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Game theory is a powerful tool in modeling actual decision-making problems. In many cases, it is difficult for players to give a crisp value of payoff. To conquer this issue, various extensions of fuzzy sets have been introduced to represent the payoffs. Although type-2 intuitionistic fuzzy (T2IF) set (T2IFS) can solve the game problem effectively, sometimes players prefer to give the primary (secondary) membership and non-membership degrees with some approximate ranges rather than crisp values. T2IFS cannot express such uncertain payoffs. Thus, this paper initiates a new concept called type-2 interval-valued intuitionistic fuzzy (T2IVIF) set (T2IVIFS) which has stronger ability than T2IFS and interval-valued intuitionistic fuzzy set (IVIFS) in representing uncertain information. Hamacher operations of T2IVIFSs are given. Hamming and Euclidean distances between T2IVIFSs are defined respectively. Some Hamacher aggregation operators for T2IVIFSs are developed and some desirable properties are analyzed. Afterwards, an effective method is proposed for solving T2IVIF matrix game, which can make game results more accurate and reliable. An example of new energy vehicle industry development is provided to validate the proposed T2IVIF matrix game. Comparative analyses reveal that the matrix game in T2IVIF environment has better flexibility and reliability than that in T2IF and IVIF environments. [ABSTRACT FROM AUTHOR]

Best-worst method (BWM) has received extensive attention because of its fewer pairwise comparisons and maintenance of consistency. Extending it to various fuzzy environments has become a hot research spot. This paper initiates a new interval-valued intuitionistic fuzzy (IVIF) BWM with additive consistency. Firstly, an IVIF fuzzy preference relation (IVIFPR) is viewed as a directed graph with IVIF weights. An approach is offered to distinguish the best and worst criteria by the defined score out-degree and accuracy out-degree of criteria. The concept of IVIF reference comparisons is introduced. The additive consistency of IVIF reference comparisons is acquired by that of IVIFPR using its left and right intuitionistic fuzzy preference relations. We derive the relationship between the IVIF reference comparisons and the IVIF priority weight vector. Based on this relationship, a linear goal programming model is constructed to generate the IVIF priority weights. Two consistency indexes are analytically obtained and the consistency ratio is then defined to check the consistency of IVIF reference comparisons. For the unacceptably additive consistency, a new approach is put forward to enhance the consistency. Thereby, the proposed IVIF BWM is summarized step by step. Three examples of applications are furnished to demonstrate its effectiveness and validation. [ABSTRACT FROM AUTHOR]

Intuitionistic multiplicative preference relation (IMPR) is an efficient tool for describing the paired comparisons between objectives in group decision making (GDM). Existing GDM methods with IMPRs overlook the hesitancy of IMPRs and lack a feedback mechanism of adjustment in the consensus reaching process (CRP). Thus, to ensure that the adjusted IMPRs can provide reliable information for decision making, the hesitancy measure for IMPRs is first incorporated into the process of enhancing consistency and consensus. A new consistency index for IMPRs is defined based on distance measure. Some goal programming models are constructed for enhancing consistency of IMPR. For a collection of IMPRs with unacceptable consistency and consensus, based on the optimization model and the identification rule and direction rule (IR-DR), an interactive iterative algorithm is designed for enhancing consistency and consensus, which can greatly save the completion time of consensus reaching and maintain primitive information to the maximum. Subsequently, a distance-based aggregation model is constructed to derive the group IMPR by considering different experts' decision-making principles. Thereby, a new GDM method with IMPRs considering minimum adjustment is proposed. Moreover, the rationality and effectiveness of the proposed method are verified through a numerical example and some related simulation experiments. Meanwhile its merits are illustrated by comparison analyses. [ABSTRACT FROM AUTHOR]

The fuzzy linear program has various applications in knapsack problem, investment problem, capital budgeting problem, and transportation problem, etc. Considering the acceptance degree of decision maker that the fuzzy constraints may be violated, this paper develops a new method for the fuzzy linear program in which all the objective coefficients, technological coefficients and resources are trapezoidal fuzzy numbers (TrFNs). The order relationship for TrFNs is firstly given by using the interval expectation of TrFNs. According to the order relationship of TrFNs, the trapezoidal fuzzy linear program is transformed into the interval objective program. Combined with the ranking order relation between intervals and the acceptance degree of fuzzy constraints violated, the interval objective program is further transformed into the bi-objective linear program which is solved by the proposed goal programming approach. The proposed method of this paper is not only mathematically rigorous, but also can sufficiently consider the acceptance degree of the fuzzy constraints violated. The effectiveness and superiority of the proposed method are verified with a fuzzy knapsack problem and an investment problem. Finally, a decision support system is developed for the proposed method. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to propose a new approach to interactive multi-attribute group decision making with triangular Atanassov's intuitionistic fuzzy numbers (TAIFNs). The contribution of this study is fivefold: (1) Minkowski distance between TAIFNs is firstly defined; (2) We define the possibility attitudinal expected values of TAIFNs and thereby present a novel risk attitudinal ranking method of TAIFNs which can sufficiently consider the risk attitude of decision maker; (3) The weighted average operator (TAIFWA) and generalized ordered weighted average (TAIFGWA) operator of TAIFNs are defined as well as the hybrid ordered weighted average (TAIFHOWA) operator; (4) To study the interaction between attributes, we further develop the generalized Choquet (TAIF-GC) integral operator and generalized hybrid Choquet (TAIF-GHC) integral operator of TAIFNs. Their desirable properties are also discussed; (5) The individual overall value of alternative is obtained by TAIF-GC operator and the collective one is derived through TAIFWA operator. Fuzzy measures of attribute subsets and expert weights are objectively derived through constructing multi-objective optimization model which is transformed into the goal programming model to solve. The system analyst selection example verifies effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

As an important component of group decision making, the hybrid multi-criteria group decision making (MCGDM) is very complex and interesting in real applications. The purpose of this paper is to develop a novel interval-valued intuitionistic fuzzy (IVIF) mathematical programming method for hybrid MCGDM considering alternative comparisons with hesitancy degrees. The subjective preference relations between alternatives given by each decision maker (DM) are formulated as an IVIF set (IVIFS). The IVIFSs, intuitionistic fuzzy sets (IFSs), trapezoidal fuzzy numbers (TrFNs), linguistic variables, intervals and real numbers are used to represent the multiple types of criteria values. The information of criteria weights is incomplete. The IVIFS-type consistency and inconsistency indices are defined through considering the fuzzy positive and negative ideal solutions simultaneously. To determine the criteria weights, we construct a novel bi-objective IVIF mathematical programming of minimizing the inconsistency index and meanwhile maximizing the consistency index, which is solved by the technically developed linear goal programming approach. The individual ranking order of alternatives furnished by each DM is subsequently obtained according to the comprehensive relative closeness degrees of alternatives to the fuzzy positive ideal solution. The collective ranking order of alternatives is derived through establishing a new multi-objective assignment model. A real example of critical infrastructure evaluation is provided to demonstrate the applicability and effectiveness of this method. [ABSTRACT FROM AUTHOR]

Abstract: Fuzzy linear programming with trapezoidal fuzzy numbers (TrFNs) is considered and a new method is developed to solve it. In this method, TrFNs are used to capture imprecise or uncertain information for the imprecise objective coefficients and/or the imprecise technological coefficients and/or available resources. The auxiliary multi-objective programming is constructed to solve the corresponding possibility linear programming with TrFNs. The auxiliary multi-objective programming involves four objectives: minimizing the left spread, maximizing the right spread, maximizing the left endpoint of the mode and maximizing the middle point of the mode. Three approaches are proposed to solve the constructed auxiliary multi-objective programming, including optimistic approach, pessimistic approach and linear sum approach based on membership function. An investment example and a transportation problem are presented to demonstrate the implementation process of this method. The comparison analysis shows that the fuzzy linear programming with TrFNs developed in this paper generalizes the possibility linear programming with triangular fuzzy numbers. [Copyright &y& Elsevier]

This paper abstracts the complex heterogeneous multi-attribute group decision-making (CHMAGDM) characterized by two-layer decision-makers (DMs), individual attribute sets, complex relationships among attributes and heterogeneous evaluation information. DMs are composed by internal decision-makers (IDMs) and external decision-makers (EDMs). The evaluation information is represented by linguistic variables (LVs), intervals and real numbers. To handle such CHMAGDM, this paper puts forward an integrated method of prospect theory, DEMATEL (decision-making trial and evaluation laboratory) and QUALIFLEX (qualitative flexible). Firstly, a novel reference point determining approach is proposed based on three special indicators. A linguistic variable inverse prospect value function is designed and introduced to the transformation process from LVs to clouds to reduce the impacts of DMs' psychological behaviors on decision-making. Secondly, a cloud-based DEMATEL approach is proposed to determine the attribute weights, where LVs are employed to judge the relationships among attributes. A new linguistic scale function is initiated and introduced to another transformation process from clouds to LVs. A representative indicator of cloud is designed for facilitating the normalization of direct relation matrix. Moreover, a linear programming model is built to calculate the attribute weights. Thirdly, an extended QUALIFLEX approach is developed to obtain the optimal ranking and EDM weights, where adoption coefficient is provided by IDMs. Another linear programming model is constructed to calculate the optimal collective concordance/discordance index of each permutation. The optimal ranking is generated by the maximum collective concordance/discordance index. Finally, a photovoltaic power station site selection example validates the proposed method. The advantages are demonstrated with sensitivity and comparison analyses. [ABSTRACT FROM AUTHOR]

This paper aims to develop a Fermatean fuzzy ELECTRE method for solving multi-criteria group decision-making problems with unknown weights of decision makers and incomplete weights of criteria. First, a new distance measure between Fermatean fuzzy sets is proposed based on the Jensen–Shannon divergence. The cross entropy for Fermatean fuzzy sets is defined. Three kinds of dominance relationships for Fermatean fuzzy sets are proposed. Then, two optimization models are constructed to obtain positive ideal decision-making information and negative ideal decision-making information, respectively. Accordingly, the credibility degree of each decision maker is calculated. Decision makers' dynamic weights are determined by their credibility degrees. Besides, to obtain the weights of criteria, an optimization model is constructed based on grey relational analysis for Fermatean fuzzy numbers. Finally, the strong, medium and weak Fermatean fuzzy concordance and discordance sets are identified to construct the Fermatean fuzzy concordance and discordance matrices, respectively. A practical case study is carried out to illustrate the feasibility and applicability of the proposed ELECTRE method. Comparative analyses are performed to demonstrate the superiority and effectiveness of the proposed ELECTRE method. [ABSTRACT FROM AUTHOR]

This paper presents a new consistency definition of interval multiplicative preference relation (IMPR). Several desirable properties of this new consistency are fully discussed, and the sufficient and necessary conditions of the new consistency definition are also provided. It is proven that this new consistency of IMPR has robustness and invariance with respect to permutation of the compared objects' labels. Moreover, comparative analyses are conducted to reveal the relationships among five existing consistency definitions and this new consistency definition of IMPR. Based on the new consistency definition of IMPR, a new consistency index is introduced to measure the consistency degree of IMPR. An iterative algorithm is proposed to improve the consistency level of an inconsistent IMPR. Subsequently, a goal programming model is built to derive an interval priority vector from an acceptably consistent IMPR. Eventually, a new individual decision making method with an IMPR is put forward. Numerical examples and simulation analyses are conducted to illustrate the superiority and validity of the proposed individual decision making method. [ABSTRACT FROM AUTHOR]

Battery is the core component of new energy vehicles. The choice of proper battery supplier is crucial for new energy vehicle companies since it directly affects the market share and core competitiveness. Some criteria of battery suppliers cannot be evaluated in the short period and need to be continuously evaluated at different periods (or time). Decision makers (DMs) may present some hesitancy when giving their evaluations. Thus, this paper formulates the battery supplier selection as a type of time-series based multi-criteria large-scale group decision making (LSGDM) with intuitionistic fuzzy information. A novel method is proposed to effectively resolve the battery supplier selection. Firstly, considering the importance of different periods, the comprehensive time weights are determined by combining the exponential decay model and the maximal entropy ordered weighted averaging (OWA) operator weights determining model. Secondly, DMs are divided into different clusters by using the proposed intuitionistic fuzzy Hamming distance-based fuzzy c-means (FCM) algorithm on each criterion. Combining the confidence levels of DMs and the corresponding clustering results, the DMs' weights with respect to each criterion are determined. Then, the comprehensive criteria weights are obtained by integrating the intuitionistic fuzzy entropy and the constructed multi-objective programming model. Thirdly, the individual consensus level and group consensus degree at each period are defined, respectively. Then, a new identification approach is proposed to identify DMs to be adjusted. Subsequently, a total adjustment minimization model is built to adjust these DMs' evaluation information. The optimal alternative is generated according to the collective global overall evaluations. Finally, a real example of batter supplier selection is demonstrated to verify the feasibility and superiority of the proposed method. [ABSTRACT FROM AUTHOR]

This paper aims to develop a new hesitant fuzzy mathematical programming method for hybrid multi-criteria group decision making (MCGDM) with hesitant fuzzy truth degrees and incomplete criteria weight information. In this method, the types of assessment information on criteria are expressed by Atanassov intuitionistic fuzzy sets, hesitant fuzzy sets, trapezoidal fuzzy numbers, intervals and real numbers, respectively. Firstly, the distances of each alternative to positive ideal solution (PIS) and negative ideal solution (NIS) are calculated. Then the hesitant fuzzy positive ideal group consistency index (HFPGCI) and hesitant fuzzy positive ideal group inconsistency index (HFPGICI), the hesitant fuzzy negative ideal group consistency index (HFNGCI) and hesitant fuzzy negative ideal group inconsistency index (HFNGICI) are defined, respectively. To derive the PIS, NIS and the criteria weights simultaneously, a new four-objective hesitant fuzzy mathematical programming model is constructed by minimizing the HFPGICI and HFNGICI as well as maximizing the HFPGCI and HFNGCI. Using the geometric-mean score functions of hesitant fuzzy sets, the four-objective programming model is transformed to a single objective program to resolve. Subsequently, the relative closeness degrees of alternatives for each decision maker (DM) are obtained and applied to derive the individual ranking order of alternatives. To generate the collective ranking order of alternatives, a multi-objective assignment model is established and converted into a single objective programming model to resolve. Thus, a new hesitant fuzzy mathematical programming method is proposed to solve hybrid MCGDM. Finally, a real example is provided to demonstrate the applicability and validity of the proposed method. [ABSTRACT FROM AUTHOR]

Triangular Atanassov's intuitionistic fuzzy number (TAIFN) has better ability to model fuzzy ill-defined quantity. The information aggregation of TAIFNs is of great importance in multi-attribute group decision-making (MAGDM). In this paper, some arithmetic aggregation operators for TAIFNs are defined, with the triangular Atanassov's intuitionistic fuzzy weighted average (TAIFWA) operator, ordered weighted average (TAIFOWA) operator and hybrid weighted average (TAIFHWA) operator included. Then we further investigate the Atanassov's triangular intuitionistic fuzzy generalized ordered weighted average (TAIFGOWA) operator and generalized hybrid weighted average (TAIFGHWA) operator. Some desirable and useful properties of these operators, such as idempotence, monotonicity and boundedness, are also discussed. For the MAGDM with TAIFNs and incomplete attribute weight information, a multi-objective programming model is constructed by minimizing total deviation between all alternatives and fuzzy positive ideal solution, which is transformed into a linear goal programming. Consequently, the attribute weights are objectively derived. Thereby, an innovated MAGDM method is proposed on the basis of the TAIFWA and TAIFGHWA operators. Finally, a green supplier selection example is provided to illuminate the practicability of the proposed method in this paper. [ABSTRACT FROM AUTHOR]

Multi-attribute group decision making (MAGDM) has attracted more and more attention in many fields. Correspondingly, a number of usable methods have been proposed for various MAGDM problems, nevertheless, very few research focus on the aggregation techniques of intuitionistic fuzzy information. The aim of this paper is to aggregate decision information into interval-valued intuitionistic fuzzy numbers (IVIFNs) to solve heterogeneous MAGDM problem in which the decision information involves real numbers, interval numbers, triangular fuzzy numbers (TFNs) and trapezoidal fuzzy numbers (TrFNs). There are three issues being addressed in this paper. The first is to propose a new general method to aggregate the attribute value vector into IVIFNs under heterogeneous MAGDM environment utilizing the relative closeness in technique for order preference by similarity to ideal solution (TOPSIS). The second is to construct a multiple objective intuitionistic fuzzy programming model to determine the attribute weights. Borrowing the results of the former two issues, the last is to present a new method to solve heterogeneous MAGDM problem. A comparison analysis with existing method is conducted to demonstrate the advantages of the proposed method. Two examples are provided to verify the practicality and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

• Trust relationships among recommenders are applied in fusion method. • Personalized individual semantics of trustor and recommenders are considered. • A new definition of harmony degree based on heterogeneous opinions is proposed. • The weights of other recommenders for a recommender are determined from four aspects. • The comprehensive weights of criteria consider subjective and objective information. This paper develops a new trust and personalized individual semantics (PISs) based fusion method for heterogeneous multi-criteria group decision making (HMCGDM) and applies to the selection of live streaming commerce plan. Firstly, a consistency-driven optimization model is built to determine the PIS of linguistic terms in linguistic preference relation of criteria given by the trustor and recommenders. Secondly, this paper defines a harmony degree to reflect the degree of difference in the evaluation information of different recommenders in HMCGDM problem. Then, considering the trust relationship between trustor and recommenders and between the recommenders themselves, two multi-objective mathematical programming models are constructed. One purpose is to produce values to positions that are not assigned, and the other purpose is to fuse the evaluation information of recommenders. In addition, combining the preference information of criteria given by trustor and Shannon entropy based on the collective evaluation information, the subjective and objective weights of criteria can be determined respectively. The comprehensive criteria's weights are acquired by an optimization model which aims at minimizing the Jenson-Shannon divergence between the subjective and objective weights. Finally, an example of selection of influencer or celebrity in live streaming commerce for promoting new products sales is offered to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

• A new definition of distance between PLTSs is proposed. • DM's difference in linguistic terms is reflected by personalized individual semantic. • The CRP (consensus reaching process) considers DMs' willingness. • Construct minimum preference adjustment models to obtain the adjusted PLPRs. • The CL (consensus level) of the adjusted DM is increasing in each adjustment round. This paper develops a new personalized individual semantic (PIS) based consensus reaching process (CRP) for large-scale group decision making (LSGDM) with probabilistic linguistic preference relations (PLPRs) and applies to the selection of COVID-19 surveillance plans. Firstly, considering that a linguistic term means different things to different decision makers (DMs), a new definition of distance between probabilistic linguistic term sets (PLTSs) is defined considering the PIS of a DM. Then, a consistency-driven optimization model is built to determine the PIS of linguistic terms in a PLPR of a DM by maximizing the consistency of a PLPR. DMs' weights can be acquired through a programming model by minimizing the distance between the individual semantic and the collective semantic. Besides, a clustering algorithm based on PIS is devised for dividing DMs into several subgroups with similar semantic. Based on the obtained subgroups, the corresponding moderators can be identified by DMs with unacceptable consensus level (CL). Several minimum preference adjustment models are constructed to obtain the adjusted PLPRs. These models not only can sufficiently consider the willingness of DMs to modify their preferences but also can improve their CLs in CRP. Finally, an illustration example of selection of college COVID-19 surveillance plans is offered to demonstrate the proposed method and to verify the effectiveness of the proposed model. [ABSTRACT FROM AUTHOR]

Abstract: Triangular intuitionistic fuzzy numbers (TIFNs) are a special intuitionistic fuzzy set (IFS) on a real number set, which are very useful for decision makers (DMs) to depict their fuzzy preference information. In this work, we investigate multiple attribute group decision-making (MAGDM) problems in which the ratings of alternatives are expressed with TIFNs, and the weights of the attributes and DMs are completely unknown. Firstly, the crisp weighted possibility mean of TIFNs is defined, and the Hamming distance and Euclidean distance for TIFNs are defined based on Hausdorff distance. The triangular intuitionistic fuzzy weighted average (TIF-WA) operator is developed. Then, the weights of attributes are calculated by applying Shannon entropy measure and the weights of DMs are determined objectively combining the evidence theory with Bayes approximation. The individual decision matrixes for all DMs are aggregated into the group decision matrix by using the TIF-WA operator. Thereby, the classic Vlsekriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method is extended for solving the MAGDM with TIFNs. Finally, the ranking order of alternative is given according to the closeness of alternative with respect to the ideal solution. The personnel selection example verifies the effectiveness of the proposed method. [Copyright &y& Elsevier]

This paper develops an integrated trapezoidal interval type-2 fuzzy (TrIT2F) technique for democratic–autocratic multi-criteria group decision making based on best–worstmethod (BWM) and VIKOR (VIsekriterijumska optimizacija i KOm-promisno Resenje), which is called TrIT2F-BW-VIKOR. In this technique, the pairwise comparisons and evaluations are represented by trapezoidal interval type-2 fuzzy sets (TrIT2FSs). The existing definition of TrIT2FS is perfected by adding two rational constraints proposed in this paper. A weight-normalizing theorem is initiated to normalize the TrIT2F weights. To determine the TrIT2F weights of junior decision makers (JDMs) and criteria, the classical BWM is extended into TrIT2F environment, which is called TrIT2F-BWM. In this TrIT2F-BWM , the weight-normalizing theorem is applied to normalize the TrIT2F weights, a consistency ratio is designed to check the reliability of the obtained TrIT2F weights. Based on the determined weights of JDMs and criteria, an extended VIKOR is developed to rank alternatives. The proposed technique can not only effectively retain the inherent fuzzy information of TrIT2FSs, but also flexibly handle different decision situations. The validity of the proposed technique is demonstrated with a makeshift (fangcang) hospital selection example on COVID-19. Some sensitivity and comparison analyses are provided to show the stability, flexibility, and superiorities of the proposed technique. [ABSTRACT FROM AUTHOR]

Due to the increasing complexity and uncertainty in green supplier selection, there would be some hesitations for decision makers (DMs) to provide evaluation information of suppliers. Hesitant fuzzy set is a suitable tool to model such hesitations. This paper develops a hesitant fuzzy Preference Ranking Organization Method for Enrichment Evaluations (PROMETHEE) for multi-criteria group decision-making and applies to green supplier selection. First, a new hesitancy index of hesitant fuzzy element (HFE) is defined. Then, a generalized hesitant fuzzy Hausdorff distance is proposed considering the individual deviation of membership values and the hesitancy index simultaneously. A combined hesitant fuzzy entropy is presented integrating the defined fuzziness entropy and hesitancy entropy of HFEs. Subsequently, a linear programming model is established to derive DMs' weights objectively. To determine the criteria weights for each DM, a nonlinear programming model is built through minimizing the relative entropy. The PROMETHEE is employed to obtain individual ranking of alternatives for each DM. To obtain the collective ranking of alternatives, a multi-objective assignment model is constructed and transformed into a single-objective assignment model for resolution. Thereby, a hesitant fuzzy PROMETHEE method is presented. A green supplier selection example is demonstrated to validate the proposed method. [ABSTRACT FROM AUTHOR]

In group decision making (GDM) with intuitionistic fuzzy preference relations (IFPRs), the consistency and consensus are two key issues. This paper develops a novel method for checking and improving the consistency of individual IFPRs and the consensus among experts. To measure the consistency degree of IFPRs, a consistency index is introduced and then an acceptable consistency is defined. For an IFPR with unacceptable consistency, a mathematical programming approach is developed to improve its consistency. To evaluate the consensus degree among experts, a consensus measure is presented by the proximity degree between one expert and other experts. When several individual IFPRs are unacceptable consistent or consensus is unacceptable, a goal program is built to improve the consistency and consensus simultaneously. By the consistency and proximity degrees of individual IFPRs, experts’ objective weights are determined. Combining the experts’ subjective weights, the experts’ comprehensive weights are derived. Then, an intuitionistic fuzzy geometric weighted mean (IFGWM) operator is proposed to integrate individual IFPRs into a collective one. Moreover, an attractive property is proved that the collective IFPR is acceptable consistent if all individual IFPRs are acceptable consistent. Two examples are provided to illustrate the validity of the proposed method. [ABSTRACT FROM AUTHOR]

In order to reduce costs and enhance their core competitiveness, many companies tend to choose the logistics outsourcing. The selection of logistics outsourcing provider plays an important role for the success of outsourcing. In this paper, we formulate the logistics outsourcing provider selection as a kind of group decision making (GDM) problems with intuitionistic fuzzy preference relations (IFPRs). A new intuitionistic fuzzy linear programming method is proposed for solving such problems. First, we construct an intuitionistic fuzzy linear programming model to derive priority weights from IFPRs. Depended on the construction of non-membership functions, this intuitionistic fuzzy linear programming model is solved by the developed three kinds of approaches including the optimistic, pessimistic and mixed approaches. Then by the idea of TOPSIS (technique for order preference by similarity to ideal solution), the experts’ weights are determined objectively. Combining the experts’ weights with the derived priority weights, the corresponding method for GDM with IFPRs is presented. An example of logistics outsourcing provider selection is provided to illustrate the proposed method. Finally, the intuitionistic fuzzy programming method is further generalized to the case of more general membership and non-membership functions. [ABSTRACT FROM AUTHOR]