Fuzzy system reliability evaluation using time-dependent intuitionistic fuzzy set

In general, fuzzy sets are used to analyse the system reliability. In this article, the concept of fuzzy set is extended by the idea of intuitionistic fuzzy set (IFS) and a new general procedure is proposed to construct the membership and non-membership functions of the fuzzy reliability using time-dependent IFS. Here, failure rate function of the system is represented by a triangular intuitionistic fuzzy number (IFN). Also, using proposed approach, membership and non-membership functions of fuzzy reliability of series and parallel systems are constructed, where the failure rate of each component is taken as a time-dependent triangular IFN. The major advantage of using IFS over fuzzy sets is that IFS separate the positive and negative evidences for membership of an element in the set. Numerical examples are given to illustrate the proposed approach.     

A risk assessment methodology using intuitionistic fuzzy set in FMEA

Most current risk assessment methods use the risk priority number (RPN) value to evaluate the risk of failure. However, conventional RPN methodology has been criticised as having five main shortcomings as follows: (1) the assumption that the RPN elements are equally weighted leads to over simplification; (2) the RPN scale itself has some non-intuitive statistical properties; (3) the RPN elements have many duplicate numbers; (4) the RPN is derived from only three factors mainly in terms of safety; and (5) the conventional RPN method has not considered indirect relations between components. To address the above issues, an efficient and comprehensive algorithm to evaluate the risk of failure is needed. This article proposes an innovative approach, which integrates the intuitionistic fuzzy set (IFS) and the decision-making trial and evaluation laboratory (DEMATEL) approach on risk assessment. The proposed approach resolves some of the shortcomings of the conventional RPN method. A case study, which assesses the risk of 0.15?µm DRAM etching process, is used to demonstrate the effectiveness of the proposed approach. Finally, the result of the proposed method is compared with the listing approaches of risk assessment methods.     

Weight computation of criteria in a decision-making problem by knowledge measure with intuitionistic fuzzy set and interval-valued intuitionistic fuzzy set

The aim of this study is to propose an objective method for determining weights of criteria (also called attributes) based on a new measure of intuitionistic fuzzy information, called knowledge measure, in a real-world multi-criteria decision-making problem under intuitionistic fuzzy and interval-valued intuitionistic fuzzy environment. To address this issue, we first analyze the existing entropy measures and show that their use in objective weight determination process may lead us to produce unreliable weights of criteria by citing appropriate examples. Then we analyze important properties of knowledge measure of intuitionistic fuzzy set (IFS) and also define knowledge measure for interval-valued intuitionistic fuzzy set. Then a new method to determine the weights of criteria is developed on the basis of knowledge measure where information about criteria weights is completely unknown and partly known. A real-life example is presented to illustrate the proposed weight determination method and a comparative analysis is carried out to indicate the practicality and effectiveness of knowledge-based weight-generation method under both intuitionistic fuzzy and interval-valued intuitionistic fuzzy environment. Finally, we formulate the axioms for knowledge measure associated with IFSs and we also propose families (classes) of knowledge measures.     

直觉模糊集的结构化分析

直觉模糊集理论采用隶属度函数和非隶属度函数刻画不确定性信息,具有一定程度的主观性。为了研究直觉模糊集的本质特征,提出一种直觉模糊集的结构化分析方法,定义了直觉模糊相容关系,给出了直觉模糊集的同构原理,讨论了直觉模糊集的结构化特征。所得结果表明,直觉模糊集也具有客观性的一面。     

A revised method for ranking fuzzy numbers using maximizing set and minimizing set

A large number of methods have been proposed for ranking fuzzy numbers in the last few decades. Nevertheless, none of these methods can always guarantee a consistent result for every situation. Some of them are even non-intuitive and not discriminating. Chen proposed a ranking method in 1985 to overcome these limitations and simplify the computational procedure based on the criteria of total utility through maximizing set and minimizing set. However, there were some shortcomings associated with Chen’s ranking method. Therefore, we propose a revised ranking method that can overcome these shortcomings. Instead of considering just a single left and a single right utility in the total utility, the proposed method considers two left and two right utilities. In addition, the proposed method also takes into account the decision maker’s optimistic attitude of fuzzy numbers. Several comparative examples and an application demonstrating the usage, advantages, and applicability of the revised ranking method are presented. It can be concluded that the revised ranking method can effectively resolve the issues with Chen’s ranking method. Moreover, the revised ranking method can be used to differentiate different types of fuzzy numbers.     

Characterization of rough set approximations in Atanassov intuitionistic fuzzy set theory

The primitive notions in rough set theory are lower and upper approximation operators defined by a fixed binary relation and satisfying many interesting properties. Many types of generalized rough set models have been proposed in the literature. This paper discusses the rough approximations of Atanassov intuitionistic fuzzy sets in crisp and fuzzy approximation spaces in which both constructive and axiomatic approaches are used. In the constructive approach, concepts of rough intuitionistic fuzzy sets and intuitionistic fuzzy rough sets are defined, properties of rough intuitionistic fuzzy approximation operators and intuitionistic fuzzy rough approximation operators are examined. Different classes of rough intuitionistic fuzzy set algebras and intuitionistic fuzzy rough set algebras are obtained from different types of fuzzy relations. In the axiomatic approach, an operator-oriented characterization of rough sets is proposed, that is, rough intuitionistic fuzzy approximation operators and intuitionistic fuzzy rough approximation operators are defined by axioms. Different axiom sets of upper and lower intuitionistic fuzzy set-theoretic operators guarantee the existence of different types of crisp/fuzzy relations which produce the same operators.     

Entropy-based shadowed set approximation of intuitionistic fuzzy sets

We propose a method to approximate Intuitionistic Fuzzy Sets (IFSs) with Shadowed Sets that could be used, in decision making or similar tasks, when the full information about membership values is not necessary, is difficult to process or to interpret. Our approach is based on an information-theoretic perspective and aims at preserving the uncertainty, represented through an entropy measure, in the original IFS by minimizing the difference between the entropy in the input IFS and the output Shadowed Set. We propose three different efficient optimization algorithms that retain Fuzziness, Lack of Knowledge, or both, and illustrate their computation through an illustrative example. We also evaluate the application of the proposed approximation methods in the Machine Learning setting by showing that the approximation, through the proposed methods, of IFS k-Nearest Neighbors is able to outperform, in terms of running time, the standard algorithm.     

Group decision making in medical system: An intuitionistic fuzzy soft set approach

In medical system, there may be many critical diseases, where experts do not have sufficient knowledge to handle those problems. For these cases, experts may provide their opinion only about certain aspects of the disease and remain silent for those unknown features. Feeling the need of prioritizing different experts based on their given information, this article uses a novel concept for assigning confident weights to different experts which are mainly based on their provided information. Experts provide their opinions about various symptoms using intuitionistic fuzzy soft matrix (IFSM). In this article, we propose an algorithmic approach based on intuitionistic fuzzy soft set (IFSS) which explores a particular disease reflecting the agreement of all experts. This approach is guided by the group decision making (GDM) model and uses cardinals of IFSS as novel concept. We have used choice matrix (CM) as an important parameter which is based on choice parameters of individual expert. This article has also validated the proposed approach using distance measurements and consents of the majority of experts. The effectiveness of the proposed approach is demonstrated using a suitable case study.     

A graphical method for ranking Atanassov's intuitionistic fuzzy values using the uncertainty index and entropy

Many different types of ranking methods based on the score and accuracy functions of intuitionistic fuzzy values (IFVs) exist in the literature. The notion of knowledge bases, as in the case of rough set theory, is very handy to show that every ranking technique produces a unique classification of IFVs with a unique order among the classes. This means these rankings give rise to unique knowledge bases. Therefore, ranking of IFVs by two or more distinct techniques may produce different results. In this study, a graphical ranking method based on the uncertainty index and entropy is proposed. This approach is tested on several numerical examples existing in the literature and shown to be intuitive and convenient for applications in real-life scenarios.     

Multiattribute decision making based on power operators for linguistic intuitionistic fuzzy set using set pair analysis

The aim of the presented paper is to give a multiattribute decision making (MADM) method under the linguistic intuitionistic fuzzy (LIF) environment using the set pair analysis (SPA) theory. LIF set can express the qualitative information in terms of linguistic variables, whereas the connection number (CN) based on the “identity,” “discrepancy,” and “contrary” degrees of the SPA theory handles the uncertainties and certainties systems. On the basis of these features, we develop some series of linguistic CN (LCN) power weighted and ordered weighted geometric aggregation operator to aggregate the different LCNs. Several properties of the operators are also studied. Afterward, we present a novel MADM method to solve decision‐making problems under LIF set environment and illustrate with several examples to validate it. A comparative analysis is also presented to show the results.     

Resource service optimal-selection based on intuitionistic fuzzy set and non-functionality QoS in manufacturing grid system

In manufacturing grid (MGrid) system, according to functional requirements of a task, there exist a lot of resource services which have similar functional characteristics. Multiple resource services with similar functional characteristics raise the concern over resource service optimal-selection (RSOS). It is important to select the optimal resource service according to their non-functionality characteristics or quality of service (QoS). However, QoS attributes are not easy to measure due to their complexity and involvement of ill-structured information. In this study, user’s feeling is taken into account in RSOS in an MGrid system. The non-functionality QoS evaluation of resource services is based on users’ feeling and transaction experiences using intuitionistic fuzzy set (IFS). Furthermore, the dynamics of non-functionality QoS is considered, and a time-decay function is introduced into non-functionality QoS evaluation. A new method is proposed for RSOS based on IFS and non-functionality QoS, and the procedures are presented in detail. A practice case study is used to illustrate the proposed method and procedure. The performance and advantage of the proposed method are discussed.     

Fabrication process suitability ranking for micro-electro-mechanical systems using a fuzzy inference system

In this paper we present the development of a system to evaluate alternatives for manufacturing process steps for micro-electro-mechanical systems (MEMS). We explain in detail a formal process flow definition for MEMS fabrication. Then, we develop a fuzzy inference system which allows MEMS developers to capture users’ preferences to rank the alternatives available to complete the process steps required to fabricate a device. In the last part to this work, we present two case studies: alternatives evaluation for impurity doping and for lead zirconate titanate (PZT) patterning. Using an assortment of user preference data to rate a variety of criteria for potential alternatives, our approach produces a clear preference for one specific alternative in each case, which exemplifies the usefulness of the system proposed and illustrates how effective this methodology is towards improving the fabrication process for MEMS.     

A new measure using intuitionistic fuzzy set theory and its application to edge detection

In this paper, a new attempt has been made using Attanassov's intuitionistic fuzzy set theory for image edge detection. Intuitionistic fuzzy set takes into account the uncertainty in assignment of membership degree known as hesitation degree. Also a new distance measure, called intuitionistic fuzzy divergence, has been proposed. With this proposed distance measure, edge detection is carried out, and the results are found better with respect to the previous methods.     

犹豫直觉模糊集的知识测度及其应用

犹豫直觉模糊集集成了直觉模糊集与犹豫模糊集的优点,能够更好地处理决策者偏好不一致时的不确定性问题。通过考虑决策者提供信息的犹豫性与模糊性,给出了犹豫直觉模糊集上知识测度的公理化定义,并且构建出犹豫直觉模糊集上一类含参知识测度,这类知识测度可以有效地刻画犹豫直觉模糊集所包含的信息量和决策者的态度特征。接下来,基于对该类知识测度中的参数进行讨论,得到一系列代表决策者不同态度特征的知识测度,进一步验证了知识测度与决策者态度系数的变化成正比。最后,基于犹豫直觉模糊集的知识测度提出多属性群决策方法,并将此方法应用于某互联网公司的空调安装公司选择的案例中,证明了所提出的知识测度具有有效性与实用性。     

基于区间直觉犹豫模糊集的高速列车系统关键部件辨识

关键部件作为系统可靠性分析的重要组成以及系统维修策略制定的重要基础,其辨识方法与识别结果的准确性一直是研究热点与难点.为有效识别关键部件保证高速列车系统安全可靠性运行,本文提出一种新的基于区间直觉犹豫模糊集的关键部件辨识方法.首先通过回顾现有复杂系统网络建模方法及其优缺点,归纳总结部件的提取规则与部件间作用关系的定义和类型,提出由局部到整体的高速列车系统全局拓扑网络模型构建方法.其次鉴于现有针对同一高速列车同一节车辆同一部件的故障维修记录数据量少、随机性大等特点,提出将节点属性值区间化,构建节点属性的区间直觉犹豫模糊集,其中节点属性包括由故障数据分析获得的节点可靠性属性值以及由所建全局拓扑网络得到的拓扑属性.最后利用区间直觉犹豫模糊积分算子综合节点的多种属性辨识系统中的关键部件.以转向架系统的拓扑结构以及历史故障数据为基础的实例分析表明,所提出的辨识方法能够准确的识别出系统中的关键部件,且与专家经验的分析结果基本一致.     

Greenness assessment of supply chains via intuitionistic fuzzy based approaches

The increase in the consumption level of products with various materials has resulted in many problems. A worrisome result of this situation is environmental problems. Thus, environmental considerations during the planning, designing, implementation, and controlling of business activities in the entire supply chain have taken more attention in recent years. Therefore, many studies have been performed considering the greenness of different activities within supply chains. Greenness assessment of supply chains is one of the most critical and essential subjects of the related literature. The companies can learn their weak sides and provide the required amendments to improve their supply chains' greenness as a result of the assessment. Hence, in this study, a greenness assessment methodology is proposed for four logistics stages including in-bound, in-plant, out-bound, and reverse logistics. By investigating the greenness of different logistics stages separately, their characteristics can be analyzed in a more systematic way. Also, a detailed KPI determination process is realized, and a comprehensive KPI set is proposed for all the logistics stages for the first time in the literature. Moreover, as another novelty, a methodology based on intuitionistic fuzzy-based techniques, an integrated IF-DEMATEL and IF-ANP approach, is utilized for the greenness assessment. The related steps of the developed methodology are explicitly provided within the study, an application is realized for a company, and results are analyzed in a detailed way.     

Mining stock price using fuzzy rough set system

In this study of mining stock price data, we attempt to predict the stronger rules of stock prices. To address this problem, we proposed an effective method, a fuzzy rough set system to predict a stock price at any given time. Our system has two agents: one is a visual display agent that helps stock dealers monitor the current price of a stock and the other is a mining agent that helps stock dealers make decisions about when to buy or sell stocks. To demonstrate that our system is effective, we used it to predict the stronger rules of stock price and achieved at least 93% accuracy after 180 trials.     

A rank ordered filter for medical image edge enhancement and detection using intuitionistic fuzzy set

This paper gives a novel scheme using intuitionistic fuzzy set theory to enhance the edges of medical images. Medical images contain lots of uncertainties, as they are poorly illuminated and fuzzy/vague in nature. So, direct segmentation techniques will not produce better results. There are lots of researches on edge enhancement starting from non-fuzzy to fuzzy set, but proper enhancement (highlighting important structures) is not obtained. Enhancement of edges helps in recovering the important structures that are not visible properly. Even minute pathological blood vessels/cells are not visible properly and in that case edge enhancement will enhance these blood vessels/cells. Intuitionistic fuzzy set theory is found suitable in medical image processing as it considers more (two) uncertainties as compared to fuzzy set theory. In the processing phase, image is initially converted to intuitionistic fuzzy image and intuitionistic fuzzy entropy is used to obtain the optimum value of the parameter in the membership and non-membership functions. Then it computes the total variation of the pixels with respect to the median value of the image window (rank order filtering). This enhances the borders or the edges of the image. The resulting image is then segmented (edge detected) using standard Canny's edge detector, when simply using Canny's edge detector does not give better result. From the result it is observed that on comparing with non-fuzzy and fuzzy methods, the proposed method gives better information about the images, which is helpful to the pathologists in accurate diagnosing of diseases.     

Generating a causal model of supply chain collaboration using the fuzzy DEMATEL technique

Supply chain collaboration is usually adopted by manufacturers as a strategic measure to increase overall supply chain performance. However, such collaborations arguably have the highest failure record of the various supply chain management practices that are currently being applied. Part of the problem has been the uncertain external environment, an overreliance on technology, and lack of trust among partners. Based on Transaction Cost Economics (TCE) and Relational Exchange Theory (RET), it is clear that environment, asset specificity, and trust are key determinants for the success of collaborations among firms. However, the fuzziness of the interdependency among these determinants and their influences on supply chain collaborative processes still remains unknown. This study thus focuses on Taiwanese manufacturing firms as an example case, and empirically probes the relationships among these dimensions and their effects on these processes. To accommodate the vagueness of human opinions, the fuzzy Decision Making Trial and Evaluation Laboratory (DEMATEL) technique is applied to examine this issue, and to produce a causal relations map. This study also provides a discussion and insights for supply chain practitioners.     

Researching the development of Atanassov intuitionistic fuzzy set: Using a citation network analysis

Since Atanassov presented the intuitionistic fuzzy set (IFS) in 1983, a great amount of extended content has been made by experts in IFS field and then the citations of a more formal paper, which developed from the first proposal and was presented in 1986, have been cited over 4000 times in Google Scholar ending November 6, 2014. However, the research on the development track of this discipline has not caused extensive attention among scholars in this discipline. Therefore, in this paper, we plan to determine the development track of this discipline based on some statistics and network analysis methodologies, as a new attempt. Note that we only take the citation information on IFSs ending November 6, 2014 into account. Therefore all of the data in this paper have time restriction. We derive a historical graph about the development course of IFS and use some basic statistics to identify some influential journals, authors, etc. Then we analyze a small range of influential literatures based on the SNA (social network analysis) theory to figure out the position of several cardinal IFS literatures. As result suggests, Atanassov [1] is the most influential paper in IFS field. Most literatures referring to IFS cited this paper and on the basis of it, increasingly scholars combine other subjects with IFS subject.