The multiple attribute group decision making problem in which the input arguments take the form of intuitionistic uncertain linguistic information is studied in the paper.Based on the operational principles of intuiti...The multiple attribute group decision making problem in which the input arguments take the form of intuitionistic uncertain linguistic information is studied in the paper.Based on the operational principles of intuitionistic uncertain linguistic variables and the concept of the expected value and accuracy function,some new dependent aggregation operators with intuitionistic uncertain linguistic information including the dependent intuitionistic uncertain linguistic ordered weighted average(DIULOWA)operator,the dependent intuitionistic uncertain linguistic ordered weighted geometric(DIULOWG)operator,the generalized dependent intuitionistic uncertain linguistic ordered weighted aggregation(GDIULOWA)operator and so on are developed,in which the associated weights only depend on the aggregated arguments.Also,we study some desirable properties of the aggregation operators.Moreover,the approach of multiple attribute group decision making with intuitionistic uncertain linguistic information based on the developed operators is proposed.Finally,an illustrative numerical example is given to show the practicality and effectiveness of the proposed approaches.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
Pythagorean fuzzy set(PFS) can provide more flexibility than intuitionistic fuzzy set(IFS) for handling uncertain information, and PFS has been increasingly used in multi-attribute decision making problems. This paper...Pythagorean fuzzy set(PFS) can provide more flexibility than intuitionistic fuzzy set(IFS) for handling uncertain information, and PFS has been increasingly used in multi-attribute decision making problems. This paper proposes a new multiattribute group decision making method based on Pythagorean uncertain linguistic variable Hamy mean(PULVHM) operator and VIKOR method. Firstly, we define operation rules and a new aggregation operator of Pythagorean uncertain linguistic variable(PULV) and explore some properties of the operator.Secondly, taking the decision makers' hesitation degree into account, a new score function is defined, and we further develop a new group decision making approach integrated with VIKOR method. Finally, an investment example is demonstrated to elaborate the validity of the proposed method. Sensibility analysis and comprehensive comparisons with another two methods are performed to show the stability and advantage of our method.展开更多
A kind of multiple attribute group decision making (MAGDM) problem is discussed from the perspective of statistic decision-making. Firstly, on the basis of the stability theory, a new idea is proposed to solve this ...A kind of multiple attribute group decision making (MAGDM) problem is discussed from the perspective of statistic decision-making. Firstly, on the basis of the stability theory, a new idea is proposed to solve this kind of problem. Secondly, a con- crete method corresponding to this kind of problem is proposed. The main tool of our research is the technique o~ the jackknife method. The main advantage of the new method is that it can identify and determine the reliability degree of the existed decision making information. Finally, a traffic engineering example is given to show the effectiveness of the new method.展开更多
Uncertain and hesitant information, widely existing in the real-world qualitative decision making problems, brings great challenges to decision makers. Hesitant fuzzy linguistic term sets(HFLTSs), an effective linguis...Uncertain and hesitant information, widely existing in the real-world qualitative decision making problems, brings great challenges to decision makers. Hesitant fuzzy linguistic term sets(HFLTSs), an effective linguistic computational tool in modeling and eliciting such information, have hence aroused many scholars’ interests and some extensions have been introduced recently.However, these methods are based on the discrete linguistic term framework with the limited expression domain, which actually depict qualitative information using several single values. Therefore,it is hard to ensure the integrity of the semantics representation and the accuracy of the computation results. To deal with this problem, a semantics basis framework called complete linguistic term set(CLTS) is designed, which adopts a separation structure of linguistic scale and expression domain, enriching semantics representation of decision makers. On this basis the concept of fuzzy interval linguistic sets(FILSs) is put forward that employs the interval linguistic term with probability to increase the flexibility of eliciting and representing uncertain and hesitant qualitative information. For practical applications, a fuzzy interval linguistic technique for order preference by similarity to ideal solution(FILTOPSIS) method is developed to deal with multi-attribute group decision making(MAGDM) problems. Through the cases of movie and enterprise resource planning(ERP) system selection, the effectiveness and validity of the proposed method are illustrated.展开更多
A method is proposed to deal with the uncertain multiple attribute group decision making problems,where 2-dimension uncertain linguistic variables(2DULVs)are used as the reliable way for the experts to express their f...A method is proposed to deal with the uncertain multiple attribute group decision making problems,where 2-dimension uncertain linguistic variables(2DULVs)are used as the reliable way for the experts to express their fuzzy subjective evaluation information.Firstly,in order to measure the 2DULVs more accurately,a new method is proposed to compare two 2DULVs,called a score function,while a new function is defined to measure the distance between two 2DULVs.Secondly,two optimization models are established to determine the weight of experts and attributes based on the new distance formula and a weighted average operator is used to determine the comprehensive evaluation value of each alternative.Then,a score function is used to determine the ranking of the alternatives.Finally,the effectiveness of the proposed method is proved by an illustrated example.展开更多
Given that the classical performance evaluation models can not deal with the group decision making problems since they simply average the index,we propose an enterprise knowledge management evaluation model based on m...Given that the classical performance evaluation models can not deal with the group decision making problems since they simply average the index,we propose an enterprise knowledge management evaluation model based on multiple attribute group decision making (MAGDM). Find the differences between Ordered Weighted Averaging (OWA) and methods for uncertain decision making. Also,analyze the multiple attribute group decision making process and implement the algorithm. Finally,apply the method on performance evaluation of four enterprises and make sensitivity analysis towards the evaluation results.展开更多
The Paraconsistent Many-Valued Similarity (PMVS) method for multi-attribute decision making will be incomplete as a decision model if it is not extended to the realm of group decision-making. Therefore, in this articl...The Paraconsistent Many-Valued Similarity (PMVS) method for multi-attribute decision making will be incomplete as a decision model if it is not extended to the realm of group decision-making. Therefore, in this article, our primary objective is to show how the paraconsistent many-valued similarity method can be used to solve group decision-making problems involving choice making or ranking of a finite set of decision alternatives. Moreover, since weights are very important parameters in multi-attribute decision-making, we have introduced the Borda rule to calculate the weights of experts and that of every criterion under consideration. To demonstrate how the proposed method works, a numerical example on energy sources of an economy from the points of view of a group of experts is investigated. Further, we compare the results of this new approach with that of fuzzy TOPSIS group decision-making method to illustrate the robustness and effectiveness of the former.展开更多
Group decision making problems are investigated with uncertain multiplicative linguistic preference relations.An unbalanced multiplicative linguistic label set is introduced,which can be used by the experts to express...Group decision making problems are investigated with uncertain multiplicative linguistic preference relations.An unbalanced multiplicative linguistic label set is introduced,which can be used by the experts to express their linguistic preference information over alternatives.The uncertain linguistic weighted geometric mean operator is utilized to aggregate all the individual uncertain multiplicative linguistic preference relations into a collective one,and then a simple approach is developed to determine the experts' weights by utilizing the consensus degrees among the individual uncertain multiplicative linguistic preference relations and the collective uncertain multiplicative linguistic preference relations.Furthermore,a practical interactive procedure for group decision making is proposed based on uncertain multiplicative linguistic preference relations,in which a possibility degree formula and a complementary matrix are used to rank the given alternatives.Finally,the proposed procedure is applied to solve the group decision making problem of a manufacturing company searching the best global supplier for one of its most critical parts used in assembling process.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
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
For group decision-making problems with linguistic assessment information, a new method based on two-tuple and WC-OWA operator is proposed, in which the criteria's weights and the decision-makers' preference informa...For group decision-making problems with linguistic assessment information, a new method based on two-tuple and WC-OWA operator is proposed, in which the criteria's weights and the decision-makers' preference information might take the form of linguistic grade, or might be between two continuous linguistic grades, or might be linguistic interval, or might be default. In this method, all linguistic values are transformed into two-tuple, and an aggregative decision-making matrix is obtained by using interval operation. The group aggregative values of each criterion on alternatives are computed by using a WC-OWA operator, the aggregative values on alternatives are worked out, and transformed into two-tuple. And the rank of the alternatives is obtained by using the order property of two-tuple. An example shows the feasibility and effectiveness of the proposed method.展开更多
To study the fuzzy and grey information in the problems of multi-attribute group decision making, the basic concepts of both fuzzy grey numbers and grey interval numbers are given firstly, then a new model of fuzzy gr...To study the fuzzy and grey information in the problems of multi-attribute group decision making, the basic concepts of both fuzzy grey numbers and grey interval numbers are given firstly, then a new model of fuzzy grey multi-attribute group decision making based on the theories of fuzzy mathematics and grey system is presented. Furthermore, the grey interval relative degree and deviation degree is defined, and both the optimistic algorithm of the grey interval relational degree and the algorithm of deviation degree minimization for solving this new model are also given. Finally, a decision making example to demonstrate the feasibility and rationality of this new method is given, and the results by using these two algorithms are uniform.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
The group decision making problem with linguistic pref- erence relations is studied. The concept of additive consistent linguistic preference relation is defined, and then some properties of the additive consistent li...The group decision making problem with linguistic pref- erence relations is studied. The concept of additive consistent linguistic preference relation is defined, and then some properties of the additive consistent linguistic preference relation are studied. In order to rank the alternatives in the group decision making with the linguistic preference relations, the weighted average is first utilized to combine the group linguistic preference relations to one linguistic preference relation, and then the transformation function is proposed to transform the linguistic preference relation to the multiplicative preference relation, and thus the Saaty's eigenvec- tor method (EM) of multiplicative preference relation is utilized to rank the alternatives in group decision making with the linguistic preference relations. Finally, an illustrative numerical example is given to verify the proposed method. A comparative study to the linguistic ordered weighted averaging (LOWA) operator method is also demonstrated.展开更多
The technique for order performance by similarity to ideal solution (TOPSIS) is one of the major techniques in dealing with multiple criteria decision making (MCDM) problems, and the belief structure (BS) model ...The technique for order performance by similarity to ideal solution (TOPSIS) is one of the major techniques in dealing with multiple criteria decision making (MCDM) problems, and the belief structure (BS) model has been used successfully for uncertain MCDM with incompleteness, impreciseness or ignorance. In this paper, the TOPSIS method with BS model is proposed to solve group belief MCDM problems. Firstly, the group belief MCDM problem is structured as a belief decision matrix in which the judgments of each decision maker are described as BS models, and then the evidential reasoning approach is used for aggregating the multiple decision makers' judgments. Subsequently, the positive and negative ideal belief solutions are defined with the principle of TOPSIS. To measure the separation from ideal solutions, the concept and algorithm of belief distance measure are defined, which can be used for comparing the difference between BS models. Finally, the relative closeness and ranking index are calculated for ranking the alternatives. A numerical example is given to illustrate the proposed method.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
Linguistic single-valued neutrosophic set(LSVNS)is a more reliable tool,which is designed to handle the uncertainties of the situations involving the qualitative data.In the present manuscript,we introduce some power ...Linguistic single-valued neutrosophic set(LSVNS)is a more reliable tool,which is designed to handle the uncertainties of the situations involving the qualitative data.In the present manuscript,we introduce some power aggregation operators(AOs)for the LSVNSs,whose purpose is to diminish the influence of inevitable arguments about the decision-making process.For it,first we develop some averaging power operators,namely,linguistic single-valued neutrosophic(LSVN)power averaging,weighted average,ordered weighted average,and hybrid averaging AOs along with their desirable properties.Further,we extend it to the geometric power AOs for LSVNSs.Based on the proposed work;an approach to solve the group decision-making problems is given along with the numerical example.Finally,a comparative study and the validity tests are present to discuss the reliability of the proposed operators.展开更多
基金Supported by the National Natural Science Foundation of China(71761027)Ningbo Natural Science Foundation(2015A610161)。
文摘The multiple attribute group decision making problem in which the input arguments take the form of intuitionistic uncertain linguistic information is studied in the paper.Based on the operational principles of intuitionistic uncertain linguistic variables and the concept of the expected value and accuracy function,some new dependent aggregation operators with intuitionistic uncertain linguistic information including the dependent intuitionistic uncertain linguistic ordered weighted average(DIULOWA)operator,the dependent intuitionistic uncertain linguistic ordered weighted geometric(DIULOWG)operator,the generalized dependent intuitionistic uncertain linguistic ordered weighted aggregation(GDIULOWA)operator and so on are developed,in which the associated weights only depend on the aggregated arguments.Also,we study some desirable properties of the aggregation operators.Moreover,the approach of multiple attribute group decision making with intuitionistic uncertain linguistic information based on the developed operators is proposed.Finally,an illustrative numerical example is given to show the practicality and effectiveness of the proposed approaches.
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.
基金supported by the National Natural Science Foundation of China(61402260,61473176)Taishan Scholar Project of Shandong Province(TSQN201812092)
文摘Pythagorean fuzzy set(PFS) can provide more flexibility than intuitionistic fuzzy set(IFS) for handling uncertain information, and PFS has been increasingly used in multi-attribute decision making problems. This paper proposes a new multiattribute group decision making method based on Pythagorean uncertain linguistic variable Hamy mean(PULVHM) operator and VIKOR method. Firstly, we define operation rules and a new aggregation operator of Pythagorean uncertain linguistic variable(PULV) and explore some properties of the operator.Secondly, taking the decision makers' hesitation degree into account, a new score function is defined, and we further develop a new group decision making approach integrated with VIKOR method. Finally, an investment example is demonstrated to elaborate the validity of the proposed method. Sensibility analysis and comprehensive comparisons with another two methods are performed to show the stability and advantage of our method.
基金supported by the National Key Basic Research Program of China(973 Program)(2012CB725402)the National High-Tech R&D Program of China(863 Program)(SS2014AA110303)the Science Foundation for Post-doctoral Scientists of Jiangsu Province(1301011A)
文摘A kind of multiple attribute group decision making (MAGDM) problem is discussed from the perspective of statistic decision-making. Firstly, on the basis of the stability theory, a new idea is proposed to solve this kind of problem. Secondly, a con- crete method corresponding to this kind of problem is proposed. The main tool of our research is the technique o~ the jackknife method. The main advantage of the new method is that it can identify and determine the reliability degree of the existed decision making information. Finally, a traffic engineering example is given to show the effectiveness of the new method.
基金supported by the National Natural Science Foundation of China(61273275)
文摘Uncertain and hesitant information, widely existing in the real-world qualitative decision making problems, brings great challenges to decision makers. Hesitant fuzzy linguistic term sets(HFLTSs), an effective linguistic computational tool in modeling and eliciting such information, have hence aroused many scholars’ interests and some extensions have been introduced recently.However, these methods are based on the discrete linguistic term framework with the limited expression domain, which actually depict qualitative information using several single values. Therefore,it is hard to ensure the integrity of the semantics representation and the accuracy of the computation results. To deal with this problem, a semantics basis framework called complete linguistic term set(CLTS) is designed, which adopts a separation structure of linguistic scale and expression domain, enriching semantics representation of decision makers. On this basis the concept of fuzzy interval linguistic sets(FILSs) is put forward that employs the interval linguistic term with probability to increase the flexibility of eliciting and representing uncertain and hesitant qualitative information. For practical applications, a fuzzy interval linguistic technique for order preference by similarity to ideal solution(FILTOPSIS) method is developed to deal with multi-attribute group decision making(MAGDM) problems. Through the cases of movie and enterprise resource planning(ERP) system selection, the effectiveness and validity of the proposed method are illustrated.
基金This work was supported by the Natural Science Foundation of Liaoning Province(2013020022).
文摘A method is proposed to deal with the uncertain multiple attribute group decision making problems,where 2-dimension uncertain linguistic variables(2DULVs)are used as the reliable way for the experts to express their fuzzy subjective evaluation information.Firstly,in order to measure the 2DULVs more accurately,a new method is proposed to compare two 2DULVs,called a score function,while a new function is defined to measure the distance between two 2DULVs.Secondly,two optimization models are established to determine the weight of experts and attributes based on the new distance formula and a weighted average operator is used to determine the comprehensive evaluation value of each alternative.Then,a score function is used to determine the ranking of the alternatives.Finally,the effectiveness of the proposed method is proved by an illustrated example.
文摘Given that the classical performance evaluation models can not deal with the group decision making problems since they simply average the index,we propose an enterprise knowledge management evaluation model based on multiple attribute group decision making (MAGDM). Find the differences between Ordered Weighted Averaging (OWA) and methods for uncertain decision making. Also,analyze the multiple attribute group decision making process and implement the algorithm. Finally,apply the method on performance evaluation of four enterprises and make sensitivity analysis towards the evaluation results.
文摘The Paraconsistent Many-Valued Similarity (PMVS) method for multi-attribute decision making will be incomplete as a decision model if it is not extended to the realm of group decision-making. Therefore, in this article, our primary objective is to show how the paraconsistent many-valued similarity method can be used to solve group decision-making problems involving choice making or ranking of a finite set of decision alternatives. Moreover, since weights are very important parameters in multi-attribute decision-making, we have introduced the Borda rule to calculate the weights of experts and that of every criterion under consideration. To demonstrate how the proposed method works, a numerical example on energy sources of an economy from the points of view of a group of experts is investigated. Further, we compare the results of this new approach with that of fuzzy TOPSIS group decision-making method to illustrate the robustness and effectiveness of the former.
基金supported by the National Natural Science Foundation of China (70571087)the National Science Fund for Distinguished Young Scholars of China (70625005)
文摘Group decision making problems are investigated with uncertain multiplicative linguistic preference relations.An unbalanced multiplicative linguistic label set is introduced,which can be used by the experts to express their linguistic preference information over alternatives.The uncertain linguistic weighted geometric mean operator is utilized to aggregate all the individual uncertain multiplicative linguistic preference relations into a collective one,and then a simple approach is developed to determine the experts' weights by utilizing the consensus degrees among the individual uncertain multiplicative linguistic preference relations and the collective uncertain multiplicative linguistic preference relations.Furthermore,a practical interactive procedure for group decision making is proposed based on uncertain multiplicative linguistic preference relations,in which a possibility degree formula and a complementary matrix are used to rank the given alternatives.Finally,the proposed procedure is applied to solve the group decision making problem of a manufacturing company searching the best global supplier for one of its most critical parts used in assembling process.
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the Key Project of National Natural Science Foundation of China (70631004)the National Natural Science Foundation of China (70771115)
文摘For group decision-making problems with linguistic assessment information, a new method based on two-tuple and WC-OWA operator is proposed, in which the criteria's weights and the decision-makers' preference information might take the form of linguistic grade, or might be between two continuous linguistic grades, or might be linguistic interval, or might be default. In this method, all linguistic values are transformed into two-tuple, and an aggregative decision-making matrix is obtained by using interval operation. The group aggregative values of each criterion on alternatives are computed by using a WC-OWA operator, the aggregative values on alternatives are worked out, and transformed into two-tuple. And the rank of the alternatives is obtained by using the order property of two-tuple. An example shows the feasibility and effectiveness of the proposed method.
基金This project was supported by the National Natural Science Foundation of China (70671050 70471019)the Key Project of Hubei Provincial Department of Education (D200627005).
文摘To study the fuzzy and grey information in the problems of multi-attribute group decision making, the basic concepts of both fuzzy grey numbers and grey interval numbers are given firstly, then a new model of fuzzy grey multi-attribute group decision making based on the theories of fuzzy mathematics and grey system is presented. Furthermore, the grey interval relative degree and deviation degree is defined, and both the optimistic algorithm of the grey interval relational degree and the algorithm of deviation degree minimization for solving this new model are also given. Finally, a decision making example to demonstrate the feasibility and rationality of this new method is given, and the results by using these two algorithms are uniform.
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 the National Natural Science Foundation of China(70771025)Hohai University Central University Special Fund Basic Scientific Research and Operational Costs
文摘The group decision making problem with linguistic pref- erence relations is studied. The concept of additive consistent linguistic preference relation is defined, and then some properties of the additive consistent linguistic preference relation are studied. In order to rank the alternatives in the group decision making with the linguistic preference relations, the weighted average is first utilized to combine the group linguistic preference relations to one linguistic preference relation, and then the transformation function is proposed to transform the linguistic preference relation to the multiplicative preference relation, and thus the Saaty's eigenvec- tor method (EM) of multiplicative preference relation is utilized to rank the alternatives in group decision making with the linguistic preference relations. Finally, an illustrative numerical example is given to verify the proposed method. A comparative study to the linguistic ordered weighted averaging (LOWA) operator method is also demonstrated.
基金supported by National Natural Science Foundation of China (No.70971131, 70901074)
文摘The technique for order performance by similarity to ideal solution (TOPSIS) is one of the major techniques in dealing with multiple criteria decision making (MCDM) problems, and the belief structure (BS) model has been used successfully for uncertain MCDM with incompleteness, impreciseness or ignorance. In this paper, the TOPSIS method with BS model is proposed to solve group belief MCDM problems. Firstly, the group belief MCDM problem is structured as a belief decision matrix in which the judgments of each decision maker are described as BS models, and then the evidential reasoning approach is used for aggregating the multiple decision makers' judgments. Subsequently, the positive and negative ideal belief solutions are defined with the principle of TOPSIS. To measure the separation from ideal solutions, the concept and algorithm of belief distance measure are defined, which can be used for comparing the difference between BS models. Finally, the relative closeness and ranking index are calculated for ranking the alternatives. A numerical example is given to illustrate the proposed method.
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.
文摘Linguistic single-valued neutrosophic set(LSVNS)is a more reliable tool,which is designed to handle the uncertainties of the situations involving the qualitative data.In the present manuscript,we introduce some power aggregation operators(AOs)for the LSVNSs,whose purpose is to diminish the influence of inevitable arguments about the decision-making process.For it,first we develop some averaging power operators,namely,linguistic single-valued neutrosophic(LSVN)power averaging,weighted average,ordered weighted average,and hybrid averaging AOs along with their desirable properties.Further,we extend it to the geometric power AOs for LSVNSs.Based on the proposed work;an approach to solve the group decision-making problems is given along with the numerical example.Finally,a comparative study and the validity tests are present to discuss the reliability of the proposed operators.