evaluation values of alternatives against attributes would be interval numbers because of the inherent, uncertain property of the problems. By using a number of linear programming models, Bryson and Mobolurin propose an approach to compute attribute weights and overall values of the alternatives in the form of interval numbers. The intervals of the overall values of alternatives are then transformed into points or crisp values for comparisons among the alternatives. However, the attribute weights are different because of the use of linear programming models in Bryson and Mobolurin's approach. Thus, the alternatives are not comparable because different attribute weights are employed to calculate the overall values of the alternatives. A new approach is proposed to overcome the drawbacks of Bryson and Mobolurin's approach. By transforming the decision matrix with intervals into the one with crisp values, a new linear programming model is proposed, to calculate the attribute weights for conducting alternative ranking.
基金the National Natural Science Foundation of China (70701008)National Science Foundationfor Distinguished Young Scholars of China (70525002)
文摘With respect to the multiple attribute decision making problems with linguistic preference relations on alternatives in the form of incomplete linguistic judgment matrix, a method is proposed to analyze the decision problem. The incomplete linguistic judgment matrix is transformed into incomplete fuzzy judgment matrix and an optimization model is developed on the basis of incomplete fuzzy judgment matrix provided by the decision maker and the decision matrix to determine attribute weights by Lagrange multiplier method. Then the overall values of all alternatives are calculated to rank them. A numerical example is given to illustrate the feasibility and practicality of the proposed method.
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.
基金Supported by the National Natural Science Foundation of China (No. 50135020), the National High-Tech Research and Devel- opment (863) Program of China (No. 2001AA337010) and the Key Grant Project of the Ministry of Education, China (No. 0203)
文摘Industrial risk and the diversification of risk types both increase with industrial development. Many uncertain factors and high risk are inherent in the implementation of new green manufacturing methods. Because of the shortage of successful examples and complete and certain knowledge, decision-making methods using probabilities to represent risk, which need many examples, cannot be used to evaluate risk in the implementation of green manufacturing projects. Therefore, a fuzzy multiple attribute decision-making (FMADM) method was developed with a three-level hierarchical decision-making model to evaluate the aggregate risk for green manufacturing projects. A case study shows that the hierarchical decision-making model of the aggregate risk and the FMADM method effectively reflect the characteristics of the risk in green manufacturing projects.
基金Supported by the National Natural Science Foundation of China (N10501009)
文摘This paper presents a fuzzy multiple attribute decision-making (FMADM) method in which the attribute weights and decision matrix elements (attribute values) are fuzzy variables. Fuzzy arithmetic and the expected value operator of fuzzy variables are used to develop the expected value method to solve the FMADM problem. A numerical example is given to demonstrate the feasibility and effectiveness of the method.
基金Supported by the Natural Science Foundation of Higher Education of Jiangsu Province(18KJB110024)the High Training Funded for Professional Leaders of Higher Vocational Colleges in Jiangsu Province(2018GRFX038)Science and Technology Research Project of Nantong Shipping College(HYKY/2018A03)
文摘As an generalization of hesitant fuzzy set, interval-valued hesitant fuzzy set and dual hesitant fuzzy set, interval-valued dual hesitant fuzzy set has been proposed and applied in multiple attribute decision making. Hamacher t-norm and t-conorm is an generalization of algebraic and Einstein t-norms and t-conorms. In order to combine interval-valued dual hesitant fuzzy aggregation operators with Hamacher t-norm and t-conorm. We first introduced some new Hamacher operation rules for interval-valued dual hesitant fuzzy elements. Then, several interval-valued dual hesitant fuzzy Hamacher aggregation operators are presented, some desirable properties and their special cases are studied. Further, a new multiple attribute decision making method with these operators is given,and an numerical example is provided to demonstrate that the developed approach is both valid and practical.
基金Supported by the Science and Technology Research Project of Chongqing Municipal Education Commission(KJQN201901505)the Key Project of Humanities and Social Sciences Research of Chongqing Education Commission in 2019(19SKGH181)
文摘In this paper,we investigate the multiple attribute decision making(MADM)problems in which the attribute values take the form of hesitant trapezoid fuzzy information.Firstly,inspired by the idea of hesitant fuzzy sets and trapezoid fuzzy numbers,the definition of hesitant trapezoid fuzzy set and some operational laws of hesitant trapezoid fuzzy elements are proposed.Then some hesitant trapezoid fuzzy aggregation operators based on Hamacher operation are developed,such as the hesitant trapezoid fuzzy Hamacher weighted average(HTr FHWA)operator,the hesitant trapezoid fuzzy Hamacher weighted geometric(HTr FHWG)operator,the hesitant trapezoid fuzzy Hamacher Choquet average(HTr FHCA),the hesitant trapezoid fuzzy Hamacher Choquet geometric(HTr FHCG),etc.Furthermore,an approach based on the hesitant trapezoid fuzzy Hamacher weighted average(HTr FHWA)operator and the hesitant trapezoid fuzzy Hamacher weighted geometric(HTr FHWG)operator is proposed for MADM problems under hesitant trapezoid fuzzy environment.Finally,a numerical example for supplier selection is given to illustrate the application of the proposed approach.
基金the National Natural Science Foundation of China(No.71471147)the Natural Science Research Project of Shaanxi Province(No.2015JQ7273)the Seed Foundation of Innovation and Creation for Graduate Students in Northwestern Polytechnical University(No.Z2016087)
文摘An effective maintenance schedule can largely improve productivity and reduce maintenance costs for enterprises. Many factors, such as resource, production, cost and crew, should be considered when we make maintenance plans. However, it is difficult to meet all requests of the production targets in practical engineering.The multiple attribute decision making for equipment maintenance is proposed in this paper, and the multiple objectives decision making method is utilized to solve the problem in the maintenance process. In the particular environment and resources, a case is studied to illustrate the model and methods. The model gives the optimal maintenance plan with the analytic hierarchy process method in accordance with the particular criteria. It has been proved that this model and decision methods are scientific and operable.
基金supported by the National Natural Science Foundation of China (70771025)the Fundamental Research Funds for the Central Universities of Hohai University (2009B04514)Humanities and Social Sciences Foundations of Ministry of Education of China(10YJA630067)
文摘The multiple attribute decision making problems are studied, in which the information about attribute weights is partly known and the attribute values take the form of intuitionistic fuzzy numbers. The operational laws of intuitionistic fuzzy numbers are introduced, and the score function and accuracy function are presented to compare the intuitionistic fuzzy numbers. The intuitionistic fuzzy ordered weighted averaging (IFOWA) operator which is an extension of the well-known ordered weighted averaging (OWA) operator is investigated to aggregate the intuitionistic fuzzy information. In order to determine the weights of intuitionistic fuzzy ordered weighted averaging operator, a linear goal programming procedure is proposed for learning the weights from data. Finally, an example is illustrated to verify the effectiveness and practicability of the developed method.