The evidential reasoning approach for MADA under both probabilistic and fuzzy uncertainties

Many multiple attribute decision analysis (MADA) problems are characterised by both quantitative and qualitative attributes with various types of uncertainties. Incompleteness (or ignorance) and vagueness (or fuzziness) are among the most common uncertainties in decision analysis. The evidential reasoning (ER) approach has been developed in the 1990s and in the recent years to support the solution of MADA problems with ignorance, a kind of probabilistic uncertainty. In this paper, the ER approach is further developed to deal with MADA problems with both probabilistic and fuzzy uncertainties.In this newly developed ER approach, precise data, ignorance and fuzziness are all modelled under the unified framework of a distributed fuzzy belief structure, leading to a fuzzy belief decision matrix. A utility-based grade match method is proposed to transform both numerical data and qualitative (fuzzy) assessment information of various formats into the fuzzy belief structure. A new fuzzy ER algorithm is developed to aggregate multiple attributes using the information contained in the fuzzy belief matrix, resulting in an aggregated fuzzy distributed assessment for each alternative. Different from the existing ER algorithm that is of a recursive nature, the new fuzzy ER algorithm provides an analytical means for combining all attributes without iteration, thus providing scope and flexibility for sensitivity analysis and optimisation. A numerical example is provided to illustrate the detailed implementation process of the new ER approach and its validity and wide applicability.     

Fuzzy multi-objective programming for supplier selection and risk modeling: A possibility approach

Selection of supply chain partners is an important decision involving multiple criteria and risk factors. This paper proposes a fuzzy multi-objective programming model to decide on supplier selection taking risk factors into consideration. We model a supply chain consisting of three levels and use simulated historical quantitative and qualitative data. We propose a possibility approach to solve the fuzzy multi-objective programming model. Possibility multi-objective programming models are obtained by applying possibility measures of fuzzy events into fuzzy multi-objective programming models. Results indicate when qualitative criteria are considered in supplier selection, the probability of a certain supplier being selected is affected.     

Multi-criteria analysis for dredger dispatching under uncertainty

Dredger dispatching is a complex decision making process in which multiple requirements and uncertain site conditions have to be taken into consideration simultaneously, for a specific dredging task. In evaluating the suitability of dredgers, besides quantitative assessments, qualitative assessments are often required to deal with uncertainty, subjectiveness and imprecision, which are best represented with fuzzy data. This paper formulates dredger dispatching as a fuzzy multi-criteria analysis model, and presents an effective algorithm for handling both crisp and fuzzy data in a straightforward manner. As a result, effective decisions can be made based on consistent evaluation results. An empirical study of a real case in China is conducted to demonstrate the applicability of the model. With its simplicity in both concept and computation, the model can be implemented as an effective decision aid in selecting dredgers for specific dredging tasks.     

A method of fuzzy preference relation to authorize the worldwide interoperability for microwave access license in Taiwan

This study proposes a preference relation based evaluation framework to help the National Communication Commission (NCC) in Taiwan authorize a worldwide interoperability for microwave access (WiMAX) license under a fuzzy environment where the uncertainty, subjectivity and vagueness are dealt with linguistic variables parameterized by triangular fuzzy numbers. This study applies the fuzzy multi-criteria decision making approach to determine the importance weights of evaluation criteria and consolidate the performance ratings of possible alternatives. Aggregated the evaluators’ opinions toward the criteria and alternatives, the fuzzy preference relation approach is utilized to obtain the non-dominated degree of each alternative for the decision makers to make a final decision. Simultaneously, an empirical case involving sixteen quantitative and fifteen qualitative evaluation criteria, thirteen telecommunication applicants assessed by twelve specialists from various fields of telecommunication industry in Taiwan is solicited to demonstrate the proposed approach.     

搜索引擎定量评价模型研究

搜索引擎性能的评价一般采用定性或定量的方法,在确定搜索引擎评价指标体系的基础上,本文利用模糊多属性决策研究了搜索引擎定量评价问题,为定量评价搜索引擎提供了一种途径.     

An effective Markov based approach for calculating the Limit Matrix in the analytic network process

Analytic network process is a multiple criteria decision analysis (MCDA) method that aids decision makers to choose among a number of possible alternatives or prioritize the criteria for making a decision in terms of importance. It handles both qualitative and quantitative criteria, that are compared in pairs, in order to forge a best compromise answer according to the different criteria and influences involved. The method has been widely applied and the literature review reveals a rising trend of ANP-related articles. The ‘power’ matrix method, a procedure necessary for the stability of the decision system, is one of the critical calculations in the mathematical part of the method. The present study proposes an alternative mathematical approach that is based on Markov chain processes and the well-known Gauss-Jordan elimination. The new approach obtains practically the same results as the power matrix method, requires slightly less time and number of calculations and handles effectively cyclic supermatrices, optimizing thus the whole procedure.     

The GOWA operator based approach to multiattribute decision making using intuitionistic fuzzy sets

The aim of this paper is to develop a methodology for solving multiattribute decision making (MADM) problems in which weights of attributes and ratings of alternatives on qualitative and quantitative attributes are expressed with intuitionistic fuzzy sets (IFSs). In this methodology, relative membership/satisfaction and non-membership/non-satisfaction degrees are formulated to construct IFSs for numerical values of alternatives on quantitative attributes. Alternatives on qualitative attributes are evaluated using linguistic variables and semantics which are parameterized by IFSs. Hereby, weights and ratings of alternatives on both qualitative attributes and quantitative attributes may be expressed with IFSs in a unified way. The generalized ordered weighted averaging (GOWA) operator is further extended to the situations in which the argument values are IFSs and thus a methodology is developed to solve MADM problems using IFSs. Validity and applicability of the proposed methodology in this paper are illustrated with a real numerical example.     

工程项目投资方案评价方法的研究-基于广义λ-Shapley Choquet积分

随着社会的发展,工程项目投资方案选择所受的影响因素越来越多。方案的属性值呈现出不确定性、模糊性的特征。文章对工程项目投资方案的主要影响因素进行了系统全面的分析,构造出影响因素的指标体系(即属性集)。为应对不确定信息和降低决策者的决策难度,让决策者利用所构建的语言变量给出方案属性值的定性判断,然后利用所构建的语言变量和三角模糊数之间的对应关系,将其转化为相应的三角模糊数,从而得到相应的定量模糊判断。为得到最优的综合投资方案,同时考虑属性间的交互作用,文章利用非可加测度及广义λ-Shapley Choquet积分来计算投资方案的综合评价值,属性权重由广义Shapley函数确定。基于此,给出了工程项目投资方案选择的一个新评价方法。最后,通过一个实际案例分析来验证所给方法的可行性和有效性。     

Employment of neural network and rough set in meta-learning

The selection of the optimal ensembles of classifiers in multiple-classifier selection technique is un-decidable in many cases and it is potentially subjected to a trial-and-error search. This paper introduces a quantitative meta-learning approach based on neural network and rough set theory in the selection of the best predictive model. This approach depends directly on the characteristic, meta-features of the input data sets. The employed meta-features are the degree of discreteness and the distribution of the features in the input data set, the fuzziness of these features related to the target class labels and finally the correlation and covariance between the different features. The experimental work that consider these criteria are applied on twenty nine data sets using different classification techniques including support vector machine, decision tables and Bayesian believe model. The measures of these criteria and the best result classification technique are used to build a meta data set. The role of the neural network is to perform a black-box prediction of the optimal, best fitting, classification technique. The role of the rough set theory is the generation of the decision rules that controls this prediction approach. Finally, formal concept analysis is applied for the visualization of the generated rules.     

Multicriteria evidential reasoning decision modelling and analysis—prioritizing voices of customer

In this paper, a new methodology is investigated to support the prioritization of the voices of customers through various customer satisfaction surveys. This new methodology consists of two key components: an innovative evidence-driven decision modelling framework for representing and transforming large amounts of data sets and a generic reasoning-based decision support process for aggregating evidence to prioritize the voices of customer on the basis of the Evidential Reasoning (ER) approach. Methods and frameworks for data collection and representation via multiple customer satisfaction surveys were examined first and the distinctive features of quantitative and qualitative survey data are analysed. Several novel yet natural and pragmatic rule-based functions are then proposed to transform survey data systematically and consistently from different measurement scales to a common scale, with the original features and profiles of the data preserved in the transformation process. These new transformation functions are proposed to mimic expert judgement processes and designed to be sufficiently flexible and rigorous so that expert judgements and domain specific knowledge can be taken into account naturally, systematically and consistently in the transformation process. The ER approach is used for synthesizing quantitative and qualitative data under uncertainty that can be caused due to missing data and ambiguous survey questions. A new generic method is also proposed for ranking the voices of customer based on qualitative measurement scales without having to quantify assessment grades to fixed numerical values. A case study is examined using an Intelligent Decision System (IDS) to illustrate the application of the decision modelling framework and decision support process for prioritizing the voices of customer for a world-leading car manufacturer.     

Incorporating Managerial Thinking in Prediction and Control: Case Study of Market Penetration

Managerial strategies, especially at the higher echelons of management, are often linguistically stated. This is because they need to be based on information which often defies quantification. Such verbal strategies and qualitative information have often been found to be difficult to incorporate in quantitative models. Thus, the quantitative effects of implementing one strategy as opposed to another have generally been difficult to forecast.In this paper, we show that, through the use of fuzzy logic, we can incorporate such qualitative (linguistically stated) information. Furthermore, we show that a fuzzy controller can be designed so as to reach desired goals while being cognizant of linguistically stated strategies, scenarios, and decision rules as well as quantitative data types.The approach is applied to the modeling and control of market penetration, a field which has attracted considerable attention in recent years.     

改进交叉评价DEA在模糊综合评价中的应用

借鉴对抗型交叉评价的思想,首先利用对抗型交叉评价DEA(数据包络分析)模型对模糊综合评价的量化指标进行评价,三角模糊化后将其作为模糊综合评价量化指标的输入与非量化指标数据合成进行二次评价,以此建构了一种基于对抗型交叉评价DEA的模糊综合评价方法.方法可从根本上解决已有评价方法中模糊量化结果的不确定性问题,使客观数据与主观因素并存的多属性决策更加可靠.最后,通过算例说明了方法的应用.     

Hit or miss: A decision support system framework for signing new musical talent

In the music industry, the process of signing new musical talent is one of the most complex decision-making problems. The decision, which is generally made by an artist and repertoire (A&R) team, involves consideration of various quantitative and qualitative criteria, and usually results in a low success rate. We conducted a series of mental model interviews with the aim of developing a decision support framework for A&R teams. This framework was validated by creating a decision support system that utilises multi-criteria decision analysis to support decision-making. Our framework and subsequent implementation of the decision support system involving decision rule and weighted sum methods show an improvement in the ability to analyse and decide on greater amounts of talent. This paper serves as a building block for developing systems to aid in this complex decision-making problem.     

A decision-support model for investment decisions in new ventures

The decision to invest in new ventures is characterized by incomplete information, where some measures of firm performance are quantitative, while some others are substituted by qualitative indicators. Qualitative attributes are defined in a relative sense. We develop a decision support model for identifying successful new ventures. The model integrates quantitative and qualitative variables through the use of the Analytic Hierarchy Process (AHP). The decision model gains in predictive accuracy through the use of qualitative attributes, and AHP imparts robustness to the qualitative measures.     

Fuzzy neural network modeling for product development

A fairly general product development model is formulated and analyzed based on multiple attribute decision making with emphasis on the treatment of the linguistic and vague aspects by fuzzy logic and up-dating or learning by neural network. Due to the representative ability of fuzzy set theory and the learning or intelligent ability of neural network, the proposed approaches appear to be an effective tool for handling vague and not well-defined systems.     

Synthetic Wisdom: The Design of a Mixed-Mode Modelling System for Organizational Decision Making

This paper discusses some of the early thinking about the development of a conference-based decision support system. It presents a scheme for the practical development of the mapping of argumentation (‘cognitive mapping’), particularly in the field of strategic planning. The objective is to redesign software (COPE) so that it may become both an effective conferencing system for the collection of ‘synthetic wisdom’ and yet also facilitate the analysis of the qualitative and quantitative features of the models so constructed. It stresses the need for the system to be able to cope with both the political and the behavioural aspects of the decision-making arena.     

Decision maker preferences for information in complex decision making: New directions for OR intervention

Operations research models are used in many business and non-business entities to support a variety of decision making activities, primarily well-defined, operational decisions. This is due to the traditional emphasis of these models on optimal solutions to pre-specified problems. Some attempts have been made to use OR models in support of more complex, strategic decision making. Traditionally, these models have been developed without explicit consideration for the information processing abilities and limitations of the decision makers, who interact with, provide input to, and receive output from such models.Research in judgement and decision making show that human decisions are influenced by a number of factors including, but not limited to, information presentation modes; information content, modes, e.g., quantitative versus qualitative; order effects such as primacy, recency; and simultaneous versus sequential presentation of data.This article presents empirical research findings involving executive business decision makers and their preferences for information in decision making scenarios. These preference functions were evaluated using OR techniques. The results indicate that decision makers view information in different ways. Some decision makers prefer qualitative, narrative, social information, whereas other prefer quantitative, numerical, firm specific information. Results also show that decision making tasks influence the preference structure of decision makers, but that in general, the preference are relatively stable across tasks.The results imply that for OR models to be more useful in support of non-routine decision making, attention needs to be focused on the information content and presentation effects of model inputs and outputs.     

Qualitative factors in data envelopment analysis: A fuzzy number approach

Qualitative factors are difficult to mathematically manipulate when calculating the efficiency in data envelopment analysis (DEA). The existing methods of representing the qualitative data by ordinal variables and assigning values to obtain efficiency measures only superficially reflect the precedence relationship of the ordinal data. This paper treats the qualitative data as fuzzy numbers, and uses the DEA multipliers associated with the decision making units (DMUs) being evaluated to construct the membership functions. Based on Zadeh’s extension principle, a pair of two-level mathematical programs is formulated to calculate the α-cuts of the fuzzy efficiencies. Fuzzy efficiencies contain more information for making better decisions. A performance evaluation of the chemistry departments of 52 UK universities is used for illustration. Since the membership functions are constructed from the opinion of the DMUs being evaluated, the results are more representative and persuasive.     

A new multi-criteria approach dealing with dependent and heterogeneous criteria for end-of-life product strategy

Strict regulations, technological growth and environmental impacts are influent factors in the choice of the best strategy for end-of-life (EOL) product. In fact, EOL is one stage of the life cycle having gained the attention of the market.This study proposes an integrated methodology that relies on multi-criteria analysis and takes into account both quantitative and qualitative criteria while respecting mutual interactions between them. This has been performed by introducing, on the one hand, the 2-tuple linguistic representation model dealing with non-homogeneous information data, and on the other hand, the Choquet integral interaction modeling between criteria into the PROMETHEE method. Although it has been developed for EOL selection problems, the proposed method fits to all kinds of decision-making problems with heterogeneous information. As this work demonstrates, this multi-criteria analysis approach can offer a technical-scientific decision making support tool in the EOL product sector. We also perform a sensitivity to reveal the effect of the subjective parameter variations on the originally resulted ranking.     

Group decision making based on novel fuzzy modified TOPSIS method

The aim of this paper is to present a novel fuzzy modified technique of order preference by a similarity to ideal solution (TOPSIS) method by a group of experts, which can select the best alternative by considering both conflicting quantitative and qualitative evaluation criteria in real-life applications. The proposed method satisfies the condition of being the closest to the fuzzy positive ideal solution and also being the farthest from the fuzzy negative ideal solution with multi-judges and multi-criteria. The performance rating values of alternatives versus conflicting criteria as well as the weights of criteria are described by linguistic variables and are transformed into triangular fuzzy numbers. Then a new collective index is introduced to discriminate among alternatives in the evaluation process with respect to subjective judgment and objective information. This paper shows that the proposed fuzzy modified TOPSIS method is a suitable decision making tool for the manufacturing decisions with two examples for the robot selection and rapid prototyping process selection.