An integrated quantitative and qualitative FMCDM model for location choices

International logistics is a very popular and important issue in the present international supply chain system. In order to reduce the international supply chain operation cost, it is very important for enterprises to invest in the international logistics centers. Although a number of research approaches for solving decision-making problems have been proposed, most of these approaches focused on developing quantitative models for dealing with objective data or qualitative models for dealing with subjective ratings. Few researchers proposed approaches for dealing with both objective data and subjective ratings. Thus, this paper attempts to fill this gap in current literature by establishing an integrated quantitative and qualitative fuzzy multiple criteria decision-making model for dealing with both objective crisp data and subjective fuzzy ratings. Finally, the utilization of the proposed model is demonstrated with a case study on location choices of international distribution centers.     

Application of MADM in a fuzzy environment for selecting the best barrier for offshore wells

A fuzzy Multi Attribute Decision Making (FMADM) method, which is suitable for treating group decision making problems in a fuzzy environment, is proposed for ranking offshore well barriers from a cost-benefit view point. It is obvious that much knowledge in the real world is fuzzy rather than precise. MADM decision data is usually fuzzy, crisp, or a combination of the two. A useful model is proposed here in order to handle both fuzzy and crisp data. Imprecision and ambiguity in the calculation of a performance rating are incorporated into MADM whereby fuzzy set theory provides a mathematical framework for modeling them. Human opinions often conflict in group decision-making. The purpose of fuzzy MADM is to aggregate the conflicting opinions. In general, one expert’s opinion for a given attribute may be different from others’. Therefore, it is necessary to develop an appropriate method of aggregating multiple experts’ opinions, taking into account a degree of importance of each expert in the aggregation procedure. The weights of all attributes and experts are estimated using a Fuzzy Analytical Hierarchy Process (FAHP). Finally, the best well barrier or risk control option (RCO) with respect to cost and benefit is selected using a Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method.     

Fuzzy evaluation of cogeneration alternatives in a petrochemical industry

This paper derives fuzzy net present value (NPV) and pay back year (PBY) models as decision indexes for cogeneration alternatives decision-making. The Mellin transform is employed to establish the means and variances of the fuzzy indexes in order to rank various cogeneration alternatives. It is noted that the mean and variance values depend only on the vertexes of the fuzzy index, and are independent of their height. The current paper verifies the performance of the proposed models by simulating two numerical examples and by considering a cogeneration program in a petrochemical industry. It is shown that the results of the proposed fuzzy economic models are consistent with those of the conventional crisp models, and that the developed concepts are straightforward and easily implemented compared to the fuzzy ranking methods proposed in previous studies. Furthermore, the developed methods serve as readily implemented sensitivity analysis tools for use in the arena of uncertain decision-making.     

Valuation by using a fuzzy discounted cash flow model

The objective of this paper is to extend the classical discounted cash flow (DCF) model by developing a fuzzy logic system that takes vague cash flow and imprecise discount rate into account. In order to explicitly discuss a more appropriate valuation model, uncertain information will be fuzzified as triangular fuzzy numbers to quantify and evaluate the intrinsic value of a company's financial asset under the framework of DCF approach. We will find that the fuzzy discounted cash flow (FDCF) model proposed in this paper is one extension of classical (crisp) model and should be more suitable to capture the elements of valuation than non-fuzzy models.     

Buyer–seller fuzzy inventory model for a deteriorating item with discount

Multi-objective economic lot size models of deteriorating items for both the buyer and the seller are developed in crisp and fuzzy environments. A buyer tries to minimize total average cost and at the same time the seller maximizes the total average revenue allowing discount on bulk purchase with the restricted material cost of the buyer. Here, the total average expenditure for the buyer, the estimated total average revenue for the seller and the resource for the material purchase are assumed to be crisp (Model 1) and fuzzy (Model 2) in nature. The impreciseness in the above objectives and constraint have been expressed by fuzzy linear membership functions. It has been solved by the additive goal and fuzzy additive goal programming methods with different weights. Also, to ensure the achievement level, thresholds are considered in crisp and fuzzy models. All the models are illustrated with numerical examples and the results are compared.     

A constrained non-linear optimization model for fuzzy pairwise comparison matrices using teaching learning based optimization

Non-linear optimization models have been recently proposed to derive crisp weights from fuzzy pairwise comparison matrices. In this paper, a TLBO (Teaching Learning Based Optimization) based solution is presented for solving an optimization model as a system of non-linear equations to derive crisp weights from fuzzy pairwise comparison matrices in AHP (Analytic Hierarchy Process). This fuzzy-AHP method is named as TLBO-1. It has been found that TLBO-1 can lead to inconsistent or less consistent weights. To solve the problem of inconsistent weights, a new constrained non-linear optimization model is proposed in this paper. This model is based on the min-max approach for fuzzy pairwise comparison ratios of weights. TLBO is again used to solve this optimization model, and crisp weights are derived. This fuzzy AHP method is named as TLBO-2. The effectiveness of the proposed model is illustrated by three examples. For each example, the consistency of the derived crisp weights is compared with other optimization models. The results show that the TLBO-2 method can derive more consistent weights for the fuzzy AHP based Multi-Criteria Decision Making (MCDM) systems as compared to the other optimization models.     

Discrete Interval Type 2 Fuzzy System Models Using Uncertainty in Learning Parameters

Fuzzy system modeling (FSM) is one of the most prominent tools that can be used to identify the behavior of highly nonlinear systems with uncertainty. Conventional FSM techniques utilize type 1 fuzzy sets in order to capture the uncertainty in the system. However, since type 1 fuzzy sets express the belongingness of a crisp value x' of a base variable x in a fuzzy set A by a crisp membership value mu_A(x'), they cannot fully capture the uncertainties due to imprecision in identifying membership functions. Higher types of fuzzy sets can be a remedy to address this issue. Since, the computational complexity of operations on fuzzy sets are increasing with the increasing type of the fuzzy set, the use of type 2 fuzzy sets and linguistic logical connectives drew a considerable amount of attention in the realm of fuzzy system modeling in the last two decades. In this paper, we propose a black-box methodology that can identify robust type 2 Takagi-Sugeno, Mizumoto and Linguistic fuzzy system models with high predictive power. One of the essential problems of type 2 fuzzy system models is computational complexity. In order to remedy this problem, discrete interval valued type 2 fuzzy system models are proposed with type reduction. In the proposed fuzzy system modeling methods, fuzzy C-means (FCM) clustering algorithm is used in order to identify the system structure. The proposed discrete interval valued type 2 fuzzy system models are generated by a learning parameter of FCM, known as the level of membership, and its variation over a specific set of values which generate the uncertainty associated with the system structure     

机会约束下贷款组合优化决策的方差最小化模型

通过把贷款的收益率刻画为模糊变量,提出了机会约束下贷款组合优化决策的方差最小化模型。针对贷款收益率是特殊的三角模糊变量的情况,给出模型的清晰等价类,对等价类模型用传统的方法进行求解。对于贷款收益率的隶属函数比较复杂的情况,应用集成模糊模拟、神经网络、遗传算法和同步扰动随机逼近算法的混合优化算法求解模型。数值算例验证了模型和算法的有效性。     

An epsilon-constraint method for fully fuzzy multiobjective linear programming

Linear ranking functions are often used to transform fuzzy multiobjective linear programming (MOLP) problems into crisp ones. The crisp MOLP problems are then solved by using classical methods (eg, weighted sum, epsilon-constraint, etc), or fuzzy ones based on Bellman and Zadeh's decision-making model. In this paper, we show that this transformation does not guarantee Pareto optimal fuzzy solutions for the original fuzzy problems. By using lexicographic ranking criteria, we propose a fuzzy epsilon-constraint method that yields Pareto optimal fuzzy solutions of fuzzy variable and fully fuzzy MOLP problems, in which all parameters and decision variables take on LR fuzzy numbers. The proposed method is illustrated by means of three numerical examples, including a fully fuzzy multiobjective project crashing problem.     

Multi-attribute Group Decision-making Based on Hesitant Bipolar-valued Fuzzy Information and Social Network

Fuzzy sets have undergone several expansions and generalisations in the literature, including Atanasov’s intuitionistic fuzzy sets, type 2 fuzzy sets, and fuzzy multisets, to name a few. They can be regarded as fuzzy multisets from a formal standpoint; nevertheless, their interpretation differs from the two other approaches to fuzzy multisets that are currently available. Hesitating fuzzy sets (HFS) are very useful if consultants have hesitation in dealing with group decision-making problems between several possible memberships. However, these possible memberships can be not only crisp values in [0,1], but also interval values during a practical evaluation process. Hesitant bipolar valued fuzzy set (HBVFS) is a generalization of HFS. This paper aims to introduce a general framework of multi-attribute group decision-making using social network. We propose two types of decision-making processes: Type-1 decision-making process and Type-2 decision-making process. In the Type-1 decision-making process, the experts’ original opinion is proces for the final ranking of alternatives. In Type-2 decision making processs, there are two major aspects we consider. First, consistency tests and checking of consensus models are given for detecting that the judgments are logically rational. Otherwise, the framework demands (partial) decision-makers to review their assessments. Second, the coherence and consensus of several HBVFSs are established for final ranking of alternatives. The proposed framework is clarified by an example of software packages selection of a university.     

A periodic review inventory model involving fuzzy expected demand short and fuzzy backorder rate

The purpose of this paper is to extend [Ouyang, L. Y., Chuang, B. R. (2001). A periodic review inventory-control system with variable lead time. International Journal of Information and Management Sciences, 12, 1–13] periodic review inventory model with variable lead time by considering the fuzziness of expected demand shortage and backorder rate. We fuzzify the expected shortage quantity at the end of cycle and the backorder (or lost sales) rate, and then obtain the fuzzy total expected annual cost. Using the signed distance method to defuzzify, we derive the estimate of total expected annual cost in the fuzzy sense. For the proposed model, we provide a solution procedure to find the optimal review period and optimal lead time in the fuzzy sense so that the total expected annual cost in the fuzzy sense has a minimum value. Furthermore, a numerical example is provided and the results of fuzzy and crisp models are compared.     

Applying fuzzy hierarchy multiple attributes to construct an expert decision making process

The main objective of this paper is to propose an approach within the AHP framework for tackling the uncertainty and imprecision of service evaluations during pre-negotiation stages, where the expert’s comparison judgments are represented as fuzzy triangular numbers. A fuzzy prioritization method, which derives crisp priorities from consistent and inconsistent fuzzy comparison matrices, is described. The fuzzy analytic hierarchy process (FAHP)-based decision-making method can provide decision makers or buyer a valuable reference for evaluating software quality. A case study demonstrates the effectiveness of the proposed scheme. Importantly, the proposed scheme can assist decision makers in assessing the feasibility of digital video recorder system to management public space, making it highly applicable for academic and commercial purposes.     

A Prioritized Information Fusion Method for Handling Fuzzy Decision-Making Problems

Although Yager has presented a prioritized operator for fuzzy subsets, called the non-monotonic operator, it can not be used to deal with multi-criteria fuzzy decision-making problems when generalized fuzzy numbers are used to represent the evaluating values of criteria. In this paper, we present a prioritized information fusion algorithm based on the similarity measure of generalized fuzzy numbers. The proposed prioritized information fusion algorithm has the following advantages: (1) It can handle prioritized multi-criteria fuzzy decision-making problems in a more flexible manner due to the fact that it allows the evaluating values of criteria to be represented by generalized fuzzy numbers or crisp values between zero and one, and (2) it can deal with prioritized information filtering problems based on generalized fuzzy numbers.     

连锁门店选址与配送中心选择联合决策的f-MIGP模型

建立了连锁门店选址和配送中心选择联合决策问题的模糊多目标混合整数规划模型．针对该模型的特殊结构。提出一种适用的求解策略：首先确定每个模糊目标的隶属度函数;然后将模糊多目标混合整数规划模型转化为等价的清晰多目标混合整数规划模型,通过最大最小算子求出目标值;最后借助于两阶段算法,求出问题的最优解．通过应用算例进一步说明了该模型的有效性和可行性．     

六元语言值直觉模糊的金融决策推理方法

为了处理金融决策中的不确定性信息,采用直觉格值的方法来表达语言值。基于语言真值直觉格值系统,改进了一个个人金融决策辅助系统模型。该系统的推理方法是将直觉模糊逻辑近似推理方法进行扩展,通过使用相似度的方法来处理模糊问题,实现了一种较为理想的不确定性推理方法。最后给出了一个实例,结果表明所提出的方法可以灵活有效地处理金融决策问题。     

Simulating continuous fuzzy systems

In previous studies we concentrated on utilizing crisp, numeric simulation to produce discrete event fuzzy systems simulations. Then we extended this research to the simulation of continuous fuzzy systems models. In this study, we continue our study of continuous fuzzy systems using crisp continuous simulation. Consider a crisp continuous system whose process of evolution depends on differential equations. Such a system contains a number of parameters that must be estimated. Usually point estimates are computed and used in the model. However, these point estimates typically have uncertainty associated with them. We propose to incorporate uncertainty by using fuzzy numbers as estimates of these unknown parameters. Fuzzy parameters convert the crisp system into a fuzzy system. Trajectories describing the behavior of the system become fuzzy curves. We will employ crisp continuous simulation to estimate these fuzzy trajectories. Three examples are discussed.     

A NEW METHOD FOR HANDLING MULTICRITERIA FUZZY DECISION-MAKING PROBLEMS

This paper presents a new method for handling multicriteria fuzzy decision-making problems, in which the characteristics of the alternatives are represented by interval-valued fuzzy sets, and some techniques are developed to calculate the degree of similarity between interval-valued fuzzy sets. The proposed method is more flexible than the one we presented earlier (Chen et al., 1989) because it allows the criteria values of the alternatives to be represented by real intervals rather than crisp real values between zero and one.     

Obtaining Crisp Priorities for Triangular and Trapezoidal Fuzzy Judgments

This paper proposes anoptimal fuzzy-based model for obtaining crisp priorities for Fuzzy-AHP comparison matrices. Crisp judgments cannot be given for real-life situations, as most of these include some level of fuzziness and complexity. In these situations, judgments are represented by the set of fuzzy numbers. Most of the fuzzy optimization models derive crisp priorities for judgments represented with Triangular Fuzzy Numbers (TFNs) only. They do not work for other types of Triangular Shaped Fuzzy Numbers (TSFNs) and Trapezoidal Fuzzy Numbers (TrFNs). To overcome this problem, a sum of squared error (SSE) based optimization model is proposed. Unlike some other methods, the proposed model derives crisp weights from all of the above-mentioned fuzzy judgments. A fuzzy number is simulated using the Monte Carlo method. A threshold-based constraint is also applied to minimize the deviation from the initial judgments. Genetic Algorithm (GA) is used to solve the optimization model. We have also conducted casestudiesto show the proposed approach’s advantages over the existingmethods. Results show that the proposed model outperforms other models to minimize SSE and deviation from initial judgments. Thus, the proposed model can be applied in various real time scenarios as it can reduce the SSE value upto 29% compared to the existing studies.     

An approach to decision-making with triangular fuzzy reciprocal preference relations and its application

Triangular fuzzy reciprocal preference relations (TFRPRs) are powerful tools to denoting decision-makers’ fuzzy judgments, which permit the decision-makers to apply triangular fuzzy ratio rather than real numbers to express their judgements. Consistency analysis is one of the most crucial issues in preference relations that can guarantee the reasonable ranking order. However, all previous consistency concepts cannot well address this type of preference relations. Based on the operational laws on triangular fuzzy numbers, this paper introduces an additive consistency concept for TFRPRs by using quasi TFRPRs, which can be seen as a natural extension of the crisp case. Using this consistency concept, models to judging the additive consistency of TFRPRs and to estimating missing values in complete TFRPRs are constructed. Then, an algorithm to decision-making with TFRPRs is developed. Finally, two numerical examples are offered to illustrate the application of the proposed procedure, and comparison analysis is performed.     

Bi-objective optimization of the reliability-redundancy allocation problem for series-parallel system

The main objective of this paper is to solve the bi-objective reliability redundancy allocation problem for series-parallel system where reliability of the system and the corresponding designing cost are considered as two different objectives. In their formulation, reliability of each component is considered as a triangular fuzzy number. In order to solve the problem, developed fuzzy model is converted to a crisp model by using expected values of fuzzy numbers and taking into account the preference of decision maker regarding cost and reliability goals. Finally the obtained crisp optimization problem has been solved with particle swarm optimization (PSO) and compared their results with genetic algorithm (GA). Examples are shown to illustrate the method. Finally statistical simulation has been performed for supremacy the approach.