A hybrid approach to concept selection through fuzzy analytic network process

Evaluating conceptual design alternatives in a new product development (NPD) environment has been one of the most critical issues for many companies which try to survive in the fast-growing world markets. Therefore, most companies have used various methods to successfully carry out this difficult and time-consuming evaluation process. Of these methods, analytic hierarchy process (AHP) has been widely used in multiple-criteria decision-making (MCDM) problems. But, in this study, we used analytical network process (ANP), a more general form of AHP, instead of AHP due to the fact that AHP cannot accommodate the variety of interactions, dependencies and feedback between higher and lower level elements. Furthermore, in some cases, due to the vagueness and uncertainty on the judgments of a decision-maker, the crisp pairwise comparison in the conventional ANP is insufficient and imprecise to capture the right judgments of the decision-maker. Therefore, a fuzzy logic is introduced in the pairwise comparison of ANP to make up for this deficiency in the conventional ANP, and is called as fuzzy ANP. In short, in this paper, a fuzzy ANP-based approach is proposed to evaluate a set of conceptual design alternatives developed in a NPD environment in order to reach to the best one satisfying both the needs and expectations of customers, and the engineering specifications of company. In addition, a numerical example is presented to illustrate the proposed approach.     

Effects of increasing fuzziness on analytic hierarchy process for spatial multicriteria decision analysis

Multicriteria decision analysis (MCDA) involves techniques which relatively recently have received great increase in interest for their capabilities of solving spatial decision problems. One of the most frequently used techniques of MCDA is Analytic Hierarchy Process (AHP). In the AHP, decision-makers make pairwise comparisons between different criteria to obtain values of their relative importance. The AHP initially only dealt with crisp numbers or exact values in the pairwise comparisons, but later it has been modified and adapted to also consider fuzzy values. It is necessary to empirically validate the ability of the fuzzified AHP for solving spatial problems. Further, the effects of different levels of fuzzification on the method have to be studied. In the context of a hypothetical GIS-based decision-making problem of locating a dam in Costa Rica using real-world data, this paper illustrates and compares the effects of increasing levels of uncertainty exemplified through different levels of fuzzification of the AHP. Practical comparison of the methods in this work, in accordance with the theoretical research, revealed that by increasing the level of uncertainty or fuzziness in the fuzzy AHP, differences between results of the conventional and fuzzy AHPs become more significant. These differences in the results of the methods may affect the final decisions in decision-making processes. This study concludes that the AHP is sensitive to the level of fuzzification and decision-makers should be aware of this sensitivity while using the fuzzy AHP. Furthermore, the methodology described may serve as a guideline on how to perform a sensitivity analysis in spatial MCDA. Depending on the character of criteria weights, i.e. the degree of fuzzification, and its impact on the results of a selected decision rule (e.g. AHP), the results from a fuzzy analysis may be used to produce sensitivity estimates for crisp AHP MCDA methods.     

A Fuzzy AHP Approach to Evaluating Machine Tool Alternatives

Selecting process of a machine tool has been very important issue for companies for years, because the improper selection of a machine tool might cause of many problems affecting negatively on productivity, precision, flexibility and company’s responsive manufacturing capabilities. On the other hand, selecting the best machine tool from its increasing number of existing alternatives in market are multiple-criteria decision making (MCDM) problem in the presence of many quantitative and qualitative attributes. Therefore, in this paper, an analytic hierarchy process (AHP) is used for machine tool selection problem due to the fact that it has been widely used in evaluating various kinds of MCDM problems in both academic researches and practices. However, due to the vagueness and uncertainty on judgments of the decision-maker(s), the crisp pair wise comparison in the conventional AHP seems to insufficient and imprecise to capture the right judgments of decision-maker(s). That is why; fuzzy number logic is introduced in the pair wise comparison of AHP to make up for this deficiency in the conventional AHP. Shortly, in this study, an intelligent approach is proposed, where both techniques; fuzzy logic and AHP are come together, referred to as fuzzy AHP. First, the fuzzy AHP technique is used to weight the alternatives under multiple attributes; second Benefit/Cost (B/C) ratio analysis is carried out by using both the fuzzy AHP score and procurement cost, of each alternative. The alternative with highest B/C ratio is found out and called as the ultimate machine tool among others. In addition, a case study is also presented to make this approach more understandable for a decision-maker(s).     

An integrated fuzzy multi criteria group decision making approach for ERP system selection

This paper aims to ease group decision-making by using an integration of fuzzy AHP (analytic hierarchy process) and fuzzy TOPSIS (technique for order preference by similarity to ideal solution) and its application to software selection of an electronic firm. Firstly, priority values of criteria in software selection problem have been determined by using fuzzy extension of AHP method. Fuzzy extension of AHP is suggested in this paper because of little computation time and much simpler than other fuzzy AHP procedures. Then, the result of the fuzzy TOPSIS model can be employed to define the most appropriate alternative with regard to this firm's goals in uncertain environment. Fuzzy numbers are presented in all phases in order to overcome any vagueness in decision making process. The final decision depends on the degree of importance of each decision maker so that wrong degree of importance causes the mistaken result. The researchers generally determine the degrees of importance of each decision maker according to special characteristics of each decision maker as subjectivity. In order to overcome this subjectivity in this paper, the judgments of decision makers are degraded to unique decision by using an attribute based aggregation technique. There is no study about software selection using integrated fuzzy AHP-fuzzy TOPSIS approach with group decision-making based on an attribute based aggregation technique. The results of the proposed approach and the other approaches are compared. Results indicate that our methodology allows decreasing the uncertainty and the information loss in group decision making and thus, ensures a robust solution to the firm.     

Applying fuzzy linguistic preference relations to the improvement of consistency of fuzzy AHP

The lack of consistency in decision making can lead to inconsistent conclusions. In fuzzy analytic hierarchy process (fuzzy AHP) method, it is difficult to ensure a consistent pairwise comparison. Furthermore, establishing a pairwise comparison matrix requires judgments for a level with n criteria (alternatives). The number of comparisons increases as the number of criteria increases. Therefore, the decision makers judgments will most likely be inconsistent. To alleviate inconsistencies, this study applies fuzzy linguistic preference relations (Fuzzy LinPreRa) to construct a pairwise comparison matrix with additive reciprocal property and consistency. In this study, the fuzzy AHP method is reviewed, and then the Fuzzy LinPreRa method is proposed. Finally, the presented method is applied to the example addressed by Kahraman et al. [C. Kahraman, D. Ruan, I. Do?an, Fuzzy group decision making for facility location selection, Information Sciences 157 (2003) 135-153]. This study reveals that the proposed method yields consistent decision rankings from only n − 1 pairwise comparisons, which is the same result as in Kahraman et al. research. The presented fuzzy linguistic preference relations method is an easy and practical way to provide a mechanism for improving consistency in fuzzy AHP method.     

A fully fuzzy best–worst multi attribute decision making method with triangular fuzzy number: A case study of maintenance assessment in the hospitals

This paper introduces the best–worst method to solve multi-attribute decision-making (MADM) problems in the fuzzy environment. In the proposed method, there is no need to do all the possible pairwise comparisons. In other words, only reference comparisons should be done. Reference comparisons consist of assessing the relative fuzzy preference of the best criterion (alternative) over others and all the criteria (alternatives) over the worst one. Afterward, a fully fuzzy linear mathematical model will be formulated and solved to determine the weight of the criteria. The same action will be performed to find the score of alternatives. This method has some interesting and valuable characteristics: (a) less required data for pairwise comparison, (b) high ability to provide a reliable solution, (c) it is an autonomous method along with its high capability to accompany another method. To evaluate the performance, it is compared with another fuzzy MADM method in an example. Furthermore, we apply this method for the maintenance evaluation of hospitals in Bojnord. The computational study confirms the high efficiency and satisfactory performance of the method, and results are validated by a low consistency ratio. Furthermore, the suggested methodology outperforms fuzzy AHP and well verified in the test instance.     

Generating consensus priority point vectors: a logarithmic goal programming approach

The analytic hierarchy process (Saaty, The Analytic Hierarchy Process: Planning, Priority Setting, Resource Allocation, NewYork: McGraw-Hill 1980) is a popular technique for addressing multiple-criteria decision-making problems (MCDMs). Various techniques have been proposed for using the AHP in group situations. Fundamental to the AHP is the generation of priority point vectors from matrices of pairwise comparison data. In this paper, we present a logarithmic goal programming model for generating the ‘consensus’ priority point vector from the set of individual priority point vectors.Scope and purposeWithin modern organizations, multiple-criteria decision-making problems (MCDMs) often occur within a group context, and individual priorities for decision alternatives must be synthesized into a single set of priorities which represents the consensus opinion for the group. This requires a process for aggregating individual priorities into a set of group priorities. In this paper, we examine the use of the analytic hierarchy process (AHP) MCDM technique for the group situation, and present an approach for aggregating individual priorities into a set of group ‘consensus’ priorities.     

An integrated logarithmic fuzzy preference programming based methodology for optimum maintenance strategies selection

Selecting optimum maintenance strategies plays a key role in saving cost, and improving the system reliability and availability. Analytic hierarchical process (AHP) is widely used for maintenance strategies selection in the Multiple Criteria Decision-Making (MCDM) field. But the traditional or hybrid AHP methods either produce multiple, even conflict priority results, or have complicated algorithm structures which are unstable to obtain the optimum solution. Therefore, this paper proposes an integrated Logarithmic Fuzzy Preference Programming (LFPP) based methodology in AHP to solve the optimum maintenance strategies selection problem. The multiplicative constraints and deviation variables are applied instead of additive ones to utilize both qualitative and quantitative data, and process the upper and lower triangular fuzzy judgments to obtain the same priorities. The proposed methodology can produce the unique normalized optimal priority vector for fuzzy pairwise comparison matrices, and it is capable of processing all comparison matrices to obtain the global priorities simultaneously and directly in the form of super-matrix according to the different requirements and judgments of decision-makers. Finally, an example is provided to demonstrate the feasibility and validity of the proposed methodology.     

一种结合主客观信息的多属性决策方法

研究了具有模糊偏好信息的模糊多属性决策问题．提出一种结合主观偏好信息与客观信息的综合特征向量方法．主观偏好信息由决策方案的模糊偏好互补矩阵和属性权重的两两比较互反矩阵组成，客观信息由客观决策矩阵组成．给出了求解模糊多属性决策问题的最小二乘偏差估计方法．通过建立二次规划模型决定属性权重向量，并对方案进行排序．最后，给出了使用该方法的数值例子．     

Evaluating emergency response capacity by fuzzy AHP and 2-tuple fuzzy linguistic approach

Emergency management (EM) is a very important issue with various kinds of emergency events frequently taking place. One of the most important components of EM is to evaluate the emergency response capacity (ERC) of emergency department or emergency alternative. Because of time pressure, lack of experience and data, experts often evaluate the importance and the ratings of qualitative criteria in the form of linguistic variable. This paper presents a hybrid fuzzy method consisting fuzzy AHP and 2-tuple fuzzy linguistic approach to evaluate emergency response capacity. This study has been done in three stages. In the first stage we present a hierarchy of the evaluation index system for emergency response capacity. In the second stage we use fuzzy AHP to analyze the structure of the emergency response capacity evaluation problem. Using linguistic variables, pairwise comparisons for the evaluation criteria and sub-criteria are made to determine the weights of the criteria and sub-criteria. In the third stage, the ratings of sub-criteria are assessed in linguistic values represented by triangular fuzzy numbers to express the qualitative evaluation of experts’ subjective opinions, and the linguistic values are transformed into 2-tuples. Use the 2-tuple linguistic weighted average operator (LWAO) to compute the aggregated ratings of criteria and the overall emergency response capacity (OERC) of the emergency alternative. Finally, we demonstrate the validity and feasibility of the proposed hybrid fuzzy approach by means of comparing the emergency response capacity of three emergency alternatives.     

Combining VIKOR with GRA techniques to evaluate service quality of airports under fuzzy environment

The aim of this paper was to present an effective approach for evaluating service quality of Northeast-Asian international airports by conducting customer surveys. In general, evaluation of service quality is a complex multicriteria decision-making (MCDM) problem; therefore, a complex decision process is often involved in which multiple requirements and fuzzy conditions have to be taken into consideration simultaneously. By combining concepts of VIKOR and grey relational analysis (GRA), a new fuzzy MCDM method was proposed to deal with the evaluation of service quality problems in the international airports. This model was solved by an effective algorithm, which incorporated the decision-maker’s attitude and/or preference for customers’ assessments on weights and performance ratings of each criterion. An empirical study for evaluating service quality of seven major Northeast-Asian international airports was put forth to illustrate an application of the proposed model. The study results showed that this approach is an effective means for tackling MCDM problems involving subjective assessments of qualitative attributes in a fuzzy environment.     

A hybrid fuzzy MCDM approach to machine tool selection

The selection of the appropriate machine tools for a manufacturing company is one of the important points to achieving high competitiveness in the market. Besides, an appropriate choice of machine tools is very important as it helps to realize full production quickly. Today’s market offers many more choices for machine tool alternatives. There are also many factors one should consider as part of the appropriate machine tool selection process, including productivity, flexibility, compatibility, safety, cost, etc. Consequently evaluation procedures involve several objectives and it is often necessary to compromise among possibly conflicting tangible and intangible factors. For these reasons, multiple criteria decision making (MCDM) has been found to be a useful approach to solve this kind of problem. Most of the MCDM models are basically mathematical and ignore qualitative and often subjective considerations. The use of fuzzy set theory allows incorporating qualitative and partially known information into the decision model. This paper describes a fuzzy technique for order preference by similarity to ideal solution (TOPSIS) based methodology for evaluation and selection of vertical CNC machining centers for a manufacturing company in Istanbul, Turkey. The criteria weights are calculated by using the fuzzy AHP (analytical hierarchy process).     

Fuzzy development of crisp activity relationship charts for facilities layout

The traditional activity relationship chart (ARC) represents closeness ratings among departments in a facility. Usually these ratings are based on vague quantitative and/or qualitative factors. Some of these factors may have a larger effect on the assignment of the ratings than others. Thus, this paper presents a distinct methodology to develop a crisp activity relationship charts (CARC) based on fuzzy set theory and the pairwise comparison of Saaty's analytical hierarchy process (AHP), which ensures the consistency of the designer's assignments of importance of one factor over another to find the weight of each of the factors in every activity. FUZZY, a computer program developed based on AHP, and the fuzzy decision-making system (FDMS), is used to generate CARC.     

Consensus in innovation contest categorisation by means of fuzzy partitions

Consensus decision-making is fuzzy by nature, yet fuzzy consensus decision-making in a medium to large number of decisions is not widely used since it demands additional information that requires extra decision-maker effort. Consensus decision-making rests on properly measured agreement. This paper proposes a fuzzy measure of agreement through fuzzy kappa based on fuzzy partitions. These fuzzy partitions enable decision-makers to assess their decisions with a degree of confidence. A fuzzy partition is built for each decision-maker considering his/her confidence degrees when categorising a set of alternatives or solutions. This enables decision-makers to more easily capture the fuzzy nature of the decision. In addition, this paper presents a real-life experiment based on a innovation contest to show the feasibility of using confidence degrees in real-life applications compared to traditional consensus decision-making. The results suggest that the use of confidence degrees improves the level of agreement in the consensus decision-making process through fuzzy kappa coefficients, and it also improves the level of agreement in the consensus decision-making process.     

Integration of AHP-TOPSIS method for prioritizing the solutions of reverse logistics adoption to overcome its barriers under fuzzy environment

Reverse logistics practices are gaining attention due to industrial ecology, enforced legislation and corporate citizenship but presence of barriers make reverse logistics (RL) implementation difficult and hence reduce the success rate. To increase RL adoption, robust and flexible strategies are required to overcome its barriers. This study focuses on identification and ranking the solutions of reverse logistics adoption in electronics industry to overcome its barriers. It aids firms to ponder on high rank solutions and develop strategies to implement them on priority. This paper proposes a methodology based on fuzzy analytical hierarchy process (AHP) and fuzzy technique for order performance by similarity to ideal solution (TOPSIS) to identify and rank the solutions of RL adoption to overcome its barriers. Fuzzy AHP is applied to get weights of the barriers as criteria by pairwise comparison and final ranking of the solutions of RL adoption is obtained through fuzzy TOPSIS. The empirical case of Indian electronics industry is shown to illustrate the use of the proposed method. This proposed method offers a more precise, efficient and effective decision support tool for stepwise implementation of the solutions due to consideration of fuzzy environment. Finally sensitivity analysis is performed to illustrate the robustness of the method.     

Fuzzy multiple attributes group decision-making based on the ranking values and the arithmetic operations of interval type-2 fuzzy sets

In this paper, we present a new method to handle fuzzy multiple attributes group decision-making problems based on the ranking values and the arithmetic operations of interval type-2 fuzzy sets. First, we present the arithmetic operations between interval type-2 fuzzy sets. Then, we present a fuzzy ranking method to calculate the ranking values of interval type-2 fuzzy sets. We also make a comparison of the ranking values of the proposed method with the existing methods. Based on the proposed fuzzy ranking method and the proposed arithmetic operations between interval type-2 fuzzy sets, we present a new method to handle fuzzy multiple attributes group decision-making problems. The proposed method provides us with a useful way to handle fuzzy multiple attributes group decision-making problems in a more flexible and more intelligent manner due to the fact that it uses interval type-2 fuzzy sets rather than traditional type-1 fuzzy sets to represent the evaluating values and the weights of attributes.     

A fuzzy AHP approach to the determination of importance weights of customer requirements in quality function deployment

Quality function deployment (QFD) is an important tool in product planning that could contribute to increase in customer satisfaction and shorten product design and development time. During the QFD process, determination of the importance weights of customer requirements is a crucial and essential step. The analytic hierarchy process (AHP) has been used in weighting the importance. However, due to the vagueness and uncertainty existing in the importance attributed to judgement of customer requirements, the crisp pairwise comparison in the conventional AHP seems to be insufficient and imprecise to capture the degree of importance of customer requirements. In this paper, fuzzy number is introduced in the pairwise comparison of AHP. An AHP based on fuzzy scales is proposed to determine the importance weights of customer requirements. The new approach can improve the imprecise ranking of customer requirements which is based on the conventional AHP. Finally, an example of bicycle splashguard design is used to illustrate the proposed approach.     

多属性群决策中一种基于主观偏好确定属性权重的方法

提出一种多属性群决策中同时考虑专家群体对属性主观赋权的偏好和决策者对决策重要性认识的偏好来确定属性权重的方法,能够兼容专家实数型、区间型和语言型等类型的属性权重赋值.首先建立标准属性重要差异矩阵以实现专家对属性赋权的优劣比较和差异规范,定义统一的决策者偏好映射对其进行调整;然后求解各矩阵的排序向量以量化属性的相对重要程度,并与专家权重聚合得到属性权重向量;最后给出了方法的具体步骤,并通过算例说明了该方法的具体应用.     

Hierarchical semi-numeric method for pairwise fuzzy group decision making

Gradual improvements to a single-level semi-numeric method, i.e., linguistic labels preference representation by fuzzy sets computation for pairwise fuzzy group decision making are summarized. The method is extended to solve multiple criteria hierarchical structure pairwise fuzzy group decision-making problems. The problems are hierarchically structured into focus, criteria, and alternatives. Decision makers express their evaluations of criteria and alternatives based on each criterion by using linguistic labels. The labels are converted into and processed in triangular fuzzy numbers (TFNs). Evaluations of criteria yield relative criteria weights. Evaluations of the alternatives, based on each criterion, yield a degree of preference for each alternative or a degree of satisfaction for each preference value. By using a neat ordered weighted average (OWA) or a fuzzy weighted average operator, solutions obtained based on each criterion are aggregated into final solutions. The hierarchical semi-numeric method is suitable for solving a larger and more complex pairwise fuzzy group decision-making problem. The proposed method has been verified and applied to solve some real cases and is compared to Saaty's (1996) analytic hierarchy process (AHP) method.