Product design and selection using fuzzy QFD and fuzzy MCDM approaches

Quality function deployment (QFD) is a useful analyzing tool in product design and development. To solve the uncertainty or imprecision in QFD, numerous researchers have applied the fuzzy set theory to QFD and developed various fuzzy QFD models. Three issues are investigated by examining their models. First, the extant studies focused on identifying important engineering characteristics and seldom explored the subsequent prototype product selection issue. Secondly, the previous studies usually use fuzzy number algebraic operations to calculate the fuzzy sets in QFD. This approach may cause a great deviation in the result from the correct value. Thirdly, few studies have paid attention to the competitive analysis in QFD. However, it can provide product developers with a large amount of valuable information. Aimed at these three issues, this study integrates fuzzy QFD and the prototype product selection model to develop a product design and selection (PDS) approach. In fuzzy QFD, the α-cut operation is adopted to calculate the fuzzy set of each component. Competitive analysis and the correlations among engineering characteristics are also considered. In prototype product selection, engineering characteristics and the factors involved in product development are considered. A fuzzy multi-criteria decision making (MCDM) approach is proposed to select the best prototype product. A case study is given to illustrate the research steps for the proposed PDS method. The proposed method provides product developers with more useful information and precise analysis results. Thus, the PDS method can serve as a helpful decision-aid tool in product design.     

Extension of the TOPSIS method for decision making problems under interval-valued intuitionistic fuzzy environment

TOPSIS is one of the well-known methods for multiple attribute decision making (MADM). In this paper, we extend the TOPSIS method to solve multiple attribute group decision making (MAGDM) problems in interval-valued intuitionistic fuzzy environment in which all the preference information provided by the decision-makers is presented as interval-valued intuitionistic fuzzy decision matrices where each of the elements is characterized by interval-valued intuitionistic fuzzy number (IVIFNs), and the information about attribute weights is partially known. First, we use the interval-valued intuitionistic fuzzy hybrid geometric (IIFHG) operator to aggregate all individual interval-valued intuitionistic fuzzy decision matrices provided by the decision-makers into the collective interval-valued intuitionistic fuzzy decision matrix, and then we use the score function to calculate the score of each attribute value and construct the score matrix of the collective interval-valued intuitionistic fuzzy decision matrix. From the score matrix and the given attribute weight information, we establish an optimization model to determine the weights of attributes, and construct the weighted collective interval-valued intuitionistic fuzzy decision matrix, and then determine the interval-valued intuitionistic positive-ideal solution and interval-valued intuitionistic negative-ideal solution. Based on different distance definitions, we calculate the relative closeness of each alternative to the interval-valued intuitionistic positive-ideal solution and rank the alternatives according to the relative closeness to the interval-valued intuitionistic positive-ideal solution and select the most desirable one(s). Finally, an example is used to illustrate the applicability of the proposed approach.     

Evolutionary search for difficult problem instances to support the design of job shop dispatching rules

Dispatching rules are simple scheduling heuristics that are widely applied in industrial practice. Their popularity can be attributed to their ability to flexibly react to shop floor disruptions that are prevalent in many real-world manufacturing environments. However, it is a challenging and time-consuming task to design local, decentralised dispatching rules that result in a good global performance of a complex shop.An evolutionary algorithm is developed to generate job shop problem instances for which an examined dispatching rule fails to achieve a good solution due to a single suboptimal decision. These instances can be easily analysed to reveal limitations of that rule which helps with the design of better rules. The method is applied to a job shop problem from the literature, resulting in new best dispatching rules for the mean flow time measure.     

An attribute weight based feedback model for multiple attributive group decision analysis problems with group consensus requirements in evidential reasoning context

In an evidential reasoning context, a group consensus (GC) based approach can model multiple attributive group decision analysis problems with GC requirements. The predefined GC is reached through several rounds of group analysis and discussion (GAD) in the approach. However, the GAD with no guidance may not be the most appropriate way to reach the predefined GC because several rounds of GAD will spend a lot of time of all experts and yet cannot help them to effectively emphasize on the assessments which primarily damage the GC. In this paper, an attribute weight based feedback model is constructed to effectively identify the assessments primarily damaging the GC and accelerate the GC convergence. Considering important attributes with the weights more than or at least equal to the mean of the weights of all attributes, the feedback model constructs identification rules to identify the assessments damaging the GC for the experts to renew. In addition, a suggestion rule is introduced to generate appropriate recommendations for the experts to renew their identified assessments. The identification rules are constructed at three levels including the attribute, alternative and global levels. The feedback model is used to solve an engineering project management software selection problem to demonstrate its detailed implementation process, its validity and applicability, and its advantages compared with the GC based approach.     

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.     

一种新型风险型多指标决策方法研究

传统的风险型多指标决策模型没有考虑决策者对风险的态度,而决策者对风险的态度会影响决策的结果,针对这一问题文章在累积前景理论与灰色关联方法的基础上,提出一种考虑决策者风险偏好的风险型多指标决策的方法.该方法首先利用极差化法对风险决策矩阵进行规范化处理,并在此基础上构造出最优与最劣方案;然后利用累积前景理论与灰色关联方法构建前景值函数,并给出利用灰色关联思想确定指标权重的方法与步骤;最终求出各个方案的综合前景值并进行排序选优.通过某电信运营商对管道资源建设方案选择的实例分析说明了方法的可行性与有效性.     

一种基于组合不确定型OWA算子的区间数群决策方法

在群决策中,由于决策环境的不确定性,决策者给出区间效信息.基于区间数可能度矩阵公式和互补判断矩阵的排序公式,提出了一种组合不确定型OWA算子,它是不确定型OWA算子的推广.该算子能集结群决策中区间数信息,文中给出了其在应用的具体步骤,最后实例分析说明了该方法的有效性和可行性.     

Optimal risk probability for first passage models in semi-Markov decision processes

This paper studies the risk minimization problem in semi-Markov decision processes with denumerable states. The criterion to be optimized is the risk probability (or risk function) that a first passage time to some target set doesn't exceed a threshold value. We first characterize such risk functions and the corresponding optimal value function, and prove that the optimal value function satisfies the optimality equation by using a successive approximation technique. Then, we present some properties of optimal policies, and further give conditions for the existence of optimal policies. In addition, a value iteration algorithm and a policy improvement method for obtaining respectively the optimal value function and optimal policies are developed. Finally, two examples are given to illustrate the value iteration procedure and essential characterization of the risk function.     

Global Priority Estimation in Multiperson Decision Making

The analytic hierarchy process generalized to synthesizing local preferences across a complex hierarchy structure into global priorities in multiperson decision making is considered in various approaches. They include classic eigenvector synthesis and multiplicative method, and several other suggested techniques, such as three-dimensional eigenvectors, and simultaneous linear and nonlinear estimations by whole hierarchy structure in synthetic optimizing procedures. A numerical example from marketing research with many criteria, subcriteria, alternatives, and respondents is presented. The quality of approximation compared by different approaches shows that the best results are produced by the nonlinear synthetic priority techniques. The techniques described have been successfully used in dozens of real-world projects and are very helpful for practical managerial decision making in complex hierarchies. Dr. Stan Lipovetsky is Senior Research Director, GfK Custom Research North America, Marketing Science, Research Center for Excellence. The author thanks Professor T. Rapcsak and two reviewers for insightful suggestions that improved the paper.     

Qualitative operators for reasoning maps: Evaluating multi-criteria options with networks of reasons

Cognitive/causal maps have been widely used as a powerful way of capturing decision-makers’ views about a problem, representing it as a cause–effect discourse. Several ways of making causal inferences from this type of model have been proposed in the Operational Research and Artificial Intelligence literatures, but none, as far as we are aware, has attempted to use a causal map structure to perform a multi-criteria evaluation of decision alternatives. Recently, we have proposed a new multi-criteria method, denominated as a Reasoning Map, which permits the use of decision-makers’ reasoning, structured as a network of means-and-ends (a particular type of causal map) to perform such an evaluation. In this manner, the model resembles the way that people talk and think about decisions in practice. The method also pays explicit attention to the cognitive limitations of decision-makers in providing preference information. Thus it employs qualitative assessment of preferences, utilises aggregation operators for qualitative data and provides also qualitative outputs. In this paper we discuss and evaluate possible ways of aggregating qualitative performance information in Reasoning Maps.