A fuzzy multi-criteria decision analysis model for advanced technology assessment at Kennedy Space Center

The rapid development of computer and information technology has made project evaluation and selection a difficult task at the Kennedy Space Center (KSC) Shuttle Project Engineering Office. Decision Makers (DMs) are required to consider a vast amount of intuitive and analytical information in the decision process. Fuzzy Euclid is a Multi-criteria Decision Analysis (MCDA) model that captures the DMs’ beliefs through a series of intuitive and analytical methods such as the analytic hierarchy process (AHP) and subjective probability estimation. A defuzzification method is used to obtain crisp values from the subjective judgments provided by multiple DMs. These crisp values are synthesized with Entropy and the theory of displaced ideal to assist the DMs in their selection process by plotting the alternative projects in a four-zone graph based on their Euclidean distance from the ‘ideal choice’.     

A new data envelopment analysis method for priority determination and group decision making in the analytic hierarchy process

The DEAHP method for weight deviation and aggregation in the analytic hierarchy process (AHP) has been found flawed and sometimes produces counterintuitive priority vectors for inconsistent pairwise comparison matrices, which makes its application very restrictive. This paper proposes a new data envelopment analysis (DEA) method for priority determination in the AHP and extends it to the group AHP situation. In this new DEA methodology, two specially constructed DEA models that differ from the DEAHP model are used to derive the best local priorities from a pairwise comparison matrix or a group of pairwise comparison matrices no matter whether they are perfectly consistent or inconsistent. The new DEA method produces true weights for perfectly consistent pairwise comparison matrices and the best local priorities that are logical and consistent with decision makers (DMs)’ subjective judgments for inconsistent pairwise comparison matrices. In hierarchical structures, the new DEA method utilizes the simple additive weighting (SAW) method for aggregation of the best local priorities without the need of normalization. Numerical examples are examined throughout the paper to show the advantages of the new DEA methodology and its potential applications in both the AHP and group decision making.     

An intuitionistic fuzzy programming method for group decision making with interval-valued fuzzy preference relations

The paper develops a new intuitionistic fuzzy (IF) programming method to solve group decision making (GDM) problems with interval-valued fuzzy preference relations (IVFPRs). An IF programming problem is formulated to derive the priority weights of alternatives in the context of additive consistent IVFPR. In this problem, the additive consistent conditions are viewed as the IF constraints. Considering decision makers’ (DMs’) risk attitudes, three approaches, including the optimistic, pessimistic and neutral approaches, are proposed to solve the constructed IF programming problem. Subsequently, a new consensus index is defined to measure the similarity between DMs according to their individual IVFPRs. Thereby, DMs’ weights are objectively determined using the consensus index. Combining DMs’ weights with the IF program, a corresponding IF programming method is proposed for GDM with IVFPRs. An example of E-Commerce platform selection is analyzed to illustrate the feasibility and effectiveness of the proposed method. Finally, the IF programming method is further extended to the multiplicative consistent IVFPR.     

A fuzzy opportunity and threat aggregation approach in multicriteria decision analysis

Economic expansion in developed countries coupled with dramatically growing economies in countries such as China and India have precipitated a steady increase in demand for oil and natural gas. The Caspian Sea region holds large quantities of both oil and natural gas. Because the Caspian Sea is landlocked and the region’s nations are distant from the largest energy markets, transportation must at least begin by pipeline. While some lines currently exist, pipelines with the capacity of transporting larger amounts of energy resources must be constructed to meet the global demand. This study is conducted for a multinational oil and natural gas producer to develop a multicriteria decision analysis (MCDA) framework for evaluating five possible pipeline routes in the Caspian Sea region. The proposed MCDA model considers a large number of conflicting criteria in the evaluation process and captures decision makers’ (DMs’) beliefs through a series of intuitive and analytical methods such as the analytic network process and fuzzy scoring. A defuzzification method is used to obtain crisp values from the subjective judgments and estimates provided by multiple DMs. These crisp values are aggregated and synthesized with the concept of entropy and the theory of the displaced ideal. The alternative routes are plotted on a diagram in a polar coordinate system and a classification scheme is used along with the Euclidean distance to measure which alternative is closer to the ideal route.     

考虑决策者风险偏好的区间直觉模糊多属性群决策方法

提出了一种考虑决策者风险偏好且属性权重信息不完全的区间直觉模糊数多属性群决策方法。同时考虑相似度和接近度,确定每一属性的决策者权重。为了考虑决策者风险偏好对决策结果的影响和避免区间直觉模糊矩阵的渐进性,引入了决策者风险偏好系数,将集结后的综合决策矩阵转换成区间数矩阵。然后,为了客观地求出属性权重信息不完全环境下属性的权重,构建了基于区间直觉模糊交叉熵的属性权重目标规划模型,该模型不仅考虑了评价值的偏差,也强调了评价值自身的可信度。最后,通过研发项目选择问题的实例分析说明了所提方法的合理性和优越性。     

An interactive sorting approach based on the assignment examples of multiple decision makers with different priorities

Although group decision-making is often adopted by many organizations in today??s highly complicated business environment, the multiple criteria sorting (MCS) problem in the context of group decision-making has not been studied sufficiently. To this end, we propose a new interactive method to assist a group of decision makers (DMs) with different priorities. With the goal of relieving the cognitive effort exerted by DMs, this method uses the assignment examples provided by the DMs to draw the parameters for the group preference model. In the iterative MCS process that we employ, the DMs are supported from two perspectives. When the assignment examples provided by the DMs are inconsistent, a RINCON algorithm is developed to identify all the possible solutions that the DMs can use to resolve the conflicts. When the examples are consistent, the potential and the fittest assignments of each alternative are deduced using linear programming techniques. These are then presented to the DMs to help them provide more information for the decision-making process. Furthermore, the priority of each DM is objectively and subjectively evaluated, and then progressively updated to reflect the decision-making performance of a DM at each iteration. Meanwhile, the priorities are integrated into the linear programming model to deduce the fittest assignment, as well as into the RINCON algorithm. Hence, the assignment examples of the DMs with higher priorities are emphasized in the fittest assignment, and are less likely to be revised for inconsistency. A practical example featuring MBA programs is also presented to demonstrate the proposed method.     

A method for group decision-making based on determining weights of decision makers using TOPSIS

In general, weights of decision makers (DMs) play a very important role in multiple attribute group decision-making (MAGDM), how to measure the weights of DMs is an interesting research topic. This paper presents a new approach for determining weights of DMs in group decision environment based on an extended TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution) method. We define the positive ideal solution as the average of group decision. The negative ideal solution includes two parts: left and right negative ideal solution, which are the minimum and maximum matrixes of group decision, respectively. We give an example to illustrate the developed approach. Finally, the advantages and disadvantages of this study are also compared.     

Interactive fuzzy programming approach to Bi-level quadratic fractional programming problems

In this paper we propose an interactive fuzzy programming method for obtaining a satisfactory solution to a “bi-level quadratic fractional programming problem” with two decision makers (DMs) interacting with their optimal solutions. After determining the fuzzy goals of the DMs at both levels, a satisfactory solution is efficiently derived by updating the satisfactory level of the DM at the upper level with consideration of overall satisfactory balance between both levels. Optimal solutions to the formulated programming problems are obtained by combined use of some of the proper methods. Theoretical results are illustrated with the help of a numerical example.     

A new decision support model in multi-criteria decision making with intuitionistic fuzzy sets based on risk preferences and criteria reduction

In this paper, we propose a new model for decision support to address the ‘large decision table’ (eg, many criteria) challenge in intuitionistic fuzzy sets (IFSs) multi-criteria decision-making (MCDM) problems. This new model involves risk preferences of decision makers (DMs) based on the prospect theory and criteria reduction. First, we build three relationship models based on different types of DMs’ risk preferences. By building different discernibility matrices according to relationship models, we find useful criteria for IFS MCDM problems. Second, we propose a technique to obtain weights through discernibility matrix. Third, we also propose a new method to rank and select the most desirable choice(s) according to weighted combinatorial advantage values of alternatives. Finally, we use a realistic voting example to demonstrate the practicality and effectiveness of the proposed method and construct a new decision support model for IFS MCDM problems.     

Consensus building with a group of decision makers under the hesitant probabilistic fuzzy environment

As a generalized fuzzy number, the hesitant fuzzy element (HFE) has been receiving increased attention and has recently become a popular topic. However, we find that the occurring probabilities of the possible values in the HFE are equal, which is obviously impractical. Consequently, in this paper, we propose a hesitant fuzzy number with probabilities, called the hesitant probabilistic fuzzy number, and construct its score function, deviation function, comparison laws, and its basic operations. It is well known that in the context of a group of decision makers (DMs), one of the basic approaches to built consensus is to aggregate individual evaluations or individual priorities. Thus, to use the hesitant fuzzy numbers for consensus building with a group of DMs, we further propose a method called maximizing score deviation method to obtain the DMs’ weights under the HPFE environment, based on which two extended and four new ordered weighted operators are provided to fuse the HPFE information and build the consensus of the DMs. We also analyze the differences among these ordered weighted operators and provide their application scopes. Finally, a practical case is provided to demonstrate consensus building with a group of DMs under the HPFE environment using the proposed approaches.     

Analytic hierarchy process-hesitant group decision making

In this paper, we consider that the judgments provided by the decision makers (DMs) cannot be aggregated and revised, then define them as hesitant judgments to describe the hesitancy experienced by the DMs in decision making. If there exist hesitant judgments in analytic hierarchy process-group decision making (AHP-GDM), then we call it AHP-hesitant group decision making (AHP-HGDM) as an extension of AHP-GDM. Based on hesitant multiplicative preference relations (HMPRs) to collect the hesitant judgments, we develop a hesitant multiplicative programming method (HMPM) as a new prioritization method to derive ratio-scale priorities from HMPRs. The HMPM is discussed in detail with examples to show its advantages and characteristics. The practicality and effectiveness of our methods are illustrated by an example of the water conservancy in China.     

A complex multi-attribute large-group PLS decision-making method in the interval-valued intuitionistic fuzzy environment

In the complex multi-attribute large-group decision-making (CMALGDM) problems in interval-valued intuitionistic fuzzy (IVIF) environment, attributes of the alternatives are often stratified and correlated. This paper proposes a decision-making method for these problems based on partial least squares (PLS) path modelling, which not only fully exploits the decision information of decision makers (DMs), but also effectively addresses the relativity problem in the decision attributes and objectively assigned weights to the primary decision attributes (i.e., “latent variables for decision making”). The method can be outlined in three steps. First, a two-stage method is proposed to transform the interval-valued intuitionistic fuzzy number (IVIFN) samples into single-valued samples. In this step, an improved C-OWA operator is first given to transform the IVIFN samples into intuitionistic fuzzy number (IFN) samples, which makes the preference information of the DMs more objectively aggregated. Then a proposed membership-based method is applied to reduce the information loss and transform the IFN samples into single-valued samples. Second, the estimated values and weights of the “latent variables for decision-making” are obtained by means of the PLS path modelling algorithm. Finally, a multi-alternative sorting method is devised in accordance with the estimated values and weights. An example is provided to illustrate the proposed technique and evaluate its feasibility and validity.     

An interactive method for the optimal selection problem with two decision makers

We develop in this paper an interactive approach for the bilateral optimal selection problem. The decision model involves two decision makers (DMs) observing a sequence of n offers, sequentially, one at a time, in order to choose a compromise offer. Our method is based on an aggregation of the individual expected utilities of the two DMs whenever a conflict occurs. A conflicting situation arises when the two DMs do not agree to choose the same decision. We develop and simulate our approach on different forms of utilities.     

基于序列稳定性的冲突当局者行为分析模型

不同稳定性可以折射冲突当局者的不同行为类型,为了更全面且深入地了解当局者的行为类型,本文将现有四种基本稳定性拓展至六种,构建了一个能够提高冲突分析图模型理论普遍实用性的决策方法。首先,提出了强、弱序列稳定性(SEQ稳定)的逻辑概念,以此分析当局者具有不同程度的过度自信下的冲突决策过程。然后,定义了强、弱SEQ稳定的矩阵表达,以此促进相应稳定解的计算和编程算法的实现。最后,使用“制造商与零售商渠道价格冲突”案例说明强弱SEQ稳定的意义。研究发现:冲突当局者的过度自信偏差并不都会产生负面影响,有时会利于当局者的集体利益。     

A new method for multiple criteria group decision making with incomplete weight information under linguistic environment

A new method is proposed to solve multiple criteria group decision making (MCGDM) problems, in which both the criteria values and criteria weights take the form of linguistic information, and the information about linguistic criteria weights is partly known or completely unknown. Firstly, to get reasonable decision result, instead of assigning the same weight to the decision maker (DM) for all criteria, we propose a method to determine the weight of DM with respect to each criterion under linguistic environment by calculating the similarity degree between individual 2-tuple linguistic evaluation value and the mean given by all decision makers (DMs). Secondly, for the situations where the information about the criteria weights is partly known or completely unknown, we establish optimization models to determine the criteria weights by defining 2-tuple linguistic positive ideal solution (TL-PIS), 2-tuple linguistic right negative ideal solution (TL-RNIS) and 2-tuple linguistic left negative ideal solution (TL-LNIS) of the collective 2-tuple linguistic decision matrix. Thirdly, we propose a new method to solve MCGDM problems with partly known or completely unknown linguistic weight information. Finally, an illustrative example is given to demonstrate the calculation process of the proposed method.     

Generalized metarationalities in the graph model for conflict resolution

A metarational tree is defined within the graph model for conflict resolution paradigm, providing a general framework within which rational behavior in models with two decision makers (DMs) can be described more comprehensively. A new definition of stability for a DM that depends on the total number, h, of moves and counter-moves allowed is proposed. Moreover, the metarational tree can be refined so that all moves must be unilateral improvements, resulting in a new set of stability definitions for each level of the tree. Relationships among stabilities at various levels of the basic and refined trees are explored, and connections are established to existing stability definitions including Nash stability, general metarationality, symmetric metarationality, sequential and limited-move stability, and policy equilibria.     

Mixed valuation methods: a combined AHP-GP procedure for individual and group multicriteria agricultural valuation

This paper introduces a new assessment method classification, in which a third procedure, mixed valuation, is jointly included with the traditional economic and non-economic methodologies. The paper considers a case of multiple actors (from a previous work by the same authors—Aznar et al. (Estudios de Economía Aplicada, 25(2):389–409, 2007), in which a new technique for multicriteria agriculture valuation (MAVAM) was proposed. The method is specifically designed for situations in which scarce information about the elements being compared (quantified or not) is available. It works in individual and group decision making contexts and attempts to both obtain and incorporate the objective information associated with the tangible aspects of the problem and the subjective knowledge associated with the human factor into the valuation process. It combines two of the most extended multicriteria decision making techniques: the Analytic Hierarchy Process (AHP) and Goal Programming (GP). The first of these enables tangible and intangible information stemming from known elements to be collected by using pairwise comparisons; the second allows the scarce information available and the personal approach to the valuation to be included in the valuation process. The proposed methodology is illustrated by means of its application to a case of individual and group valuation of an agricultural asset in the La Ribera district, Valencia (Spain).     

A modified procedure for synthesising ratio judgements in the analytic hierarchy process

The analytic hierarchy process (AHP) has been widely applied to solve problems arising in group decision making, by synthesising different or conflicting judgements. However, directly synthesising conflicting judgements by calculating the geometric mean of preference weights (ratios) in AHP may not reach consensus from all members in a decision making group, especially, when those members represent the stakeholders of the decision making problem. This study proposes a new method that uses the genetic algorithm and utility function to synthesise preference weights to prevent this fallacy occurring when implementing the classical AHP approach. Using the proposed method, the final decision can be achieved with only minimally-adjusted preference weights.     

A new fuzzy multiple attributive group decision making methodology and its application to propulsion/manoeuvring system selection problem

In this paper, a new fuzzy multiple attribute decision-making (FMADM) method, which is suitable for multiple attributive group decision making (GDM) problems in fuzzy environment, is proposed to deal with the problem of ranking and selection of alternatives. Since the subjectivity, imprecision and vagueness in the estimates of a performance rating enter into multiple attribute decision-making (MADM) problems, fuzzy set theory provides a mathematical framework for modelling vagueness and imprecision. In the proposed approach, an attribute based aggregation technique for heterogeneous group of experts is employed and used for dealing with fuzzy opinion aggregation for the subjective attributes of the decision problem. The propulsion/manoeuvring system selection as a real case study is used to demonstrate the versatility and potential of the proposed method for solving fuzzy multiple attributive group decision-making problems. The proposed method is a generalised model, which can be applied to great variety of practical problems encountered in the naval architecture from propulsion/manoeuvring system selection to warship requirements definition.