Intelligent wars can take place not only in the physical domain and information domain but also in the cognitive domain.The cognitive domain will become the key domain to win in the future intelligent war.A Lanchester...Intelligent wars can take place not only in the physical domain and information domain but also in the cognitive domain.The cognitive domain will become the key domain to win in the future intelligent war.A Lanchester equation considering cognitive domain is proposed to fit the development tendency intelligent wars in this paper.One party is considered to obtain the exponential enhancement advantage on combat forces in combat if it can gain an advantage in the cognitive domain over the other party according to the systemic advantage function.The operational effectiveness of the cognitive domain in war is considered to consist of a series of indicators.Hesitant fuzzy sets and linguistic term sets are powerful tools when evaluating indicators,hence the indicators are scored by experts using hesitant fuzzy linguistic terms sets here.A unique hesitant fuzzy hybrid arithmetical averaging operator is used to aggregate the evaluation.展开更多
In order to solve the problem of uncertainty and fuzzy information in the process of weapon equipment system selec-tion,a multi-attribute decision-making(MADM)method based on probabilistic hesitant fuzzy set(PHFS)is p...In order to solve the problem of uncertainty and fuzzy information in the process of weapon equipment system selec-tion,a multi-attribute decision-making(MADM)method based on probabilistic hesitant fuzzy set(PHFS)is proposed.Firstly,we introduce the concept of probability and fuzzy entropy to mea-sure the ambiguity,hesitation and uncertainty of probabilistic hesitant fuzzy elements(PHFEs).Sequentially,the expert trust network is constructed,and the importance of each expert in the network can be obtained by calculating the cumulative trust value under multiple trust propagation paths,so as to obtain the expert weight vector.Finally,we put forward an MADM method combining the probabilistic hesitant fuzzy entropy and grey rela-tion analysis(GRA)model,and an illustrative case is employed to prove the feasibility and effectiveness of the method when solving the weapon system selection decision-making problem.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
The hesitant fuzzy set(HFS) is an important tool to deal with uncertain and vague information.In equipment system portfolio selection, the index attribute of the equipment system may not be expressed by precise data;i...The hesitant fuzzy set(HFS) is an important tool to deal with uncertain and vague information.In equipment system portfolio selection, the index attribute of the equipment system may not be expressed by precise data;it is usually described by qualitative information and expressed as multiple possible values.We propose a method of equipment system portfolio selection under hesitant fuzzy environment.The hesitant fuzzy element(HFE) is used to describe the index and attribute values of the equipment system.The hesitation degree of HFEs measures the uncertainty of the criterion data of the equipment system.The hesitant fuzzy grey relational analysis(GRA) method is used to evaluate the score of the equipment system, and the improved HFE distance measure is used to fully consider the influence of hesitation degree on the grey correlation degree.Based on the score and hesitation degree of the equipment system,two portfolio selection models of the equipment system and an equipment system portfolio selection case is given to illustrate the application process and effectiveness of the method.展开更多
As a generalization of fuzzy set,hesitant probabilistic fuzzy set and pythagorean triangular fuzzy set have their own unique advantages in describing decision information.As modern socioeconomic decision-making proble...As a generalization of fuzzy set,hesitant probabilistic fuzzy set and pythagorean triangular fuzzy set have their own unique advantages in describing decision information.As modern socioeconomic decision-making problems are becoming more and more complex,it also becomes more and more difficult to appropriately depict decision makers’cognitive information in decision-making process.In order to describe the decision information more comprehensively,we define a pythagorean probabilistic hesitant triangular fuzzy set(PPHTFS)by combining the pythagorean triangular fuzzy set and the probabilistic hesitant fuzzy set.Firstly,the basic operation and scoring function of the pythagorean probabilistic hesitant triangular fuzzy element(PPHTFE)are proposed,and the comparison rule of two PPHTFEs is given.Then,some pythagorean probabilistic hesitant triangular fuzzy aggregation operators are developed,and their properties are also studied.Finally,a multi-attribute decision-making(MADM)model is constructed based on the proposed operators under the pythagorean probabilistic hesitant triangular fuzzy information,and an illustration example is given to demonstrate the practicability and validity of the proposed decision-making method.展开更多
A dynamic hesitant fuzzy linguistic group decisionmaking(DHFLGDM) problem is studied from the perspective of information reliability based on the theory of hesitant fuzzy linguistic term sets(HFLTSs). First, an approa...A dynamic hesitant fuzzy linguistic group decisionmaking(DHFLGDM) problem is studied from the perspective of information reliability based on the theory of hesitant fuzzy linguistic term sets(HFLTSs). First, an approach is applied to transform the dynamic HFLTSs(DHFLTSs) into a set of proportional linguistic terms to eliminate the time dimension. Second, expert reliability is measured by considering both group similarity and degree of certainty, and an optimization method is employed to quantify the linguistic terms by maximizing the group similarity. Third, through computing the attribute stability as well as its reliability, a combination rule which considers both reliability and weight is proposed to aggregate the information, and then the aggregated grade values and degree of stability are used to make a selection. Finally,the application and feasibility of the proposed method are verified through a case study and method comparison.展开更多
基金supported by the National Natural Science Foundation of China (61703426)the National Social Science Foundation of China.
文摘Intelligent wars can take place not only in the physical domain and information domain but also in the cognitive domain.The cognitive domain will become the key domain to win in the future intelligent war.A Lanchester equation considering cognitive domain is proposed to fit the development tendency intelligent wars in this paper.One party is considered to obtain the exponential enhancement advantage on combat forces in combat if it can gain an advantage in the cognitive domain over the other party according to the systemic advantage function.The operational effectiveness of the cognitive domain in war is considered to consist of a series of indicators.Hesitant fuzzy sets and linguistic term sets are powerful tools when evaluating indicators,hence the indicators are scored by experts using hesitant fuzzy linguistic terms sets here.A unique hesitant fuzzy hybrid arithmetical averaging operator is used to aggregate the evaluation.
基金supported by the National Natural Science Foundation of China(71901214).
文摘In order to solve the problem of uncertainty and fuzzy information in the process of weapon equipment system selec-tion,a multi-attribute decision-making(MADM)method based on probabilistic hesitant fuzzy set(PHFS)is proposed.Firstly,we introduce the concept of probability and fuzzy entropy to mea-sure the ambiguity,hesitation and uncertainty of probabilistic hesitant fuzzy elements(PHFEs).Sequentially,the expert trust network is constructed,and the importance of each expert in the network can be obtained by calculating the cumulative trust value under multiple trust propagation paths,so as to obtain the expert weight vector.Finally,we put forward an MADM method combining the probabilistic hesitant fuzzy entropy and grey rela-tion analysis(GRA)model,and an illustrative case is employed to prove the feasibility and effectiveness of the method when solving the weapon system selection decision-making problem.
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supported by the National Natural Science Foundation of China (7190121471690233)。
文摘The hesitant fuzzy set(HFS) is an important tool to deal with uncertain and vague information.In equipment system portfolio selection, the index attribute of the equipment system may not be expressed by precise data;it is usually described by qualitative information and expressed as multiple possible values.We propose a method of equipment system portfolio selection under hesitant fuzzy environment.The hesitant fuzzy element(HFE) is used to describe the index and attribute values of the equipment system.The hesitation degree of HFEs measures the uncertainty of the criterion data of the equipment system.The hesitant fuzzy grey relational analysis(GRA) method is used to evaluate the score of the equipment system, and the improved HFE distance measure is used to fully consider the influence of hesitation degree on the grey correlation degree.Based on the score and hesitation degree of the equipment system,two portfolio selection models of the equipment system and an equipment system portfolio selection case is given to illustrate the application process and effectiveness of the method.
基金supported by the Key Research and Development Project of Hunan Province(2019SK2331)the Natural Science Foundation of Hunan Province(2019JJ40099,2019JJ40100,2020JJ4339)+2 种基金the Key Scientific Research Project of Hunan Education Department(18A317,19A202)the Scientific Research Fund of Hunan Provincial Education Department(20B272)the Innovation Foundation for Postgraduate of Hunan Institute of Science and Technology(YCX2020A34).
文摘As a generalization of fuzzy set,hesitant probabilistic fuzzy set and pythagorean triangular fuzzy set have their own unique advantages in describing decision information.As modern socioeconomic decision-making problems are becoming more and more complex,it also becomes more and more difficult to appropriately depict decision makers’cognitive information in decision-making process.In order to describe the decision information more comprehensively,we define a pythagorean probabilistic hesitant triangular fuzzy set(PPHTFS)by combining the pythagorean triangular fuzzy set and the probabilistic hesitant fuzzy set.Firstly,the basic operation and scoring function of the pythagorean probabilistic hesitant triangular fuzzy element(PPHTFE)are proposed,and the comparison rule of two PPHTFEs is given.Then,some pythagorean probabilistic hesitant triangular fuzzy aggregation operators are developed,and their properties are also studied.Finally,a multi-attribute decision-making(MADM)model is constructed based on the proposed operators under the pythagorean probabilistic hesitant triangular fuzzy information,and an illustration example is given to demonstrate the practicability and validity of the proposed decision-making method.
基金supported by the National Natural Science Foundation of China(71171112 71502073+2 种基金 71601002)the Scientific Innovation Research of College Graduates in Jiangsu Province(KYZZ150094)the Anhui Provincial Natural Science Foundation(1708085MG168)
文摘A dynamic hesitant fuzzy linguistic group decisionmaking(DHFLGDM) problem is studied from the perspective of information reliability based on the theory of hesitant fuzzy linguistic term sets(HFLTSs). First, an approach is applied to transform the dynamic HFLTSs(DHFLTSs) into a set of proportional linguistic terms to eliminate the time dimension. Second, expert reliability is measured by considering both group similarity and degree of certainty, and an optimization method is employed to quantify the linguistic terms by maximizing the group similarity. Third, through computing the attribute stability as well as its reliability, a combination rule which considers both reliability and weight is proposed to aggregate the information, and then the aggregated grade values and degree of stability are used to make a selection. Finally,the application and feasibility of the proposed method are verified through a case study and method comparison.
