Failure mode and effects analysis based on a novel fuzzy evidential method

Failure mode and effect analysis (FMEA) has been widely applied to examine potential failures in systems, designs, and products. The risk priority number (RPN) is the key criteria to determine the risk priorities of the failure modes. Traditionally, the determination of RPN is based on the risk factors like occurrence (O), severity (S) and detection (D), which require to be precisely evaluated. However, this method has many irrationalities and needs to be improved for more applications. To overcome the shortcomings of the traditional FMEA and better model and process uncertainties, we propose a FMEA model based on a novel fuzzy evidential method. The risks of the risk factors are evaluated by fuzzy membership degree. As a result, a comprehensive way to rank the risk of failure modes is proposed by fusing the feature information of O, S and D with Dempster–Shafer (D–S) evidence theory. The advantages of the proposed method are that it can not only cover the diversity and uncertainty of the risk assessment, but also improve the reliability of the RPN by data fusion. To validate the proposed method, a case study of a micro-electro-mechanical system (MEMS) is performed. The experimental results show that this method is reasonable and effective for real applications.     

A perceptual computing-based method to prioritize failure modes in failure mode and effect analysis and its application to edible bird nest farming

A failure mode and effect analysis (FMEA) procedure that incorporates a novel Perceptual Computing (Per-C)–based Risk Priority Number (RPN) model is proposed in this paper. The proposed model considers linguistic uncertainties and vagueness of words, because it is more natural to use words, instead of numerals, for an FMEA user to express his/her knowledge when he/she provides an assessment. Therefore, it is important to consider the inherited uncertainties in words used by humans for assessment as an additional risk factor in the entire FMEA reasoning process. As such, we propose to use Per-C to analyze the uncertainties in words provided by different FMEA users. There are three potential sources of risks. Firstly, the risk factors of Severity (S), Occurrence (O), and Detection (D) are graded using words by each FMEA user, and indicated as interval type-2 fuzzy sets (IT2FSs). Secondly, the relative importance of S, O, and D are reflected by the weights given by each FMEA user in words, which are indicated as IT2FSs. Thirdly, the expertise level of each FMEA user is reflected by words, which are expressed as IT2FSs too. The proposed Per-C-RPN model allows these three sources of risks from each FMEA user to be considered and combined in terms of IT2FSs. A case study related to edible bird nest farming in Borneo Island is reported. The results indicate the effectiveness of the proposed model. In summary, this paper contributes to a new Per-C-RPN model that utilizes imprecise assessment grades pertaining to group decision making in FMEA.     

A novel approach for failure mode and effects analysis using combination weighting and fuzzy VIKOR method

Failure mode and effects analysis (FMEA) is one of the most popular reliability analysis tools for identifying, assessing and eliminating potential failure modes in a wide range of industries. In general, failure modes in FMEA are evaluated and ranked through the risk priority number (RPN), which is obtained by the multiplication of crisp values of the risk factors, such as the occurrence (O), severity (S), and detection (D) of each failure mode. However, the conventional RPN method has been considerably criticized for various reasons. To deal with the uncertainty and vagueness from humans’ subjective perception and experience in risk evaluation process, this paper presents a novel approach for FMEA based on combination weighting and fuzzy VIKOR method. Integration of fuzzy analytic hierarchy process (AHP) and entropy method is applied for risk factor weighting in this proposed approach. The risk priorities of the identified failure modes are obtained through next steps based on fuzzy VIKOR method. To demonstrate its potential applications, the new fuzzy FMEA is used for analyzing the risk of general anesthesia process. Finally, a sensitivity analysis is carried out to verify the robustness of the risk ranking and a comparison analysis is conducted to show the advantages of the proposed FMEA approach.     

Identifying and evaluating enterprise architecture risks using FMEA and fuzzy VIKOR

Enterprise architecture (EA) is an approach for managing all components of enterprise and relationships among them. By implementing EA, the organization will be threatened from different aspects. We used failure mode and effect analysis (FMEA) which is a powerful tool for evaluating EA risks. In traditional FMEA, risk priority number (RPN), has been calculated by multiplication of three criteria, severity, occurrence and detection. Because of some drawbacks of the traditional FMEA, this paper—instead of calculating RPN—prioritizes EA risk factors with fuzzy VIKOR. VIKOR (VlseKriterijumska Optimizacija I Kompromisno Resenje in Serbian, means Multi-criteria Optimization and Compromise Solution) is a multiple attribute decision making technique which aims to rank EA risk factors with respect to the criteria. As regards using linguistic variables, fuzzy approach is used to allow experts to use linguistic variables. The proposed method is used for evaluating twenty EA risk factors, which integrates knowledge and experience acquired from professional experts.     

An extended FMEA approach based on the Z-MOORA and fuzzy BWM for prioritization of failures

Identification and prioritization of failure modes in a system and planning for corrective actions are among the most important components of risk management in any organization. Meanwhile, conventional Failure Mode and Effects Analysis (FMEA) is one of the most commonly used methods for prioritization of the failures. Despite the widespread applications of this method in various industries, FMEA is associated with some shortcomings that can lead to unrealistic results. In this study, a proposed approach is presented in three phases to cover some of the shortcomings of the FMEA technique. In the first phase, FMEA is used to identify the failure modes and assign values to the Risk Priority Number (RPN) determinant factors. In the second phase, the Fuzzy Best-Worst Method (FBWM) based on the experts’ opinions is used to measure the weights of these factors. In the third phase, the outputs of the previous phases are used as a basis to prioritize the failures using the proposed Multi-Objective Optimization by Ratio Analysis based on the Z-number theory (Z-MOORA). In addition to assigning different weights to the RPN determinant factors and considering uncertainties of them, the Z-number theory is used in this approach to cover reliability in different failure modes. The proposed approach was implemented in the automotive spare parts industry, and the results indicate a full prioritization of the failures in comparison with other conventional methods such as FMEA and fuzzy MOORA.     

An essay on the linguistic roots of fuzzy sets

This paper mainly tries to show that the membership function of a fuzzy set labeled P does show some intrinsic property related with how P is actually managed in the universe of discourse. Its final goal is to analyze an answer to the question, which intrinsic but simple property allows a function to represent a fuzzy set labeled P? The presented property exhibits that the membership function just ‘measures’ in some scale the extent up to which x is P in language, for all x in the universe of discourse.Such study is done in a form allowing to consider how to represent the ‘collective’ originated by a predicate reflecting a collective noun. As particular cases of what is presented, and when the degrees can be some kinds of numerical subsets, the Zadeh’s fuzzy sets, the interval-valued, the intuitionistic, and the type-2 fuzzy sets, appear as particular cases and to some extent are discussed. A ‘unification’ of all different kinds of fuzzy sets based on a linguistic origin is achieved.     

Some properties of fuzzy reasoning in propositional fuzzy logic systems

In order to analyze the logical foundation of fuzzy reasoning, this paper first introduces the concept of generalized roots of theories in ?ukasiewicz propositional fuzzy logic ?uk, Gödel propositional fuzzy logic Göd, Product propositional fuzzy logic Π, and nilpotent minimum logic NM (the R₀-propositional fuzzy logic L^∗). Next, it is proved that all consequences of a theory Γ, named D(Γ), are completely determined by its generalized root whenever Γ has a generalized root. Moreover, it is proved that every finite theory Γ has a generalized root, which can be expressed by a specific formula. Finally, we demonstrate the existence of a non-fuzzy version of Fuzzy Modus Ponens (FMP) in ?uk, Göd, Π and NM (L^∗), and we provide its numerical version as a new algorithm for solving FMP.     

A motion compression/reconstruction method based on max t-norm composite fuzzy relational equations

A motion compression/reconstruction method based on max t-norm composite fuzzy relational equations (MCF) is proposed, where into intra-pictures (I-pictures) and predictive-pictures (P-pictures) of the original motion are compressed by uniform and non-uniform coders, respectively. The non-uniform coders of the proposed method can preserve edge information of P-pictures on the compressed image. To perform an effective compression/reconstruction of the P-pictures, a design method of non-uniform coders is proposed based on an overlap level of fuzzy sets and a fuzzy equalization. An experiment using 10 P-pictures confirms that the root mean square error of the reconstructed images obtained by the proposed non-uniform coders is decreased to 89.4% of that one of the uniform coders under the condition that compression rate (the ratio between the file size of compressed image and original one) is 0.0057. Two test motions (‘Tennis’ and ‘Woman’, 100 frames) are compressed and reconstructed by the proposed MCF.     

Node connectivity and arc connectivity of a fuzzy graph

The fuzzy graph approach is more powerful in cluster analysis than the usual graph - theoretic approach due to its ability to handle the strengths of arcs effectively. The concept of node-strength sequence is introduced and is studied in a complete fuzzy graph. Two new connectivity parameters in fuzzy graphs namely, fuzzy node connectivity (κ) and fuzzy arc connectivity (κ^′) are introduced and obtained the fuzzy analogue of Whitney’s theorem. Fuzzy node cut, fuzzy arc cut and fuzzy bond are defined. Fuzzy bond is a special type of a fuzzy bridge. It is proved that at least one of the end nodes of a fuzzy bond is a fuzzy cutnode. It is shown that κ=κ^′ for a fuzzy tree and it is the minimum of the strengths of its strong arcs. The relationships of the new parameters with already existing vertex and edge connectivity parameters are studied and is shown that the value of all these parameters are equal in a compete fuzzy graph. Also a new clustering technique based on fuzzy arc connectivity is introduced.     

Some remarks on the lattice of fuzzy intervals

In this paper we study the connections between three related concepts which have appeared in the fuzzy literature: fuzzy intervals, fuzzy numbers and fuzzy interval numbers (FIN’s). We show that these three concepts are very closely related. We propose a new definition which encompasses the three previous ones and proceeds to study the properties ensuing from this definition. Given a reference lattice (X, ?), we define fuzzy intervals to be the fuzzy sets such that their p-cuts are closed intervals of (X, ?). We show that, given a complete lattice (X, ?), the collection of its fuzzy intervals is a complete lattice. Furthermore we show that, if (X, ?) is completely distributive, then the lattice of its fuzzy intervals is distributive. Finally we introduce a new inclusion measure, which can be used to quantify the degree in which a fuzzy interval is contained in another, an approach which is particularly valuable in engineering applications.     

Fuzzy radicals and prime fuzzy ideals of ordered semigroups

Let S be an ordered semigroup. A fuzzy subset of S is, by definition, an arbitrary mapping f: S → [0, 1], where [0, 1] is the usual interval of real numbers. Motivated by studying prime fuzzy ideals in rings, semigroups and ordered semigroups, and as a continuation of Kehayopulu and Tsingelis’s works in ordered semigroups in terms of fuzzy subsets, in this paper we introduce the notion of ordered fuzzy points of an ordered semigroup S, and give a characterization of prime fuzzy ideals of an ordered semigroup S. We also introduce the concepts of weakly prime fuzzy ideals, completely prime fuzzy ideals, completely semiprime fuzzy ideals and weakly completely prime fuzzy ideals of an ordered semigroup S, and establish the relationship between the five classes of ideals. Furthermore, we characterize weakly prime fuzzy ideals, completely semiprime fuzzy ideals and weakly completely prime fuzzy ideals of S by their level ideals. Finally, we introduce and investigate the fuzzy radicals of ordered semigroups by means of ordered fuzzy points, and prove that the fuzzy radical of every completely semiprime fuzzy ideal of an ordered semigroup S can be expressed as the intersection of all weakly completely prime fuzzy ideals containing it. As an application of the results of this paper, the corresponding results of semigroups (without order) are also obtained.     

Lipschitzian De Morgan triplets of fuzzy connectives

After studying Lipschitzian strong negations, Lipschitzian De Morgan triplets (T, S, n), where T is a triangular norm, S a triangular conorm, and n a strong negation, are investigated. The relationships between the best Lipschitzian constants of functions T, S and n are given. Several examples are included.     

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.     

Failure mode and effects analysis using intuitionistic fuzzy hybrid weighted Euclidean distance operator

Failure mode and effects analysis (FMEA) has shown its effectiveness in examining potential failures in products, process, designs or services and has been extensively used for safety and reliability analysis in a wide range of industries. However, its approach to prioritise failure modes through a crisp risk priority number (RPN) has been criticised as having several shortcomings. The aim of this paper is to develop an efficient and comprehensive risk assessment methodology using intuitionistic fuzzy hybrid weighted Euclidean distance (IFHWED) operator to overcome the limitations and improve the effectiveness of the traditional FMEA. The diversified and uncertain assessments given by FMEA team members are treated as linguistic terms expressed in intuitionistic fuzzy numbers (IFNs). Intuitionistic fuzzy weighted averaging (IFWA) operator is used to aggregate the FMEA team members’ individual assessments into a group assessment. IFHWED operator is applied thereafter to the prioritisation and selection of failure modes. Particularly, both subjective and objective weights of risk factors are considered during the risk evaluation process. A numerical example for risk assessment is given to illustrate the proposed method finally.     

On fuzzy rough sets based on tolerance relations

Dubois and Prade (1990) [1] introduced the notion of fuzzy rough sets as a fuzzy generalization of rough sets, which was originally proposed by Pawlak (1982) [8]. Later, Radzikowska and Kerre introduced the so-called (I,T)-fuzzy rough sets, where I is an implication and T is a triangular norm. In the present paper, by using a pair of implications (I,J), we define the so-called (I,J)-fuzzy rough sets, which generalize the concept of fuzzy rough sets in the sense of Radzikowska and Kerre, and that of Mi and Zhang. Basic properties of (I,J)-fuzzy rough sets are investigated in detail.     

On the triangle inequalities in fuzzy metric spaces

This paper presents level forms of the triangle inequalities in fuzzy metric spaces (X, d, L, R). To aid discussion, a fuzzy pre-metric condition is introduced. It is first pointed out that under the fuzzy pre-metric condition the first triangle inequality is always equivalent to its level form. The second triangle inequality is equivalent to one level form when R is right continuous, and to another level form also when further conditions are imposed on R. In a fuzzy metric space, the level form of the first triangle inequality and one of the level forms of the second triangle inequality are always valid. The other level form of the second triangle inequality holds for all but at most countable α ∈ [0, 1). Finally, a fixed point theorem for fuzzy metric spaces is derived as an application of the preceding results.     

Knowledge gathering of fuzzy multi-time-interval sequential patterns

Mining sequential patterns to find ordered events or subsequence patterns is essential in many applications, such as analysis of consumer shopping data, web clickstreams, and biological sequences. Traditional patterns reveal which items are frequently purchased together and in what order. However, information about the time intervals between purchases is missing. Therefore, Yang proposed using multi-time-interval sequential patterns to consider the time intervals between each pair of items in a pattern. For example, 〈Bread, ti₁, Milk, (ti₂, ti₁), Jam〉 means that Bread is bought before Milk within an interval of ti₁, and Jam is bought after Bread and Milk within intervals of ti₂ and ti₁, respectively, where ti₁ and ti₂ are predefined time intervals. Although this new type of pattern considers the intervals between all pairs of items, it contains a sharp boundary problem; that is, when the time interval between two purchases is near the boundary of two predetermined time ranges, we either ignore or overemphasize it. In this study, we applied the concept of fuzzy sets to solve the sharp boundary problem. The discovered patterns, called fuzzy multi-time-interval sequential patterns, describe time intervals in linguistic terms for better understanding. Two algorithms, FuzzMI-Apriori and FuzzMI-PrefixSpan, were developed for mining fuzzy multi-time-interval patterns. Experiments using synthetic and real datasets showed the algorithms’ computational efficiency, scalability, and effectiveness.     

结合OWA算子和模糊DEMATEL的风险评估方法

针对传统故障模式与影响分析(FMEA)方法在实际应用中的不足,提出一种基于有序加权平均(OWA)算子和决策试行与评价实验法(DEMATEL)的风险排序方法。FMEA专家对故障模式的3个风险因子给出模糊评价信息,应用OWA算子对评估信息进行集结,得到各故障原因对故障模式的影响强度。采用模糊DEMATEL法构建FMEA系统要素间的初始直接影响矩阵,经过运算可得综合影响矩阵,并计算各故障原因的原因度,据此进行产品或系统的失效风险评估。运用该方法对地铁车门系统的基础部件进行安全性分析,并将所得结果与传统RPN方法的结果做对比,验证了该方法的可行性和有效性。     

Blackwell’s Theorem for T-related fuzzy variables

In this paper, we consider Blackwell’s Theorem in which inter-arrival times are characterized as fuzzy variables under t-norm-based fuzzy operations. We first prove that Blackwell’s Theorem for T-related fuzzy variables with respect to necessity measure holds true where T is an Archimedean t-norm. Subsequently, we provide a counter example under which Blackwell’s Theorem does not hold when T = min. Finally, we evaluate the expected value of fuzzy variable with respect to credibility measure and derive fuzzy Blackwell’s Theorem based on the expected value of fuzzy variables.     

T-sum of sigmoid-shaped fuzzy intervals

The usual arithmetic operations on real numbers can be extended to arithmetical operations on fuzzy intervals by means of Zadeh’s extension principle based on a t-norm T. A t-norm is called consistent with respect to a class of fuzzy intervals for some arithmetic operation, if this arithmetic operation is closed for this class. It is important to know which t-norms are consistent with particular types of fuzzy intervals. Recently, Dombi and Gy?rbíró [J. Dombi, N. Gy?rbíró, Additions of sigmoid-shaped fuzzy intervals using the Dombi operator and infinite sum theorems, Fuzzy Sets and Systems 157 (2006) 952-963] proved that addition is closed if the Dombi t-norm is used with sigmoid-shaped fuzzy intervals. In this paper, we define a broader class of sigmoid-shaped fuzzy intervals. Then, we study t-norms that are consistent with these particular types of fuzzy intervals. Dombi and Gy?rbíró’s results are special cases of the results described in this paper.