Further results on the asymptotic agreement problem

The problem of reaching a concensus between two decision-makers provided with different information is considered. The problem in which the decision-makers may have different underlying probability models is studied. Results are developed to characterize the likelihood of an agreement being reached eventually in terms of the nature of the inter-decision-maker communications. The problem in which the decision-makers are aware of the possibility that they may have different models is treated. It is found that in this case a deadlock can be reached where neither decision maker can learn additional information from the concensus process and they cannot reach a concensus decision. This result indicates that incorporating human uncertainty in probability assessment into the asymptotic agreement problem can lead to outcomes not anticipated in the general theory previously developed     

Hybrid multilevel programming with uncertain random parameters

Multilevel programming is developed for modeling decentralized decision-making processes. For different management requirements and risk tolerances of different-level decision-makers, the decision-making criteria applied in different levels cannot be always the same. In this paper, a hybrid multilevel programming model with uncertain random parameters based on expected value model (EVM) and dependent-chance programming (DCP), named as EVM–DCP hybrid multilevel programming, is proposed. The corresponding concepts of Nash equilibrium and Stackelberg–Nash equilibrium are given. For some special case, an equivalent crisp mathematical programming is proposed. An approach integrating uncertain random simulations, Nash equilibrium searching approach and genetic algorithm is designed. Finally, a numerical experiment of uncertain random supply chain pricing decision problem is given.     

模糊环境下的最小权顶点覆盖问题*

最小权顶点覆盖问题在实际决策中应用广泛,但顶点上的权值在实际应用中通常代表费用、成本等,在很多情况下是不确定的。关注了最小权顶点覆盖问题中的模糊不确定性,对模糊环境下的最小权顶点覆盖问题进行了研究。引入了可信性理论以描述模糊不确定性,并根据不同的决策准则建立了求解模糊环境下最小权顶点覆盖问题的三个决策模型,结合模糊模拟和遗传算法设计了一种求解所建立模型的混合智能算法,并给出了数值实验。数值实验的结果验证了所提出的决策模型与算法的有效性。     

Decentralized capacity allocation of a single-facility with fuzzy demand

Capacity allocation under uncertainty environment is an important decision problem in manufacturing. The decentralized capacity allocation of a single-facility among different organizations with fuzzy demand is investigated in this paper. The objective and demand of each organization are assumed to be private information that other organizations and the facility cannot access to. In addition, we assume organizations have limited view of the capacity and loading of the facility. First, fuzzy optimization models associated with each organization and the facility are set up. Then, based on fuzzy theory, the fuzzy optimization models are converted into parametric programming models and subsequently an interactive algorithm is proposed to solve those parametric programming models. The extra benefit of this algorithm is that the whole solving process is amenable to decentralized implementation. Finally, experimental results illustrate the effectiveness of this work under two levels of information sharing: capacity information of the facility unknown to organizations and capacity information of the facility partially known to organizations.     

A survey of decision making methods based on certain hybrid soft set models

Fuzzy set theory, rough set theory and soft set theory are all generic mathematical tools for dealing with uncertainties. There has been some progress concerning practical applications of these theories, especially, the use of these theories in decision making problems. In the present article, we review some decision making methods based on (fuzzy) soft sets, rough soft sets and soft rough sets. In particular, we provide several novel algorithms in decision making problems by combining these kinds of hybrid models. It may be served as a foundation for developing more complicated soft set models in decision making.     

Multiple-attribute group decision making with different formats of preference information on attributes.

Interval utility values, interval fuzzy preference relations, and interval multiplicative preference relations are three common uncertain-preference formats used by decision-makers to provide their preference information in the process of decision making under fuzziness. This paper is devoted in investigating multiple-attribute group-decision-making problems where the attribute values are not precisely known but the value ranges can be obtained, and the decision-makers provide their preference information over attributes by three different uncertain-preference formats i.e., 1) interval utility values; 2) interval fuzzy preference relations; and 3) interval multiplicative preference relations. We first utilize some functions to normalize the uncertain decision matrix and then transform it into an expected decision matrix. We establish a goal-programming model to integrate the expected decision matrix and all three different uncertain-preference formats from which the attribute weights and the overall attribute values of alternatives can be obtained. Then, we use the derived overall attribute values to get the ranking of the given alternatives and to select the best one(s). The model not only can reflect both the subjective considerations of all decision-makers and the objective information but also can avoid losing and distorting the given objective and subjective decision information in the process of information integration. Furthermore, we establish some models to solve the multiple-attribute group-decision-making problems with three different preference formats: 1) utility values; 2) fuzzy preference relations; and 3) multiplicative preference relations. Finally, we illustrate the applicability and effectiveness of the developed models with two practical examples.     

Effects of increasing fuzziness on analytic hierarchy process for spatial multicriteria decision analysis

Multicriteria decision analysis (MCDA) involves techniques which relatively recently have received great increase in interest for their capabilities of solving spatial decision problems. One of the most frequently used techniques of MCDA is Analytic Hierarchy Process (AHP). In the AHP, decision-makers make pairwise comparisons between different criteria to obtain values of their relative importance. The AHP initially only dealt with crisp numbers or exact values in the pairwise comparisons, but later it has been modified and adapted to also consider fuzzy values. It is necessary to empirically validate the ability of the fuzzified AHP for solving spatial problems. Further, the effects of different levels of fuzzification on the method have to be studied. In the context of a hypothetical GIS-based decision-making problem of locating a dam in Costa Rica using real-world data, this paper illustrates and compares the effects of increasing levels of uncertainty exemplified through different levels of fuzzification of the AHP. Practical comparison of the methods in this work, in accordance with the theoretical research, revealed that by increasing the level of uncertainty or fuzziness in the fuzzy AHP, differences between results of the conventional and fuzzy AHPs become more significant. These differences in the results of the methods may affect the final decisions in decision-making processes. This study concludes that the AHP is sensitive to the level of fuzzification and decision-makers should be aware of this sensitivity while using the fuzzy AHP. Furthermore, the methodology described may serve as a guideline on how to perform a sensitivity analysis in spatial MCDA. Depending on the character of criteria weights, i.e. the degree of fuzzification, and its impact on the results of a selected decision rule (e.g. AHP), the results from a fuzzy analysis may be used to produce sensitivity estimates for crisp AHP MCDA methods.     

Uncertain programming models for portfolio selection with uncertain returns

In an indeterminacy economic environment, experts’ knowledge about the returns of securities consists of much uncertainty instead of randomness. This paper discusses portfolio selection problem in uncertain environment in which security returns cannot be well reflected by historical data, but can be evaluated by the experts. In the paper, returns of securities are assumed to be given by uncertain variables. According to various decision criteria, the portfolio selection problem in uncertain environment is formulated as expected-variance-chance model and chance-expected-variance model by using the uncertainty programming. Within the framework of uncertainty theory, for the convenience of solving the models, some crisp equivalents are discussed under different conditions. In addition, a hybrid intelligent algorithm is designed in the paper to provide a general method for solving the new models in general cases. At last, two numerical examples are provided to show the performance and applications of the models and algorithm.     

Hybrid Method of Multicriteria Evaluation of Decision Alternatives

In the paper we develop a hybrid decision support method in case of dependent decision criteria. It includes methods of decision theory, fuzzy sets, mathematical programming and statistics, which are adapted to different stages of the multicriteria evaluation of alternatives depending on the specific problem being solved and on the quality of the input expert information. The use of the hybrid method is illustrated by the solution of practical problems.     

A signed-distance-based approach to importance assessment and multi-criteria group decision analysis based on interval type-2 fuzzy set

Interval type-2 fuzzy sets are associated with greater imprecision and more ambiguities than ordinary fuzzy sets. This paper presents a signed-distance-based method for determining the objective importance of criteria and handling fuzzy, multiple criteria group decision-making problems in a flexible and intelligent way. These advantages arise from the method’s use of interval type-2 trapezoidal fuzzy numbers to represent alternative ratings and the importance of various criteria. An integrated approach to determine the overall importance of the criteria is also developed using the subjective information provided by decision-makers and the objective information delivered by the decision matrix. In addition, a linear programming model is developed to estimate criterion weights and to extend the proposed multiple criteria decision analysis method. Finally, the feasibility and effectiveness of the proposed methods are illustrated by a group decision-making problem of patient-centered medicine in basilar artery occlusion.     

A new method selection approach for fuzzy group multicriteria decision making

Fuzzy multicriteria decision making (MCDM) has been widely used in ranking a finite number of decision alternatives characterized by fuzzy assessments with respect to multiple criteria. In group decision settings, different fuzzy group MCDM methods often produce inconsistent ranking outcomes for the same problem. To address the ranking inconsistency problem in fuzzy group MCDM, this paper develops a new method selection approach for selecting a fuzzy group MCDM method that produces the most preferred group ranking outcome for a given problem. Based on two group averaging methods, three aggregation procedures and three defuzzification methods, 18 fuzzy group MCDM methods are developed as an illustration to solve the general fuzzy MCDM problem that requires cardinal ranking of the decision alternatives. The approach selects the group ranking outcome of a fuzzy MCDM method which has the highest consistency degree with its corresponding ranking outcomes of individual decision makers. An empirical study on the green bus fuel technology selection problem is used to illustrate how the approach works. The approach is applicable to large-scale group multicriteria decision problems where inconsistent ranking outcomes often exist between different fuzzy MCDM methods.     

A new Chance-Variance optimization criterion for portfolio selection in uncertain decision systems

The Markowitz’s mean-variance (M-V) model has received widespread acceptance as a practical tool for portfolio optimization, and his seminal work has been widely extended in the literature. The aim of this article is to extend the M-V method in hybrid decision systems. We suggest a new Chance-Variance (C-V) criterion to model the returns characterized by fuzzy random variables. For this purpose, we develop two types of C-V models for portfolio selection problems in hybrid uncertain decision systems. Type I C-V model is to minimize the variance of total expected return rate subject to chance constraint; while type II C-V model is to maximize the chance of achieving a prescribed return level subject to variance constraint. Hence the two types of C-V models reflect investors’ different attitudes toward risk. The issues about the computation of variance and chance distribution are considered. For general fuzzy random returns, we suggest an approximation method of computing variance and chance distribution so that C-V models can be turned into their approximating models. When the returns are characterized by trapezoidal fuzzy random variables, we employ the variance and chance distribution formulas to turn C-V models into their equivalent stochastic programming problems. Since the equivalent stochastic programming problems include a number of probability distribution functions in their objective and constraint functions, conventional solution methods cannot be used to solve them directly. In this paper, we design a heuristic algorithm to solve them. The developed algorithm combines Monte Carlo (MC) method and particle swarm optimization (PSO) algorithm, in which MC method is used to compute probability distribution functions, and PSO algorithm is used to solve stochastic programming problems. Finally, we present one portfolio selection problem to demonstrate the developed modeling ideas and the effectiveness of the designed algorithm. We also compare the proposed C-V method with M-V one for our portfolio selection problem via numerical experiments.     

A hybrid fuzzy regression-fuzzy cognitive map algorithm for forecasting and optimization of housing market fluctuations

This paper presents a hybrid algorithm based on fuzzy linear regression (FLR) and fuzzy cognitive map (FCM) to deal with the problem of forecasting and optimization of housing market fluctuations. Due to the uncertainty and severe noise associated with the housing market, the application of crisp data for forecasting and optimization purposes is insufficient. Hence, in order to enable the decision-makers to make decisions with respect to imprecise/fuzzy data, FLR is used in the proposed hybrid algorithm. The best-fitted FLR model is then selected with respect to two indicators including Index of Confidence (IC) and Mean Absolute Percentage Error (MAPE). To achieve this objective, analysis of variance (ANOVA) for a randomized complete block design (RCBD) is employed. The primary objective of this study is to utilize imprecise/fuzzy data in order to improve the analysis of housing price fluctuations, in accordance with the factors obtained through the best-fitted FLR model. The secondary objective of this study is the exhibition of the resulted values in a schematic way via FCM. Hybridization of FLR and FCM provides a decision support system (DSS) for utilization of historical data to predict housing market fluctuation in the future and identify the influence of the other parameters. The proposed hybrid FLR-FCM algorithm enables the decision-makers to utilize imprecise and ambiguous data and represent the resulted values of the model more clearly. This is the first study that utilizes a hybrid intelligent approach for housing price and market forecasting and optimization.     

Multiple attribute group decision-making methods with unknown weights in intuitionistic fuzzy setting and interval-valued intuitionistic fuzzy setting

To better solve the corresponding multiple attribute group decision-making problem with unknown weights, multiple attribute group decision-making methods with completely unknown weights of decision-makers and incompletely known weights of attributes are proposed in intuitionistic fuzzy setting and interval-valued intuitionistic fuzzy setting. In the group decision-making method, two weight models are proposed based on the score function to determine the weights of both experts and attributes from the intuitionistic fuzzy decision matrices and the interval-valued intuitionistic fuzzy decision matrices. Then, overall evaluation formulas of weighted scores for each alternative are introduced in the intuitionistic fuzzy setting and the interval-valued intuitionistic fuzzy setting to obtain the ranking order of alternatives and the most desirable one(s). Finally, two numerical examples demonstrate the applicability and benefit of the proposed methods.     

基于决策者信任度的风险型混合多属性群决策方法

考虑决策者对风险型混合多属性评价结果的信任程度不同, 提出基于前景理论和改进投影理论的群决策方法. 建立一个数组以描述在不同信任度下群决策专家的评价结果, 并将数组中混合数据类型转化为三角模糊数. 在考虑决策者信任度的前提下集结群信息、确定属性权重. 引入综合前景价值和考虑权重的投影相对接近度两种方法对方案进行排序. 最后通过实例表明了所提出方法的合理性和有效性.

     

犹豫模糊语言PROMETHEE方法在川酒品牌评价中的应用

基于犹豫模糊语言集理论,提出一种犹豫模糊语言信息环境下的PROMETHEE多属性决策方法,并应用于川酒品牌评价决策问题中.研究表明,犹豫模糊语言集能够很好地描述和处理复杂定性信息环境下的川酒品牌评价与决策问题;所提出的犹豫模糊语言PROMETHEE算法简便, 且改进的偏好函数允许决策者根据其对方案的严格优于偏好对参数进行选择,可保证决策过程的科学性和决策结果的准确性.     

Continuous review inventory models with a mixture of backorders and lost sales under fuzzy demand and different decision situations

In this paper, continuous review inventory models in which a fraction of demand is backordered and the remaining fraction is lost during the stock out period are considered under fuzzy demands. In order to find the optimal decision under different situations, two decision methods are proposed. The first one is finding a minimum value of the expected annual total cost, and the second one is maximizing the credibility of an event that the total cost in the planning periods does not exceed a certain budget level. For the first decision method, an approach of ranking fuzzy numbers by their possibilistic mean value is adopted to achieve the optimal solution. For the second one, the technique of fuzzy simulation and differential evolution algorithms are integrated to design hybrid intelligent algorithms to solve the fuzzy models. Subsequently, the two decision models are compared and some advices about inventory cash flow management are given. Further, sensitivity analysis is conducted to give more general situations to illustrate the rationality of the management advices.     

Optimal system selection in fuzzy environment

The problem of the selection of an optimal decision from a set of finite number of alternatives is considered, when there is a single or multiple decision-makers present. In the single decision-maker case, the optimal decision is the one that satisfies pre-specified multiple objectives. A method is given to select the optimal decision based on membership grade. However, in the multiple decision-makers case, the problem of arriving at group decision, when each decision-maker gives his preference, has been discussed. Nevertheless, in both the situations decision-makers have the freedom to modulate their decision functions by some measure of their satisfaction or preference. Results from the theory of fuzzy sets have been applied to develop the solution methods for different situations. Illustrations are included to show the usage of the methodology.     

α-complete information in factor space

In daily life, we normally describe our concepts and problems in linguistic terms. Due to the vagueness of our natural languages, the classical approach is unable to fully capture the properties (factors) of such concepts and problems and, hence, cannot provide decision-makers' complete information for making an appropriate decision. Therefore, in this paper, we first classify general fuzzy data of a problem which are presented by human linguistic terms into different categories and based on their properties, each of them is described by an appropriate fuzzy set. Then, by investigating the properties of a problem as factors of a system, a fuzzy multiobjective linear programming (FMOLP) model is proposed from the viewpoint of evidence theory and information theory to measure the uncertainty of a fuzzy problem. A learning procedure is also designed to inquire the complete information according to the required level of sufficiency α. Finally, an example of mobile phone service (MPS) is presented to show that the proposed model can aid decision-makers to identify representative (significant) factors and obtain complete information of the MPS within a few steps     

Interval-valued intuitionistic fuzzy mathematical programming method for hybrid multi-criteria group decision making with interval-valued intuitionistic fuzzy truth degrees

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.