Fuzzy Bi-level Decision-Making Techniques: A Survey <s> F(R) is the set of all finite fuzzy numbers. The sets X and Y place additional restrictions on the decision variables, such as upper and lower bounds or integrality requirements <s> In order to model fuzzy decentralized decision-making problem, fuzzy expected value multilevel programming and chance-constrained multilevel programming are introduced. Furthermore, fuzzy simulation, neural network, and genetic algorithm are integrated to produce a hybrid intelligent algorithm for finding the Stackelberg-Nash equilibrium. Finally, two numerical examples are provided to illustrate the effectiveness of the hybrid intelligent algorithm. <s> BIB001 </s> Fuzzy Bi-level Decision-Making Techniques: A Survey <s> F(R) is the set of all finite fuzzy numbers. The sets X and Y place additional restrictions on the decision variables, such as upper and lower bounds or integrality requirements <s> Basic bilevel programming deals with hierarchical optimization problems in which the leader at the upper level attempts to optimize his/her objective, subject to a set of constraints and his/her follower's solution, and the follower at the lower level tries to find an optimized strategy according to each of possible decisions made by the leader. Three issues may be involved in a basic bilevel decision problem. One is that bilevel decision making model may involve uncertain parameters which appear either in the objective functions or constraints of the leader or the follower or both. Second, the leader and the follower may have multiple conflict objectives that should be optimized simultaneously. Third, there may have multiple followers in a real decision situation. Following our previous work, this study proposes a set of fuzzy multi-objective multi-follower linear bilevel programming models to describe the three issues. It also develops an approximation branch-and-bound algorithm to solve such kinds of problems. <s> BIB002 </s> Fuzzy Bi-level Decision-Making Techniques: A Survey <s> F(R) is the set of all finite fuzzy numbers. The sets X and Y place additional restrictions on the decision variables, such as upper and lower bounds or integrality requirements <s> A bilevel decision problem may have multiple followers as the lower decision units and have fuzzy demands simultaneously. This paper focuses on problems of fuzzy linear bilevel decision making with multiple followers who share a common objective but have different constraints (FBOSF). Based on the ranking relationship among fuzzy sets defined by cut set and satisfactory degree, a FBOSF model is presented and a particle swarm optimization based algorithm is developed. <s> BIB003 </s> Fuzzy Bi-level Decision-Making Techniques: A Survey <s> F(R) is the set of all finite fuzzy numbers. The sets X and Y place additional restrictions on the decision variables, such as upper and lower bounds or integrality requirements <s> In a bilevel decision problem, both the leader and the follower may have multiple objectives to optimize under certain constraints. In the meantime, these objective functions and constraints may contain some uncertain parameters. In addition, there may have multiple followers involved in a bilevel decision problem. These followers may share their individual decision variables with each other but keep individual objectives in reacting any of the leader's decisions, which is a common situation in real bilevel decision activities. This study deals with all above three issues, fuzzy parameters, multi-objectives, and multi-followers in a partial cooperative situation, at the same time. After a set of models for describing different cases of the fuzzy multi-objective multi-follower bilevel programming with partial cooperation (FMMBP-PC) problem, this paper develops an approximation branch-and-bound algorithm to solve this problem. <s> BIB004 </s> Fuzzy Bi-level Decision-Making Techniques: A Survey <s> F(R) is the set of all finite fuzzy numbers. The sets X and Y place additional restrictions on the decision variables, such as upper and lower bounds or integrality requirements <s> Bilevel programming deals with hierarchical optimization problems in which the leader at the upper level attempts to optimize his or her objectives, but subject to a set of constraints and the follower's reactions. Typical bilevel programming considers one leader one follower situation and supposes each of them has only one objective. In real world situations, multiple followers may be involved and they may be with different relationships such as sharing decision variables or not, sharing objectives or not. Therefore, the leader's decision will be affected not only by those followers' reactions but also by their relationships. In addition, any of the leader and/or these followers may have multiple conflict objectives that should be optimized simultaneously. Furthermore, the parameters of a bilevel programming model may be described by uncertain values. This paper addresses all these three issues as a whole by particularly focusing on the situation of sharing decision variables among followers. It first proposes a set of fuzzy multi-objective multi-follower bilevel programming (FMMBP) models to describe the complex issue. It then presents an approximation branch-and-bound algorithm to solve the FMMBP problems. Finally, two examples illustrate the proposed models and algorithm. <s> BIB005 </s> Fuzzy Bi-level Decision-Making Techniques: A Survey <s> F(R) is the set of all finite fuzzy numbers. The sets X and Y place additional restrictions on the decision variables, such as upper and lower bounds or integrality requirements <s> In a bilevel decision problem, decision making may involve multiple followers and fuzzy demands. This research focuses on the problem of fuzzy linear bilevel decision making with multiple followers who share common constraints (FBCSF). Based on the ranking relationship among fuzzy sets defined by cut set and satisfactory degree α, a FBCSF model is presented and a particle swarm optimization based algorithm is developed. The experiments reveal that solutions obtained by this algorithm are reasonable and stable. <s> BIB006 </s> Fuzzy Bi-level Decision-Making Techniques: A Survey <s> F(R) is the set of all finite fuzzy numbers. The sets X and Y place additional restrictions on the decision variables, such as upper and lower bounds or integrality requirements <s> Classic bilevel programming deals with two level hierarchical optimization problems in which the leader attempts to optimize his/her objective, subject to a set of constraints and his/her follower's solution. In modelling a real-world bilevel decision problem, some uncertain coefficients often appear in the objective functions and/or constraints of the leader and/or the follower. Also, the leader and the follower may have multiple conflicting objectives that should be optimized simultaneously. Furthermore, multiple followers may be involved in a decision problem and work cooperatively according to each of the possible decisions made by the leader, but with different objectives and/or constraints. Following our previous work, this study proposes a set of models to describe such fuzzy multi-objective, multi-follower (cooperative) bilevel programming problems. We then develop an approximation Kth-best algorithm to solve the problems. <s> BIB007 </s> Fuzzy Bi-level Decision-Making Techniques: A Survey <s> F(R) is the set of all finite fuzzy numbers. The sets X and Y place additional restrictions on the decision variables, such as upper and lower bounds or integrality requirements <s> paper deals with fuzzy goal programming approach to bi- level multi-objective programming problem with fuzzy parameters. In the proposed approach, the tolerance membership functions for the fuzzily described objective functions are defined by determining individual optimal solution of the objective functions of each of the decision makers. Since the objectives are potentially conflicting in general, possible relaxations of both level decisions are considered by providing preference bounds on the decision variables for avoiding decision deadlock. Then fuzzy goal programming technique is used for achieving highest degree of each of the membership goals by minimizing negative deviational variables. An algorithm is presented with termination criteria. An illustrative numerical example is provided to demonstrate the efficiency of the proposed approach. <s> BIB008 </s> Fuzzy Bi-level Decision-Making Techniques: A Survey <s> F(R) is the set of all finite fuzzy numbers. The sets X and Y place additional restrictions on the decision variables, such as upper and lower bounds or integrality requirements <s> In this paper, a fuzzy goal programming (FGP) algorithm for solving bi-level multi-objective programming problems with fuzzy demands is presented. These fuzzy demands reflect the experts' imprecise or fuzzy understandings of the nature of parameters in the problem formulation process are assumed to be characterized as fuzzy numbers. Using the level sets of fuzzy parameters, the corresponding non fuzzy bi-level programming problem is introduced. In the proposed algorithm, the membership functions for the defined fuzzy goals of all objective functions at the two levels, as well as the membership functions for the vector of decision variables controlled by FLDM are developed in the model formulation of the problem. Then FGP algorithm is used to achieve the highest degree of each of the membership goals by minimizing their deviational variables and thereby obtaining the most satisfactory solution for all decision makers. Illustrative numerical example is given to demonstrate the proposed algorithm. <s> BIB009
Zhang et al.  presented the linear FBLMO decision problem as shown in Definition 2 and developed an approximation Branch-and-Bound (BB) algorithm to solve it. Gao et al.  proposed a λ-cut and goalprogramming-based algorithm to solve the linear FBLMO decision problems as well. Pramanik and Dey BIB008 addressed a fuzzy goal programming approach for solving a linear FBLMO decision problem in which decision entities from different decision levels share the same constraints and prefer to cooperate with one another. Since the fuzzy goal programming approach does not follow the classical solution concepts of bilevel decision-making and neglects the upper-level decisions, Baky et al. BIB009 designed an extended fuzzy goal programming algorithm for solving the FBLMO problem. For FBLMF decision-making, a general linear FBLMF decision problem can be described as Definition 3 based on related research in BIB003 BIB006 .  where, for each x given, y i solves the ith follower's problem (3c-3d) where Gao et al. BIB003 focused on problems of fuzzy linear bilevel decision-making with multiple followers who share a common objective but have different constraints. The authors developed a partial swarm optimization (PSO) algorithm for solving these problem based on the ranking relationship among fuzzy sets defined by cut-set and satisfactory degree. Gao et al. BIB006 also studied a linear FBLMF decision problem in which multiple followers share the common constraints and developed a PSO algorithm to solve the problem. Gao and Liu BIB001 integrated fuzzy simulation, neural network and genetic algorithm to produce a hybrid intelligent algorithm for solving a nonlinear FBLMF problem. In order to solve fuzzy bi-level multi-objective multi-follower (FBLMOMF) decision problems, Zhang et al. BIB002 proposed a set of linear models and developed an extended BB algorithm. Based on it, Zhang et al. BIB004 developed an approximation BB algorithm to solve a linear FBLMOMF decision problem with a partial cooperative relationship between multiple followers. Zhang et al. BIB005 also proposed a set of decision models to describe complex FBLMOMF decision issues and presented an approximation BB algorithm to solve a linear FBLMOMF decision problem in which focusing followers share the same decision variables. Zhang and Lu BIB007 presented an approximation Kth-Best algorithm to solve a linear FBLMOMF decision problem with a cooperative relationship between multiple followers. These developments provide a strong foundation for fuzzy bi-level decision-making techniques in various situations.