带模糊约束的最大流问题

首次提出带模糊约束的最大流问题，并根据网络中的弧容量限制是否带有模糊性，分别建立数学模型，给出求解这两个模型的相应算法和有关实例。     

Extended use of the cards procedure as a simple elicitation technique for MAVT. Application to public procurement in Switzerland

The cards procedure was designed in the early 90 as a simple way to elicit weights for multiple criteria decision analysis outranking methods. It is based on the elicitation of the difference of importance between successive pairs of criteria. We propose to extend its use in two directions:     

A hybrid neuro-fuzzy analytical approach to mode choice of global logistics management

This paper presents a hybrid neuro-fuzzy methodology to identify appropriate global logistics (GL) operational modes used for global supply chain management. The proposed methodological framework includes three main developmental phases: (1) establishment of a GL strategic hierarchy, (2) formulation of GL-mode identification rules, and (3) development of a GL-mode choice model. By integrating advanced multi-criteria decision-making (MCDM) techniques including fuzzy analytical hierarchy process (Fuzzy-AHP), Fuzzy-MCDM, and the technique for order preference by similarity to an ideal solution (TOPSIS), six types of global logistics and operational modes coupled with corresponding fuzzy-based multi-criteria decision-making rules are specified in the second phase. Using the specified fuzzy decision-making rules as the input database, an adaptive neuro-fuzzy inference system (ANFIS) is then developed in the third phase to identify proper GL modes for the implementation of global supply chain management. A numerical study with a questionnaire survey database aimed at the information technology (IT) industries of Taiwan is conducted to illustrate the applicability of the proposed method.     

A class of dual fuzzy dynamic programs

In this paper we propose a large class of fuzzy dynamic programs. By use of the notion of dual binary relation we define a dual fuzzy dynamic program in the class. We establish two duality theorems between primal and dual fuzzy dynamic programs. One is for the two-parametric recursive equations. The other is for the nonparametric. We specify maximum–minimum process and minimum–minimum process in fuzzy environment and multiplicative–multiplicative process in quasi-stochastic environment. It is shown that the duality theorems hold between primal and dual programs.     

Research on two different mathematical theories on control

With a brand-new theory, this paper not only provides the differences of attributes in concept, formula expression and function type between fuzzy rough sets and probability statistics, but also introduces their differences in algorithms on target control for better solving the control problem. Some new definitions and theorems concerning fuzzy rough sets and probability statistics are given, but this paper mainly makes a comparison of two control algorithms for the target tracking. The simulation results show that the comprehensive performance of the fuzzy rough sets algorithm is better than that of the probability statistics algorithm, but its control effect is not as good as that of the latter on multisensor target control. Finally, some problems concerning the combination of fuzzy rough sets and the probability statistics phenomenon to be solved and development trends are discussed. By these investigations, we can choose the optimal control algorithms for accomplishing better target control.     

A practical prioritization by multi-level group decision support

Military capability is proposed to be defined according to the DYNPOT scoring method. Multiobjective resource allocation of shared resources by group decision-making can combine analytic and qualitative modeling. Recently it has been pointed out that the goal programming model is superior to other models though it remained to be answered how to take into account hierarchy of decision makers (and objectives) (Stummer and Vetschera in Cent Eur J Oper Res 11:3–260, 2003). In this article it is tried to present, that the quantitative model can be easily adapted to the qualitative STT/QFD model of objectives of top-level group of decision-makers. The subsequent phases of the qualitative and the analytic solution of a multiobjective cooperative resource allocation problem can be applied within the group decision-making framework of defence requirements capability-based planning.     

Linguistic quantifiers based on Choquet integrals

The introduction of linguistic quantifiers has provided an important tool to model a large number of issues in intelligent systems. Ying [M.S. Ying, Linguistic quantifiers modeled by Sugeno integrals, Artificial Intelligence 170 (2006) 581–606] recently introduced a new framework for modeling quantifiers in natural languages in which each linguistic quantifier is represented by a family of fuzzy measures, and the truth value of a quantified proposition is evaluated by using Sugeno’s integral. Representing linguistic quantifiers by fuzzy measures, this paper evaluates linguistic quantified propositions by the Choquet integral. Some elegant logical properties of linguistic quantifiers are derived within this approach, including a prenex normal form theorem stronger than that in Ying’s model. In addition, our Choquet integral approach to the evaluation of quantified statements is compared with others, in particular with Ying’s Sugeno integral approach.     

An envelope theorem and some applications to discounted Markov decision processes

In this paper, an Envelope Theorem (ET) will be established for optimization problems on Euclidean spaces. In general, the Envelope Theorems permit analyzing an optimization problem and giving the solution by means of differentiability techniques. The ET will be presented in two versions. One of them uses concavity assumptions, whereas the other one does not require such kind of assumptions. Thereafter, the ET established will be applied to the Markov Decision Processes (MDPs) on Euclidean spaces, discounted and with infinite horizon. As the first application, several examples (including some economic models) of discounted MDPs for which the et allows to determine the value iteration functions will be presented. This will permit to obtain the corresponding optimal value functions and the optimal policies. As the second application of the ET, it will be proved that under differentiability conditions in the transition law, in the reward function, and the noise of the system, the value function and the optimal policy of the problem are differentiable with respect to the state of the system. Besides, various examples to illustrate these differentiability conditions will be provided. This work was partially supported by Benemérita Universidad Aut ónoma de Puebla (BUAP) under grant VIEP-BUAP 38/EXC/06-G, by Consejo Nacional de Ciencia y Tecnología (CONACYT), and by Evaluation-orientation de la COopération Scientifique (ECOS) under grant CONACyT-ECOS M06-M01.     

A new methodology for crisp equivalent of fuzzy chance constrained programming problem

This paper deals with a chance constrained programming model, where both fuzziness and randomness are present in the objective function and constraints. The concept of fuzzy random variable, mean and variance of fuzzy random variable, minimum of fuzzy numbers are used in the model. The methodology is verified through a numerical example.