Fuzzy arithmetic based reliability allocation approach during early design and development

During early design and development stages, every engineering system has to meet its specific reliability goals. The target reliability of the system is achieved through application of an effective reliability apportionment technique to its subsystems. There are various traditional methods exist to perform the reliability allocation based on engineering factors that are assessed in a subjective manner. The conventional reliability allocation approach requires the assessment of factors like complexity, cost, and maintenance. This may not be realistic in real applications if they are assessed in a crisp manner by the domain experts of their varied expertise and background.In this paper, we treat allocation factors as fuzzy numbers, which are evaluated in fuzzy linguistic terms. As a result, fuzzy proportionality factor scales are proposed for the subsystems. In order to accomplish fuzzy division to evaluate the fuzzy proportionality factor, an approximation method based on linear programming for trapezoidal fuzzy numbers is also proposed in this paper. For the evaluation of weighting factors from fuzzy proportionality factors, centroid method of defuzzification is being employed. The allocated reliability of each subsystem is computed with the help of weighting factor thereafter. An example is provided to illustrate the potential application of the proposed fuzzy based reliability allocation approach.     

Aggregating decision information into Atanassov's intuitionistic fuzzy numbers for heterogeneous multi-attribute group decision making

The aim of this paper is to propose a new aggregation method to solve heterogeneous MAGDM problem which involves real numbers, interval numbers, triangular fuzzy numbers (TFNs), trapezoidal fuzzy numbers (TrFNs), linguistic values and Atanassov's intuitionistic fuzzy numbers (AIFNs). Firstly, motivated by the relative closeness of technique for order preference by similarity to ideal solution (TOPSIS), we propose a new general method for aggregating crisp values, TFNs, TrFNs and linguistic values into AIFNs. Thus all the group decision matrices for each alternative which involves heterogeneous information are transformed into an Atanassov's intuitionistic fuzzy decision matrix which only contains AIFNs. To determine the attribute weights, a multiple objective Atanassov's intuitionistic fuzzy programming model is constructed and solved by converting it into a linear program. Subsequently, comparison analyses demonstrate that the proposed aggregated technology can overcome the drawbacks of existing methods. An example about cloud computing service evaluation is given to verify the practicality and effectiveness of the proposed method.     

Multiple attribute group decision-making methods based on trapezoidal fuzzy two-dimension linguistic power generalized aggregation operators

On the basis of two-dimension uncertain linguistic variables, in this paper, we further presented a trapezoidal fuzzy two-dimension linguistic variable in which the first dimensional linguistic uncertain information is extended to trapezoidal fuzzy number. First, the definition, operational laws, characteristics, expectation, comparative method and distance of trapezoidal fuzzy two-dimension linguistic information are proposed. Then, the trapezoidal fuzzy two-dimension linguistic power generalized aggregation operator and the trapezoidal fuzzy two-dimension linguistic power generalized weighted aggregation (TF2DLPGWA) operator are developed, and some properties and special cases of these operators are analyzed. Furthermore, based on the TF2DLPGWA operator and the comparative formula of the trapezoidal fuzzy two-dimension linguistic variables, an approach to group decision making with trapezoidal fuzzy two-dimension linguistic variables is established. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.     

Multicriteria group decision-making method using the distances-based similarity measures between intuitionistic trapezoidal fuzzy numbers

The Hamming and Euclidean distances between intuitionistic trapezoidal fuzzy numbers and the distances-based similarity measures are proposed in this study, then an intuitionistic trapezoidal fuzzy multicriteria group decision-making method is established using the similarity measures and expected weight values, in which linguistic values of intuitionistic trapezoidal fuzzy numbers for linguistic terms are used to assess alternatives with respect to qualitative criteria and criteria weights. We establish simple and exact formulae to solve the multicriteria group decision-making problem based on the similarity measures between the ideal alternative and each alternative, the ranking order of all the alternatives and the best one can be determined by the proposed similarity measures. Finally, an illustrative example demonstrates the implementation process of the technique.     

Fuzzy cognitive map based quality function deployment approach for dishwasher machine selection

The traditional quality function deployment (QFD) approach deals with the weights of customer requirements (CRs), relationships among CRs and design requirements (DRs), correlation among DRs by using crisp values. This paper uses fuzzy numbers to improve the drawbacks of the traditional QFD method because fuzzy numbers enable to make consistent decisions in uncertain environment to decision makers. The existing papers handle a simple multiplication operation to calculate the correlation among CRs and the correlation among DRs. This study proposes fuzzy cognitive map (FCM) approach to calculate these correlations so that FCM is a successful method to handle the interactions among criteria. This paper contributes to the literature by integrating QFD approach and fuzzy cognitive map approach. The weights of DRs are defined in the result of the proposed QFD approach. These weights are used to evaluate the dishwasher machine alternatives in intuitionistic fuzzy VIKOR method. Intuitionistic fuzzy number (IFS) ensures to handle more information than type-1 fuzzy number to describe the fuzziness and the uncertainty of the real life world. Finally, the proposed approach has been implemented to a dishwasher machine selection in order to test its validity.     

Optimal location selection for an international distribution center by using a new hybrid method

The selection of a location for an international distribution center (IDC) is a most important decision for international logistics managers owing to the need to consider various criteria that involve a complex decision process in which multiple requirements and uncertain conditions have to be taken into consideration simultaneously. Moreover, the criteria often exist simultaneously as independent and dependent characteristics when the problems of location selection have become very complex. A new hybrid method combining the concepts of fuzzy DEMATEL and a new method of fuzzy multiple criteria decision-making (MCDM) in a fuzzy environment is proposed to solve the problems of IDC location selection. In this paper, the fuzzy DEMATEL is proposed to arrange a suitable structure between criteria, and the analytic hierarchy/network process (AHP/ANP) is used to construct weights of all criteria. The linguistic terms characterized by triangular fuzzy numbers are used to denote the evaluation values of all alternatives versus various criteria. Finally, the aggregation fuzzy assessments of different alternatives are ranked to determine the best selection. Furthermore, this paper uses an empirical case for optimal location selection for an IDC in Pacific Asia to illustrate the proposed method, and the results show that the method is an effective means for tackling fuzzy MCDM problems.     

Robot selection by using generalized interval-valued fuzzy numbers with TOPSIS

The aim of this paper is to propose a method to aggregate the opinion of several decision makers on different criteria, regarding a set of alternatives, where the judgment of the decision makers are represented by generalized interval-valued trapezoidal fuzzy numbers. A generalized interval valued trapezoidal fuzzy number based technique for order preference by similarity to ideal solution is proposed that can reflect subjective judgment and objective information in real life. The weights of criteria and performance rating values of criteria are linguistic variables expressed as generalized interval-valued trapezoidal fuzzy numbers. Finally, an illustrative example is provided to elaborate the proposed method for the selection of a suitable robot according to our requirements.     

SNA-based multi-criteria evaluation of multiple construction equipment: A case study of loaders selection

Selecting the proper construction equipment is a challenging task owing to a wide range of available types as well as a host of criteria to be considered during decision making. To deal with this, a heterogeneous group decision-making framework to evaluate multiple purchasing choices of construction equipment is proposed with two data forms, i.e., 2-dimension uncertain linguistic variables (2DULVs) and real numbers. Firstly, a novel way to derive weights of experts by social network analysis (SNA) is applied considering trust degrees among experts in a social trust network. Secondly, after evaluation index system is established, 2DULVs that include both the linguistic evaluations on alternatives and decision makers’ appraisals on the given evaluation results are applied to represent subjective fuzzy evaluation information, while real numbers are used to represent quantitative values. Thirdly, 2-dimension uncertain linguistic power generalized weighted aggregation (2DULPGWA) operator is applied to aggregate evaluation values among experts. Fourthly, analytic hierarchy process (AHP) and entropy method are utilized to derive combined weights of sub-criteria before the rank can be obtained by the evaluation based on distance from average solution (EDAS) method. Finally, a case study to evaluate multiple choices of loaders is proposed and a comparative analysis is conducted to prove the effectiveness of the proposed framework. This study provides a meaningful guidance for the optimal selection among various types of construction equipment.     

不确定语言信息下的大规模群体DEMATEL决策方法

针对现有不确定语言决策试验和评价实验(DEMATEL)方法大多仅适用于中小规模群体,且未考虑不确定语言变量采用非均匀标度的情况,探讨一种新的不确定语言信息下的大规模群体DEMATEL决策方法.首先,给出一种群体不确定语言DEMATEL矩阵的聚类方法,并对大规模群体DEMATEL意见进行合理分组;然后,定义三维不确定语言密度算子,并对大规模群体DEMATEL意见进行有效集结;最后,提出一种改进的基于不确定语言DEMATEL的指标权重确定方法,并在此基础上进行多属性决策.算例分析验证了所提方法的可行性与有效性,该方法采用非均匀标度来表征和呈现不确定语言变量,而且考虑了大规模群体决策的共识度,使得决策结果更为客观合理且更为可靠.     

零模的直觉模糊不确定语言集成算子研究

基于零模与共轭零模算子,探讨了直觉模糊不确定语言变量运算法则,得到了基于零模与共轭零模的直觉模糊不确定语言加权几何算子,并给出了一种使用直觉不确定语言变量的集成算子的多属性群决策方法,最后通过Matlab软件分析了直觉模糊不确定语言加权几何算子的K值与语言术语下标间关系。为多属性群决策提供了有价值的参考,有效地解决了一类具有直觉模糊不确定语言评估信息的多属性群决策问题。     

基于直觉模糊数的信息不完全的多准则规划方法

定义了直觉模糊数和直觉梯形模糊数及其期望值.针对权系数信息不完全确定和准则值为直觉梯形模糊数的多准则决策问题,提出了信息不完全确定的直觉梯形模糊多准则决策的规划方法.该方法利用权系数的不完全信息构造方案集综合期望值的最优线性规划模型,求解该模型得到各准则的最优权系数,进而得到各方案综合期望值的区间数.利用区间数可能度法对其进行比较,得到整个方案集的排序.实例分析说明了该方法的有效性和可行性.     

SUBJECTIVE MENTAL WORKLOAD ASSESSMENT BASED ON GENERALIZED FUZZY NUMBERS

In this article, a new method for subjective mental workload assessment is presented based on generalized fuzzy numbers. First, the linguistic values are modeled as generalized fuzzy numbers, which is more efficient in dealing with uncertain information and representing experts' opinions than normal fuzzy numbers due to the fact that the degree of confidence of decision makers' opinions is taken into consideration. In addition, compared with existing methods, the result of the proposed method is more reasonable because it can correctly determine the degree of similarity between the assessment and the linguistic terms. A numerical example is used to show that the proposed method can provide a useful way to handle subjective mental workload assessments in a linguistic manner.     

Group decision making process for supplier selection with VIKOR under fuzzy environment

During recent years, how to determine suitable suppliers in the supply chain has become a key strategic consideration. However, the nature of supplier selection is a complex multi-criteria problem including both quantitative and qualitative factors which may be in conflict and may also be uncertain. The VIKOR method was developed to solve multiple criteria decision making (MCDM) problems with conflicting and non-commensurable (different units) criteria, assuming that compromising is acceptable for conflict resolution, the decision maker wants a solution that is the closest to the ideal, and the alternatives are evaluated according to all established criteria. In this paper, linguistic values are used to assess the ratings and weights for these factors. These linguistic ratings can be expressed in trapezoidal or triangular fuzzy numbers. Then, a hierarchy MCDM model based on fuzzy sets theory and VIKOR method is proposed to deal with the supplier selection problems in the supply chain system. A numerical example is proposed to illustrate an application of the proposed model.     

Research on the multi-attribute decision-making under risk with interval probability based on prospect theory and the uncertain linguistic variables

With respect to risk decision making problems with interval probability in which the attribute values take the form of the uncertain linguistic variables, a multi-attribute decision making method based on prospect theory is proposed. To begin with, the uncertain linguistic variables can be transformed into the trapezoidal fuzzy number, and the prospect value function of the trapezoidal fuzzy number based on the decision-making reference point of each attribute and the weight function of interval probability can be constructed; then the prospect value of attribute for every alternative is calculated through prospect value function of the trapezoidal fuzzy number and the weight function of interval probability, and the weighted prospect value of alternative is acquired by using weighted average method according to attribute weights, and all the alternatives are sorted according to the expected values of the weighted prospect values; Finally, an illustrate example is given to show the decision-making steps, the influence on decision making for different parameters of value function and different decision-making reference point, and the feasibility of the method.     

Mining fuzzy β-certain and β-possible rules from quantitative data based on the variable precision rough-set model

The rough-set theory proposed by Pawlak, has been widely used in dealing with data classification problems. The original rough-set model is, however, quite sensitive to noisy data. Ziarko thus proposed the variable precision rough-set model to deal with noisy data and uncertain information. This model allowed for some degree of uncertainty and misclassification in the mining process. Conventionally, the mining algorithms based on the rough-set theory identify the relationships among data using crisp attribute values; however, data with quantitative values are commonly seen in real-world applications. This paper thus deals with the problem of producing a set of fuzzy certain and fuzzy possible rules from quantitative data with a predefined tolerance degree of uncertainty and misclassification. A new method, which combines the variable precision rough-set model and the fuzzy set theory, is thus proposed to solve this problem. It first transforms each quantitative value into a fuzzy set of linguistic terms using membership functions and then calculates the fuzzy β-lower and the fuzzy β-upper approximations. The certain and possible rules are then generated based on these fuzzy approximations. These rules can then be used to classify unknown objects. The paper thus extends the existing rough-set mining approaches to process quantitative data with tolerance of noise and uncertainty.     

A method for group decision making with multi-granularity linguistic assessment information

This paper proposes a method to solve the group decision making (GDM) problems with multi-granularity linguistic assessment information. In the method, the multi-granularity linguistic information provided by experts is firstly expressed in the form of fuzzy numbers. In order to make the collective opinion close to each expert’s opinion, a linear goal programming model is constructed to integrate the fuzzy assessment information and to directly compute the collective ranking values of alternatives without the need of information transformation. Then, a fuzzy preference relation on the pairwise comparisons of the collective ranking values of alternatives is constructed using the dominance possibility degree of the comparison between the fuzzy numbers. By applying a non-dominance choice degree to this fuzzy preference relation, the ranking of alternatives is determined and the most desirable alternative(s) is selected. An example is used to illustrate the applicability of the proposed method and its advantages.     

A normal wiggly hesitant fuzzy linguistic projection-based multiattributive border approximation area comparison method

As a useful information representation tool, hesitant fuzzy linguistic term set (HFLTS) allows decision makers (DMs) to express their cognitive preferences in terms of several ordered and continuous linguistic terms. Considering the fact that much valuable information related to the cognitive behavior of DMs is hidden in the original evaluation information, this paper studies how to comprehensively mine uncertain information from original hesitant fuzzy linguistic evaluation information given by DMs. To address this objective, we present a new representation tool, normal wiggly hesitant fuzzy linguistic term set (NWHFLTS), which not only retains the original evaluation information, but also delivers and quantifies potential uncertain information, and can also help DMs express their evaluation information in a more complete manner. First, we develop the basic operations, score function, and comparison rule of NWHFLTS based on linguistic scale functions (LSFs), and propose the projection measure, the normal projection measure, and the normalized projection-based distance measure to describe the degree of deviation between two NWHFLTSs. Furthermore, for the case when the attribute weight is completely unknown, we combine the multiattributive border approximation area comparison (MABAC) method and develop a new method called as normal wiggly hesitant fuzzy linguistic projection-based MABAC to solve the multiattribute decision-making problems where attribute values are expressed in the form of NWHFLTS. Finally, through a practical example of marine ecological security situation, the specific calculation steps of this method are exemplified, the feasibility and advancement of the proposed method are demonstrated via a comprehensive comparative study.     

Risk assessment in IT outsourcing using fuzzy decision-making approach: An Indian perspective

Outsourcing of Information Technology (IT) is a common practice in global business today. IT Outsourcing (ITO) refers to the contracting out of IT services (or functions) with the objective of achieving strategic advantages as well as cost benefits. Recently, many IT industries are facing daunting challenges in terms of healthy alliances on their ITO strategy due to existence of inherent risks. These risks must be recognized and properly managed towards successful establishment of effective ITO strategy. Therefore, risk assessment appears to be an important contributor to the success of an ITO venture. In this paper, a hierarchical ITO risk structure representation has been explored to develop a formal model for qualitative risk assessment. The basic parameters for defining risks have been presented including the metrics for measuring likelihood and impact that aid to achieve consistent assessment. An improved decision making method using fuzzy set theory has been attempted for converting linguistic data into numeric risk ratings. In this study, the concept of ‘Incentre of centroids method’ for generalized trapezoidal fuzzy numbers has been used to quantify the ‘degree of risk’ in terms of crisp ratings. Finally, a framework for categorizing different risk factors has been proposed on the basis of distinguished ranges of risk ratings (crisp). Consequently, an action requirement plan has been suggested for providing guidelines for the managers to successfully manage the risk in the context of ITO exercise.     

Risk evaluation in failure mode and effects analysis with extended VIKOR method under fuzzy environment

Failure mode and effects analysis (FMEA) is a widely used risk assessment tool for defining, identifying, and eliminating potential failures or problems in products, process, designs, and services. In traditional FMEA, the risk priorities of failure modes are determined by using risk priority numbers (RPNs), which can be obtained by multiplying the scores of risk factors like occurrence (O), severity (S), and detection (D). However, the crisp RPN method has been criticized to have several deficiencies. In this paper, linguistic variables, expressed in trapezoidal or triangular fuzzy numbers, are used to assess the ratings and weights for the risk factors O, S, and D. For selecting the most serious failure modes, the extended VIKOR method is used to determine risk priorities of the failure modes that have been identified. As a result, a fuzzy FMEA based on fuzzy set theory and VIKOR method is proposed for prioritization of failure modes, specifically intended to address some limitations of the traditional FMEA. A case study, which assesses the risk of general anesthesia process, is presented to demonstrate the application of the proposed model under fuzzy environment.     

Dynamic response of imprecisely defined beam subject to various loads using Adomian decomposition method

Present paper proposes a new technique based on double parametric form of fuzzy numbers to solve an uncertain beam equation using Adomian decomposition method subject to unit step and impulse loads. Uncertainties appear in the initial conditions are considered in terms of triangular convex normalized fuzzy sets. Using the single parametric form viz. α-cut form of fuzzy numbers, the fuzzy beam equation is converted first to an interval based fuzzy differential equation. Next this differential equation is transformed to crisp form by applying double parametric form of fuzzy numbers. Finally the same is solved by Adomian decomposition method symbolically to obtain the uncertain bounds of the dynamic response. Obtained results are depicted in term of plots to show the efficiency and powerfulness of the present analysis.