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
A new fully fuzzy linear programming （FFLP） problem with fuzzy equality constraints is discussed. Using deviation degree measures, the FFLP problem is transformed into a crisp 6-parametric linear programming （LP） ...A new fully fuzzy linear programming （FFLP） problem with fuzzy equality constraints is discussed. Using deviation degree measures, the FFLP problem is transformed into a crisp 6-parametric linear programming （LP） problem. Giving the value of deviation degree in each constraint, the 6-fuzzy optimal solution of the FFLP problem can be obtained by solving this LP problem. An algorithm is also proposed to find a balance-fuzzy optimal solution between two goals in conflict： to improve the values of the objective function and to decrease the values of the deviation degrees. A numerical example is solved to illustrate the proposed method.展开更多
We give a fuzzy goal programming (L-UFGP).Definition 1 Let X(?)E_n,A is called a generalized fuzzy set on E_n with respect toX iff (?)(x)∈[0,1] for x∈X and (?)(x)∈E_1 for x∈E_n\X.Definition 2 Let i∈(1,...,p),R(?)...We give a fuzzy goal programming (L-UFGP).Definition 1 Let X(?)E_n,A is called a generalized fuzzy set on E_n with respect toX iff (?)(x)∈[0,1] for x∈X and (?)(x)∈E_1 for x∈E_n\X.Definition 2 Let i∈(1,...,p),R(?)E_n,(?)={x∈R|l_i≤f_i(x)≤u_i} and (?)(f_i(x)) be ageneralized fuzzy set on E_n with respect to (?),(?) is called a fuzzy goal set of f_i(x)iff (?)(y) is a strictly increasing function on E_(?) and (?)(l_i)=0,(?)(u_i)=1.Here l_i iscalled a lower goal of f_i(x) and u_i is called an upper goal of f_i(x).展开更多
The conventional data envelopment analysis （DEA） measures the relative efficiencies of a set of decision making units with exact values of inputs and outputs. In real-world prob- lems, however, inputs and outputs ty...The conventional data envelopment analysis （DEA） measures the relative efficiencies of a set of decision making units with exact values of inputs and outputs. In real-world prob- lems, however, inputs and outputs typically have some levels of fuzziness. To analyze a decision making unit （DMU） with fuzzy input/output data, previous studies provided the fuzzy DEA model and proposed an associated evaluating approach. Nonetheless, numerous deficiencies must still be improved, including the α- cut approaches, types of fuzzy numbers, and ranking techniques. Moreover, a fuzzy sample DMU still cannot be evaluated for the Fuzzy DEA model. Therefore, this paper proposes a fuzzy DEA model based on sample decision making unit （FSDEA）. Five eval- uation approaches and the related algorithm and ranking methods are provided to test the fuzzy sample DMU of the FSDEA model. A numerical experiment is used to demonstrate and compare the results with those obtained using alternative approaches.展开更多
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.
基金supported by the National Natural Science Foundation of China(71202140)the Fundamental Research for the Central Universities(HUST:2013QN099)
文摘A new fully fuzzy linear programming （FFLP） problem with fuzzy equality constraints is discussed. Using deviation degree measures, the FFLP problem is transformed into a crisp 6-parametric linear programming （LP） problem. Giving the value of deviation degree in each constraint, the 6-fuzzy optimal solution of the FFLP problem can be obtained by solving this LP problem. An algorithm is also proposed to find a balance-fuzzy optimal solution between two goals in conflict： to improve the values of the objective function and to decrease the values of the deviation degrees. A numerical example is solved to illustrate the proposed method.
文摘We give a fuzzy goal programming (L-UFGP).Definition 1 Let X(?)E_n,A is called a generalized fuzzy set on E_n with respect toX iff (?)(x)∈[0,1] for x∈X and (?)(x)∈E_1 for x∈E_n\X.Definition 2 Let i∈(1,...,p),R(?)E_n,(?)={x∈R|l_i≤f_i(x)≤u_i} and (?)(f_i(x)) be ageneralized fuzzy set on E_n with respect to (?),(?) is called a fuzzy goal set of f_i(x)iff (?)(y) is a strictly increasing function on E_(?) and (?)(l_i)=0,(?)(u_i)=1.Here l_i iscalled a lower goal of f_i(x) and u_i is called an upper goal of f_i(x).
基金supported by the National Natural Science Foundation of China (70961005)211 Project for Postgraduate Student Program of Inner Mongolia University+1 种基金National Natural Science Foundation of Inner Mongolia (2010Zd342011MS1002)
文摘The conventional data envelopment analysis （DEA） measures the relative efficiencies of a set of decision making units with exact values of inputs and outputs. In real-world prob- lems, however, inputs and outputs typically have some levels of fuzziness. To analyze a decision making unit （DMU） with fuzzy input/output data, previous studies provided the fuzzy DEA model and proposed an associated evaluating approach. Nonetheless, numerous deficiencies must still be improved, including the α- cut approaches, types of fuzzy numbers, and ranking techniques. Moreover, a fuzzy sample DMU still cannot be evaluated for the Fuzzy DEA model. Therefore, this paper proposes a fuzzy DEA model based on sample decision making unit （FSDEA）. Five eval- uation approaches and the related algorithm and ranking methods are provided to test the fuzzy sample DMU of the FSDEA model. A numerical experiment is used to demonstrate and compare the results with those obtained using alternative approaches.
