Multi‐adjoint Relation Equations: A Decision Support System for Fuzzy Logic

Fuzzy relation equations (FRE) are an important decision support system (DSS), for example, in fuzzy logic. FRE have recently been extended to a more general framework, called multiadjoint relation equations (MARE). This paper shows MARE as a fundamental DSS in multi‐adjoint logic programming. For that purpose, multi‐adjoint logic programs will be interpreted as a MARE, and the solvability of them will be given in terms of concept lattice theory. Furthermore, two approximations (optimistic and pessimistic approximations) of unsolvable equations will be obtained from a multiadjoint object‐oriented concept lattice. Finally, a real‐life example will be studied.     

补偿模糊神经网络在模糊规则训练中的应用

目前，自治式水下机器人（Autonomous Underwater Vehicle，AUV）、自动导引驾驶小汽车、轮船等领域应用模糊规则控制已经受到许多人的关注，模糊规则的制定与训练是其中之关键所在，该文将模朔规则控制应用在无人机自由编队飞行控制中。在训练模糊规则过程中，常规的BP神经网络法存在学习速度慢、无法结合号家知识以及容易陷入局部最小等缺点，为了克服上述不足，文中引人了补偿模糊神经网络，它足一个结合了补偿模糊逻辑和神经网络的混合系统，由面向控制和面向决策的神经元组成，其模糊运算采用动态的、全局优化运算，学习速度快、学习过程稳定。将其用于无人机自由编队飞行的模糊控制规则进行训练，结果表明用补偿模糊神经网络刘模糊规则的训练效果良好。     

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.     

An integrated DEMATEL and Fuzzy ANP techniques for evaluation and selection of outsourcing provider for a telecommunication company

In recent years, strategy aspects related to core competency, risk analysis and organizational flexibility especially have been growing. This trend has led researchers and industries to become more interested in the multi-criteria decision making (MCDM) models for selecting outsourcing providers. The efficiency of decision-making mostly depends on the ability of decision-makers analyzing the complex cause and effect relationship between criteria and taking effective actions based on the analysis. Using an analytical method to select the most eligible outsourcing provider is significant for a company which desires to improve its competitiveness. In this study, a fuzzy integrated multi-criteria decision making method for evaluation and determination of an outsourcing provider for a telecommunication company is analyzed by using DEMATEL and Fuzzy ANP multi-criteria decision making techniques. First, DEMATEL method is used in order to put forward the interrelationship among the main criteria which are determined in the study for outsourcing selection process. Then, local weights of the sub-criteria and sub-subcriteria are calculated by Fuzzy ANP approach on the basis of cause-effect relationships that are exposed through DEMATEL method. The local weights are put into ANP supermatrix, and calculations are implemented to select out the most eligible outsourcing provider.     

Development of a fuzzy decision support framework for complex multi‐attribute decision problems: A case study for the selection of skilful basketball players

The selection of skilful players is a complicated process due to the problem criteria consisting of both qualitative and quantitative attributes as well as vague linguistic terms. This study seeks to develop a decision support framework for the selection of candidates eligible to become basketball players through the use of a fuzzy multi‐attribute decision making (MADM) algorithm. The proposed model is based on fuzzy analytic hierarchy process (FAHP) and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) methods. The model was employed in the Youth and Sports Center of Mugla, Turkey, with the participation of seven junior basketball players aged between 7 and 14. In the present study, physical fitness measurement values and observation values of technical skills were utilized. FAHP was used to determine the weights of the criteria and the observation values of technical skills by decision makers. Physical fitness measurement values were converted to fuzzy values by using a fuzzy set approach. Subsequently, the overall ranking of the candidate players was determined by the TOPSIS method. Results were compared with human experts’ opinions. It is observed that the developed model is more reliable to be used in decision making. The model architecture and experimental results along with illustrative examples are further demonstrated in the study.     

Fuzzy quality function deployment: determining the distributions of effort dedicated to technical change

A model is presented that develops the Quality Function Deployment (QFD) House of Quality tool into a fuzzy‐set based multi‐criteria decision‐making process to determine the distributions of effort directed toward technical changes. When customers are polled for desired product‐specific attributes, the responses are typically defined by linguistic variables that represent a fuzzy set distribution. Fuzzy sets also define customer perceptions of the product attributes and technical expert opinions about product design criteria relative to marketplace competitors. Therefore, for each technical criterion, the following factors have an effect on the decision to implement change(s): (1) fuzzy sets providing evidence of customer need for attributes; (2) motivation to change to satisfy desired customer attributes; (3) motivation for technical criterion change; and (4) the strength of the relationships between the attributes and the technical criterion. Priority rankings are linked to the distributions of effort to apply in fulfilling continuous product improvement.     

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 new flexible and reliable IVF-TOPSIS method based on uncertainty risk reduction in decision making process

One of the challenging and famous types of MCDM (Multiple Criteria Decision Making) problems that includes both quantitative and qualitative criteria is Facility location selection problem. For the common fuzzy MCDM problems (Type-1 fuzzy MCDM problems), the ratings of alternatives with respect to the criteria or/and the values of criteria weights, are expressed by the common fuzzy numbers. However, in the majority of cases, determining the exact membership degree for each element of the fuzzy sets which are considered for the ratings of alternatives with respect to the criteria or/and the values of criteria weights as a number in interval [0,1], is difficult. In this situation, the ratings of alternatives with respect to the criteria or/and the values of criteria weights, are expressed by the IVFNs (Interval Valued Fuzzy Numbers) and thereby the IVF-MCDM (Interval Valued Fuzzy MCDM) methods should be used. In this paper, the authors propose an IVF-TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) method based on uncertainty risk reduction in decision making process. By using this method, the reliability of the captured decisions in an IVF decision making problem is significantly increased. The proposed method is applied for solving a real application problem related to selecting a suitable location for digging some pits for municipal wet waste landfill in one of the largest cities in Iran. The proposed method is also compared with another IVF-TOPSIS method. As a result, the authors concluded that in addition to benefits such as simplicity and ease of use that exist in the previous IVF-TOPSIS methods, the proposed method has a significant reliability and flexibility and is practical for facility location selection problems and other IVF-MCDM problems.     

基于模糊目标和模糊约束的满意控制

研究在预测控制框架下进行模糊决策问题,提出一种基于模糊目标和模糊约束的预测控制方法。其目标函数以决策者的控制要求和最终控制的满意度来表示,比传统的加权方差具有更多的自由度;与基于二次型性能指标的预测相比,该方法可使系统设计更加灵活。仿真结果表明了该方法的有效性。     

Usability testing in 2000 and beyond

Usability testing is a widely used technique to evaluate user performance and acceptance of products and systems. It was introduced in the late 1980s and rose to popularity in the past decade. This paper provides a view of the current status of usability testing as a method and describes how it will be used in the 21st century. Although usability testing may not be the most efficient technique for discovery of usability problems, it is a reliable way to estimate quantitatively users' performance and subjective satisfaction with products. Four major trends in usability testing include: common reporting formats and methods for industry; Internet application and website testing; testing of mobile, handheld devices; and testing in more naturalistic environments such as simulated homes and classrooms. In the 21st century, ‘quick and clean’ usability testing methods are needed to provide valid and reliable data on how well people use products and systems, and how they like using them.     

广义直觉模糊几何Bonferroni平均及其多属性决策

针对直觉模糊环境中的信息集成问题,基于阿基米德T-范数和S-范数,提出新的广义直觉模糊几何Bonferroni平均算子。该算子不仅能够考虑到每种属性的重要性,而且可以有效地捕获属性间的内在联系。首先,基于阿基米德T-范数和S-范数的直觉模糊运算法则,提出一种新的广义直觉模糊几何Bonferroni平均算子,并研究该算子的几种优良性质,包括幂等性、单调性、有界性和置换不变性;其次,探讨了广义直觉模糊几何Bonferroni平均算子的几类特殊形式;最后,基于提出的算子构建一种新的直觉模糊多属性决策方法,并结合区域经济发展研究实例。实验结果表明,提出的决策方法是可行的和有效的,并且使得决策者能够依据其态度进行决策。     

Extension of weighted aggregated sum product assessment with interval-valued intuitionistic fuzzy numbers (WASPAS-IVIF)

Different methods are proposed in the framework of multi attribute utility theory for multi criteria decision making. Among the proposed methods, weighted sum and weighted product models (WSM and WPM) are well known and widely accepted. To improve the accuracy of WSM and WPM, the weighted aggregated sum product assessment (WASPAS) method was proposed which used an aggregation operator on WSM and WPM. In this paper, an extended version of WASPAS method is proposed which can be applied in uncertain decision making environment. In the proposed WASPAS-IVIF method, the uncertainty of decision maker(s) in stating their judgments and evaluations regard to criteria importance and/or alternatives performance on criteria are expressed by interval valued intuitionistic fuzzy numbers. Two numerical examples of ranking derelict buildings’ redevelopment decisions and investment alternatives are presented. The results are then compared with the rankings provided by other methods such as TOPSIS-IVIF, COPRAS-IVIF and IFOWA. Combining the strengths of IVIFS in handling uncertainty with the enhanced accuracy of WASPAS makes the proposed method as a desirable method for multi criteria decision making in real world applications.     

Soil moisture Fuzzy Estimation Approach based on Decision-Making

This paper presents a Fuzzy Estimation Approach based on Decision Making (FEADM) to estimate point soil moisture, in order to develop a regional soil moisture estimate. This keeps the advantages of an automatic irrigation system but avoiding their operational complexity. In the FEADM 's first stage, the Fuzzy Analytical Process weigh five fuzzified environmental inputs used as assessment criteria. These criteria are used by a selective assessment stage, where only the relevant criteria for each alternative are assessed. As result, the best assessments of each alternative and the best assessed alternative are obtained. In the second stage, an output membership function is assigned to every alternative for its forward aggregation and defuzzification. This process reaches a soil moisture estimate. Unlike other models, FEADM allows estimating a quantitative value from a decision making process. Furthermore, its computational cost is lower than conventional fuzzy estimation models due to the selective assessment.     

An Application of the Fuzzy ELECTRE Method for Academic Staff Selection

There are various methods regarding staff selection in different fields. Thanks to the increasing improvements in the field of education, universities around the world tend to demand high ‐quality and professional academic staff. Staff selection is a multi‐criteria decision‐making processes, and of strategic importance for most universities. This study deals with actual application of academic of staff selection using the opinion of experts to be applied into a model of group decision ‐ making called the Fuzzy ELECTRE (Elimination Et Choix Traduisant la REaite) method. There are ten qualitative criteria for selecting the best candidate amongst five prospective applications. © 2012 Wiley Periodicals, Inc.     

A new flexible and reliable interval valued fuzzy VIKOR method based on uncertainty risk reduction in decision making process: An application for determining a suitable location for digging some pits for municipal wet waste landfill

Facility location selection problem is one of the challenging and famous kinds of MCDM problems including both quantitative and qualitative criteria. For each Multiple Criteria Decision Making (MCDM) problem, when the ratings of alternatives with respect to the criteria and/or the values of criteria’s weights are presented by Interval Valued Fuzzy Numbers (IVFNs), the conventional fuzzy MCDM methods (Type-1 fuzzy MCDM methods) tend to be less effective. Therefore, the IVF-MCDM (Interval Valued Fuzzy MCDM) methods should be applied for solving such fuzzy MCDM problems. In this paper, we propose an IVF-VIKOR (VlseKriterijumska Optimizacija I Kompromisno Resenje) method based on uncertainty risk reduction in decision making process. By using such method, the reliability of the captured decisions in an IVF decision making problem is significantly increased. The proposed method is applied for solving two numerical examples that the former of which is a real application problem related to selecting a suitable location for digging some pits for municipal wet waste landfill in one of the largest cities in Iran. The second numerical example is presented with an aim of comparing our method with the two other IVF-MCDM methods. As a result, we found out the proposed method is reliable and practical for the facility location selection problems and other MCDM problems. Moreover, the proposed method has a considerable accuracy and is flexible and easy to use.     

Fuzzy optimization of units products in mix-product selection problem using fuzzy linear programming approach

In this paper, the modified S-curve membership function methodology is used in a real life industrial problem of mix product selection. This problem occurs in the production planning management where by a decision maker plays important role in making decision in an uncertain environment. As analysts, we try to find a good enough solution for the decision maker to make a final decision. An industrial application of fuzzy linear programming (FLP) through the S-curve membership function has been investigated using a set of real life data collected from a Chocolate Manufacturing Company. The problem of fuzzy product mix selection has been defined. The objective of this paper is to find an optimal units of products with higher level of satisfaction with vagueness as a key factor. Since there are several decisions that were to be taken, a table for optimal units of products respect to vagueness and degree of satisfaction has been defined to identify the solution with higher level of units of products and with a higher degree of satisfaction. The fuzzy outcome shows that higher units of products need not lead to higher degree of satisfaction. The findings of this work indicates that the optimal decision is depend on vagueness factor in the fuzzy system of mix product selection problem. Further more the high level of units of products obtained when the vagueness is low.     

A comparison between Fuzzy AHP and Fuzzy TOPSIS methods to supplier selection

Supplier selection has become a very critical activity to the performance of organizations and supply chains. Studies presented in the literature propose the use of the methods Fuzzy TOPSIS (Fuzzy Technique for Order of Preference by Similarity to Ideal Solution) and Fuzzy AHP (Fuzzy Analytic Hierarchy Process) to aid the supplier selection decision process. However, there are no comparative studies of these two methods when applied to the problem of supplier selection. Thus, this paper presents a comparative analysis of these two methods in the context of supplier selection decision making. The comparison was made based on the factors: adequacy to changes of alternatives or criteria; agility in the decision process; computational complexity; adequacy to support group decision making; the number of alternative suppliers and criteria; and modeling of uncertainty. As an illustrative example, both methods were applied to the selection of suppliers of a company in the automotive production chain. In addition, computational tests were performed considering several scenarios of supplier selection. The results have shown that both methods are suitable for the problem of supplier selection, particularly to supporting group decision making and modeling of uncertainty. However, the comparative analysis has shown that the Fuzzy TOPSIS method is better suited to the problem of supplier selection in regard to changes of alternatives and criteria, agility and number of criteria and alternative suppliers. Thus, this comparative study contributes to helping researchers and practitioners to choose more effective approaches for supplier selection. Suggestions of further work are also proposed so as to make these methods more adequate to the problem of supplier selection.     

Using quality function deployment for collaborative product design and optimal selection of module mix

In response to fast-growing and rapidly-changing markets, launching new products faster than competitors cannot only assist firms in acquiring larger market share but also reducing development lead time, significantly. However, owing to its intrinsically uncertain properties of managing NPD (new product development), manufacturing companies often struggle with the dilemma of increasing product variety or controlling manufacturing complexity. In this study, a fuzzy MCDM (multi-criteria decision making) based QFD (quality function deployment) which integrates fuzzy Delphi, fuzzy DEMATEL (decision making trial and evaluation laboratory), with LIP (linear integer programming) is proposed to assist an enterprise in fulfilling collaborative product design and optimal selection of module mix when aiming at multi-segments. In particular, Fuzzy Delphi is adopted to gather marketing information from invited customers and their assessments of marketing requirements are pooled to reach a consensus; fuzzy DEMATEL is utilized to derive the priorities of technical attributes in a market-oriented manner; and LIP is used to maximize product capability with consideration of supplier’s budget constraints of manufacturing resources. Furthermore, a real case study on developing various types of sport and water digital cameras is demonstrated to validate the proposed approach.