Multiple criteria classification with an application in water resources planning

A new kind of multiple criteria decision aid (MCDA) problem, multiple criteria classification (MCC), is studied in this paper. Traditional classification methods in MCDA focus on sorting alternatives into groups ordered by preference. MCC is the classification of alternatives into nominal groups, structured by the decision maker (DM), who specifies multiple characteristics for each group. Starting with illustrative examples, the features, definition and structures of MCC are presented, emphasizing criterion and alternative flexibility. Then an analysis procedure is proposed to solve MCC problems systematically. Assuming additive value functions, an optimization model with constraints that incorporate various classification strategies is constructed to solve MCC problems. An application of MCC in water resources planning is carried out and some future extensions are suggested.     

A Multicriteria Decision Aid Methodology for Sorting Decision Problems: The Case of Financial Distress

Sorting problems constitute a major part of real world decisions, where a set of alternative actions (solutions) must be classified into two or more predefined classes. Multicriteria decision aid (MCDA) provides several methodologies, which are well adapted in sorting problems. A well known approach in MCDA is based on preference disaggregation which has already been used in ranking problems, but it is also applicable in sorting problems. The UTADIS (UTilités Additives DIScriminantes) method, a variant of the UTA method, based on the preference disaggregation approach estimates a set of additive utility functions and utility profiles using linear programming techniques in order to minimize the misclassification error between the predefined classes in sorting problems. This paper presents the application of the UTADIS method in two real world classification problems concerning the field of financial distress. The applications are derived by the studies of Slowinski and Zopounidis (1995), and Dimitras et al. (1999). The obtained results depict the superiority of the UTADIS method over discriminant analysis, and they are also comparable with the results derived by other multicriteria methods.     

Pythagorean fuzzy TOPSIS for multicriteria group decision-making with unknown weight information through entropy measure

In this study, a new technique for order preference by similarity to ideal solution (TOPSIS)-based methodology is proposed to solve multicriteria group decision-making problems within Pythagorean fuzzy environment, where the information about weights of both the decision makers (DMs) and criteria are completely unknown. Initially, generalized distance measure for Pythagorean fuzzy sets (PFSs) is defined and used to initiate a new Pythagorean fuzzy entropy measure for computing weights of the criteria. In the decision-making process, at first, weights of DMs are computed using TOPSIS through the geometric distance model. Then, weights of the criteria are determined using the entropy weight model through the newly defined entropy measure for PFSs. Based on the evaluated criteria weights, TOPSIS is further applied to obtain the score value of alternatives corresponding to each decision matrix. Finally, the score values of the alternatives are aggregated with the calculated DMs’ weights to obtain the final ranking of the alternatives to avoid the loss of information, unlike other existing methods. Several numerical examples are considered, solved, and compared with the existing methods.     

A multi-criteria decision making approach for strategy formulation using Pythagorean fuzzy logic

The objective of this paper is to develop Pythagorean fuzzy (PF) multi-objective optimization by ratio analysis (PF-MOORA) plus full MULTIplicative form (PF-MULTIMOORA) method for solving multicriteria decision making (MCDM) problems with completely unknown information of criteria weights. In the model formulation process, a new distance measure is defined to quantify the difference between PF sets by combining Hamming distance and Hausdorff metric. This distance measure is, subsequently, implemented in entropy weight model for determining unknown weights of criteria, and also in reference point approach for obtaining preference indices of alternatives. To overcome the deficiencies occurred in existing MULTIMOORA method, like multiple comparisons, circular reasoning, and so on, an aggregation-based approach is recommended in the proposed PF-MULTIMOORA. To demonstrate the feasibility and practicality of the proposed method, an example concerning strategy prioritization of a tiles manufacturing company is presented. In the strategy evaluation process, at first, the judgement values provided by the decision maker are expressed in linguistic terms, and then those are converted into PF numbers through a PF weighting scale. The sensitivity of the proposed model is validated by changing of weights of criteria which impact on the ranks of the strategies. To show robustness of the developed method, the result attained by applying PF-MULTIMOORA is compared with existing techniques, not only in crisp and fuzzy quantitative strategic planning matrix context, but also using four other MCDM methods, namely, modified PF-MOORA, as a particular case of the proposed PF-MULTIMOORA technique, PF weighted sum, PF-TOPSIS and PF-VIKOR.     

A framework for water loss management in developing countries under fuzzy environment: Integration of Fuzzy AHP with Fuzzy TOPSIS

Facing water scarcity conditions water utilities cannot longer tolerate inefficiencies in their water systems. To guarantee sustainable water management one central task is reducing water losses from the supply systems. There are numerous challenges in managing water losses, manifested in a variety of options, their complexities, multiple evaluation criteria, inherent uncertainties and the conflicting objectives and interests of different stakeholders. This study demonstrates the effectiveness of multi criteria decision analysis (MCDA) approaches for decision support in this complex topic. The study covers identifying the key options among a set of options that have been proposed within a framework of strategies to reduce water losses in water distribution systems of developing countries. The proposed methodology was initiated by developing a hierarchical structure of the decision problem that consists of four levels: Overall objective, main criteria, evaluation criteria and options. Different stakeholders were engaged in the process of structuring and evaluating the decision problem. An integrated methodology that combines fuzzy set theory with Analytic Hierarchy Process (AHP) and Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) methods was then employed. This methodology has the potential to transform qualitative data into equivalent quantitative measures. Fuzzy AHP was used to create weights for main and evaluation criteria, while Fuzzy TOPSIS was used to aid the ranking of options in terms of their potential to meet the overall objective based on the evaluations and preferences of decision makers. The results showed that pressure management and control strategy was the most prevalent one, followed by employing advanced techniques and establishment of district metered areas. Their dominance was highly connected to the local and boundary conditions of the case study. The sensitivity analysis results showed that strongest and weakest options were less sensitive to changes in weights of evaluation criteria, which could be attributed to the strong consensus in strengthening the best option and neglecting the worst option. This study emphasized the successful application of MCDA in dealing with complicated issues in the context of water loss management. It is anticipated that, the integration of this developed framework in the planning policies of water utilities in developing countries can help in conducting better control over water losses.     

基于粒计算的犹豫模糊多准则决策方法*

提出基于粒计算的犹豫模糊多准则决策方法.给出各个准则下对应的犹豫模糊集中犹豫模糊元的大于可能度定义,并构造相应准则下的加性一致的模糊偏好矩阵.根据各准则的模糊偏好矩阵对应的预序熵及预序粒结构相似度确定属性的权重,对各个准则下模糊偏好矩阵的排序向量加权平均得到最终的排序向量.文中方法以评价数据序信息量及准则序与整体之间的关系确定准则权重,通过计算加权两两比较下的排序向量得到最终的排序决策结果.最后运用实例验证算法的有效性及可行性.     

Fuzzy measure identification for criteria coalitions using linguistic information

Modeling interactions between criteria in multiple criteria decision analysis (MCDA) is a complex task. Such complexity arises when there are visible redundancies and synergies among criteria, which traditional MCDA methods cannot deal with. The Choquet integral is a model that has been conceived to deal with these issues, but an appropriate fuzzy measure must be defined. This article shows how to compute a fuzzy measure for criteria coalitions using linguistic information efficiently. Due to the complexity to identify an adequate fuzzy measure when the criteria set cardinality increases, the proposed model reduces the effort to determine the measure of each criteria combination by focusing on relevant interactions. Then, this fuzzy measure is used on Choquet integral to establish the best alternative in a decision-making problem. Finally, a comparison between the arithmetic mean, the OWA operator and the proposed method is presented.     

MULTICRITERIA SORTING METHODOLOGY: APPLICATION TO FINANCIAL DECISION PROBLEMS

Abstract

The primary objective in the sorting approach is to assign a set of alternatives into predefined classes. This type of problem is often encountered in many real world decision problems. During the last two decades several new approaches have been proposed to overcome the shortcomings of traditional statistical and econometric techniques. This paper focuses on the multicriteria decision aid (MCDA) approach; it briefly reviews the main MCDA sorting techniques, and presents the multigroup hierarchical discrimination method. This new MCDA sorting technique is applied to the portfolio selection problem. A comparison with discriminant analysis is also performed. Furthermore, the efficiency of the proposal approach can be easily improved for solving large-scale problems in a multiprocessing environment.     

Signed distance‐based ORESTE for multicriteria group decision‐making with multigranular unbalanced hesitant fuzzy linguistic information

The objective of this study is to develop an integrated approach for solving multicriteria group decision‐making problems with multigranular unbalanced hesitant fuzzy linguistic term sets (HFLTSs). Firstly, a signed distance‐based transformation function is proposed to unify multigranular unbalanced hesitant fuzzy linguistic (HFL) assessments. Secondly, a mathematical programming model based on the maximum consensus is constructed to allocate decision‐makers (DMs)' weights objectively. Thirdly, a new signed distance‐based preference score function is defined to aggregate HFL assessments and determine the weak ranking of alternatives, and a novel preference, indifference, and incomparability test framework is constructed to identify the subtle relations among alternatives. On these bases, a signed distance‐based ORESTE (Organísation, rangement et Synthèse de données relarionnelles, in French) method, in which knowledge regarding criterion values and weights are expressed as multigranular unbalanced HFLTSs, is developed to obtain the ranking of alternatives. Finally, an illustrative example, followed by sensitivity and comparative analyses, is presented to verify the feasibility and effectiveness of the proposed approach.     

A case-based distance model for multiple criteria ABC analysis

In ABC analysis, a well-known inventory planning and control technique, stock-keeping units (SKUs) are sorted into three categories. Traditionally, the sorting is based solely on annual dollar usage. The aim of this paper is to introduce a case-based multiple-criteria ABC analysis that improves on this approach by accounting for additional criteria, such as lead time and criticality of SKUs, thereby providing more managerial flexibility. Using decisions from cases as input, preferences over alternatives are represented intuitively using weighted Euclidean distances which can be easily understood by a decision maker. Then a quadratic optimization program finds optimal classification thresholds. This system of multiple criteria decision aid is demonstrated using an illustrative case study.     

Multicriteria decision analysis for sustainable data centers location

Data centers (DCs) are complex organizational and technical infrastructures that assure the performance and reliability of modern information and communication systems. The high installation and operations costs of DCs and the stringent requirements regarding reliability and safety require close attention to the location of this type of facility. This paper proposes a multicriteria decision analysis (MCDA) approach for identifying the most interesting locations to install sustainable DCs, taking into account technical, social, economic, and environmental dimensions. For each of these main dimensions, the evaluation was formulated as a multicriteria sorting problem. These problems were analyzed using the outranking MCDA method ELECTRE TRI through the IRIS software, allowing for uncertainty about the criteria weights. The results are summarized in a graphical form, without attempting to reduce such incommensurable dimensions to a single value.     

A new multi-criteria weighting and ranking model for group decision-making analysis based on interval-valued hesitant fuzzy sets to selection problems

The multi-criteria group decision-making methods under fuzzy environments are developed to cope with imprecise and uncertain information for solving the complex group decision-making problems. A team of some professional experts for the assessment is established to judge candidates or alternatives among the chosen evaluation criteria. In this paper, a novel multi-criteria weighting and ranking model is introduced with interval-valued hesitant fuzzy setting, namely IVHF-MCWR, based on the group decision analysis. The interval-valued hesitant fuzzy set theory is a powerful tool to deal with uncertainty by considering some interval-values for an alternative under a set regarding assessment factors. In procedure of the proposed IVHF-MCWR model, weights of criteria as well as experts are considered to decrease the errors. In this regard, optimal criteria’ weights are computed by utilizing an extended maximizing deviation method based on IVHF-Hamming distance measure. In addition, experts’ judgments are taken into account for computing the criteria’ weights. Also, experts’ weights are determined based on proposed new IVHF technique for order performance by similarity to ideal solution method. Then, a new IVHF-index based on Hamming distance measure is introduced to compute the relative closeness coefficient for ranking the candidates or alternatives. Finally, two application examples about the location and supplier selection problems are considered to indicate the capability of the proposed IVHF-MCWR model. In addition, comparative analysis is reported to compare the proposed model and three fuzzy decision methods from the recent literature. Comparing these approaches and computational results shows that the IVHF-MCWR model works properly under uncertain conditions.     

Robust ordinal regression in preference learning and ranking

Multiple Criteria Decision Aiding (MCDA) offers a diversity of approaches designed for providing the decision maker (DM) with a recommendation concerning a set of alternatives (items, actions) evaluated from multiple points of view, called criteria. This paper aims at drawing attention of the Machine Learning (ML) community upon recent advances in a representative MCDA methodology, called Robust Ordinal Regression (ROR). ROR learns by examples in order to rank a set of alternatives, thus considering a similar problem as Preference Learning (ML-PL) does. However, ROR implements the interactive preference construction paradigm, which should be perceived as a mutual learning of the model and the DM. The paper clarifies the specific interpretation of the concept of preference learning adopted in ROR and MCDA, comparing it to the usual concept of preference learning considered within ML. This comparison concerns a structure of the considered problem, types of admitted preference information, a character of the employed preference models, ways of exploiting them, and techniques to arrive at a final ranking.     

Multi-class classification using hybrid soft decision model for agriculture crop selection

A hybrid soft decision model has been developed in this paper to take decision on agriculture crop that can be cultivated in a given experimental land by integrating few soft computing techniques. The proposed model comprises of three parts, namely weight calculation, classification and prediction. Twenty-seven input criteria were categorized into seven broad criteria, namely soil (11 sub-criteria), water (2 sub-criteria), season (no sub-criterion), input (6 sub-criteria), support (2 sub-criteria), facilities (3 sub-criteria) and risk (2 sub-criteria). In the proposed model, relative weights of main criteria were calculated using Shannon’s Entropy method and relative weights of sub-criteria in each main criterion were calculated using rough set approach. As VIKOR method is effective in sorting the alternatives, it is used to determine the ranking index of main criteria in this study. A soft decision system was constructed from the results of rough set method, VIKOR method and Shannon’s Entropy method. Classification rules were generated for five agriculture crops, namely paddy, groundnut, sugarcane, cumbu and ragi based on the soft decision system using bijective soft set approach. The developed model predicts each site in the validation dataset into one of the five crops. The performance of the proposed model has been sanity checked by agriculture experts.

     

一种信息不完全确定的多准则分类决策方法

针对准则权系数信息不完全确定和准则值信息不完全且有训练集的多准则分类决策问题，提出一种基于证据推理的分类方法，该方法在对训练集分类的基础上，结合不完全确定的准则权系数信息等建立非线性规划模型；然后利用遗传算法和单纯形法联合求解优化模型，得出准则权系数和分类效用阈值等参数，进而求出每一方案的效用值；最后与分类的效用阈值进行比较，得到方案集的分类．应用实例说明了该方法的有效性和可行性。     

Possibilistic programming approach for fuzzy multidimensional analysis of preference in group decision making

Multiple attribute decision making (MADM) problems are the most encountered problems in decision making. Fuzziness is inherent in decision making process and linguistic variables are well suited to assessing an alternative on qualitative attributes using fuzzy rating. A few techniques in MADM assess the weights of attributes based on preference information on alternatives. But they are not practical any more when the set of all paired comparison judgments from decision makers (DMs) on attributes are not crisp and also we have to deal with fuzzy decision matrix. This paper investigates the generation of a possibilistic model for multidimensional analysis of preference (LINMAP). The model assesses the fuzzy weights as well as locating the ideal solution with fuzzy decision making preference on attributes and fuzzy decision matrix. All of the information is assumed as triangular fuzzy numbers (TFNs). This method is developed in group decision making environments and formulates the problem as a possibilistic programming with multiple objectives.     

A PROMETHEE-based classification method using concordance and discordance relations and its application to bankruptcy prediction

Outranking relation theory has been widely used to study pattern classification. Here we propose a classification method with concepts from the flows used in PROMETHEE methods, which are extensively applied in multi-criteria decision aids. PROMETHEE uses a flow, generated on the basis of a preference index and measured by various preference functions for each criterion, to represent the preference intensity for one pattern over another pattern. However, only criteria that are concordant with the preference contribute to a preference index. In the present study, the opinions from discordant criteria are also taken into account. The proposed method newly defines an overall preference index using both concordance and discordance relations for ordinal sorting problems. The final classification decision for a new pattern depends on its net flow. The criteria weights are determined using a genetic-algorithm-based approach. Empirical results obtained for a real-world problem regarding bankruptcy prediction demonstrate that the proposed method performs well compared to other well-known classification methods.     

基于“离合”思想的混合型灰色多属性决策方法

针对方案属性值为三参数区间灰数和模糊语言的混合型灰色多属性决策问题, 提出一种基于“离合”思想的混合灰靶决策方法. 首先, 定义三参数区间灰数的距离测度和排序方法; 然后, 鉴于灰信息与模糊信息相互转化的信息损失问题, 定义?? 维模糊球形灰靶和?? 维混合球形灰靶, 讨论正负靶心的情形, 并利用奖优罚劣原则构造综合靶心距, 建立混合正负靶心灰靶决策模型; 最后, 将所提出的方法应用于黄河宁蒙段防凌防汛的方案择优问题, 分析了属性权重和决策者风险偏好的选取对决策的影响, 结果验证了所提出方法的合理性和有效性.

     

基于加权α优势关系的多属性决策排序方法*

α优势粗糙集模型利用简单平均法赋权多个阈值α的排序结果,忽视数据集本身信息,导致不同数据集的排序质量差异性较大.针对此问题,文中提出基于加权α优势关系的优势度排序方法.首先运用α优势粗糙集方法详细分析决策对象.在此基础上,为了克服α主观赋权导致多属性决策排序结果中“并列”决策现象存在的不足,依据排序结果采用2种准则赋权α,并融合2种准则下所有对象的综合优势度,进一步细化排序结果.最后在具体算例中对比分析其它排序方法,验证文中方法的可行性和有效性.     

Evaluation of the criteria and effectiveness of distance e-learning with consistent fuzzy preference relations

The electronic learning (e-learning) has gradually become more and more important in today’s school in Taiwan. Many colleges and universities offer distance e-learning courses or programs for students. An effective teaching or learning through a distance web e-learning system depends on many factors (or criteria). The analytic hierarchy process (AHP) model is suitable for dealing with the multi-criteria problems. This paper utilizes the consistent fuzzy preference relations (CFPR) in AHP model to evaluate these factors. The CFPR is computational simplicity and guarantees the consistence of decision matrices. Rating the criteria is important. An empirical example using CFPR in AHP model to find the weights is presented. The weight can point out which factor is important, especially when the time, manpower, and financial support are limited. The rating results can be directly used to evaluate the distance e-learning effectiveness and can provide teachers and decision-makers in schools important information for improving e-learning practice in the future.