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Journal ArticleDOI

A review of applications of fuzzy sets to safety and reliability engineering

01 Sep 2018-International Journal of Approximate Reasoning (Elsevier)-Vol. 100, pp 29-55
TL;DR: A review of fuzzy set theory based methodologies applied to safety and reliability engineering, which include fuzzy FTA, fuzzy FMEA, fuzzy ETA, fuzzy Bayesian networks, fuzzy Markov chains, and fuzzy Petri nets is presented.
About: This article is published in International Journal of Approximate Reasoning.The article was published on 2018-09-01 and is currently open access. It has received 108 citations till now. The article focuses on the topics: Fuzzy logic & Fuzzy set.

Summary (1 min read)

1. Introduction

  • Safety critical systems are extensively used in many industries, including the aerospace, automotive, medical, and energy sectors.
  • In addition to the FTA, Failure Mode and Effects Analysis (FMEA), Event Tree Analysis (ETA), Markov chains, Bayesian networks, and Petri nets are some of the other approaches that are used for safety and reliability evaluation of systems.
  • On the other hand, unavailability of failure data would introduce degrees of uncertainty into the analysis results.

2.2 Computing with Words, Failure Possibility and Probability

  • Computing with words (CW) is used for computing and reasoning using words and propositions from natural language instead of numbers.
  • Zadeh [270– 272], Trillas [221] and Mendel [148] have provided a detailed description of the tight relationship between fuzzy sets and CW and how CW can be used for computation where the data is in the form of perceptions.
  • Over the years, several new approaches have been proposed for CW.
  • The concept of a linguistic variable plays an important role in dealing with situations which are too complex or vague in nature, i.e., very difficult to describe using conventional quantitative expressions.

6. Other Approaches

  • Other approaches to fuzzy safety and reliability assessment include, but not limited to Bayesian networks, Markov models, and Petri nets.
  • Fuzzy set theory has also been used with these approaches to handle uncertainty in processes.
  • This section reviews some of those approaches.

7. Discussion and Future Outlook

  • There is increasing recognition that unavailability of adequate failure data can undermine the efficacy and applicability of classical safety and reliability assessments.
  • The body of research the authors cited suggests that fuzzy set theory can enable us to draw helpful conclusions about safety and reliability even in the absence of concrete failure data.
  • As the definition of appropriate membership functions and fuzzy rules has significant impact on the outcomes of the analysis, it is worthwhile trying to define guidelines for selecting and defining membership functions for different application areas or systems.
  • In general, these approaches suffer from the state-space explosion problem while modelling moderately complex systems.

8. Conclusion

  • Safety-critical systems are an integral part of their life.
  • In their classical forms, these techniques rely on precise failure data.
  • There are still challenges in this area, which the authors have discussed in detail in section 7.
  • In particular, the authors would like to emphasize the need to incorporate the use of fuzzy set theory in the context of MBSA, an emerging paradigm which although provides tools and techniques to automate system safety and reliability analysis, it is unable to deal with uncertainties.

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Citations
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Dissertation
01 Jan 1975

2,119 citations

Journal ArticleDOI
TL;DR: A review of the applications of Bayesian networks and Petri nets in system safety, reliability and risk assessments is presented, highlighting the potential usefulness of the BN and PN based approaches over other classical approaches, and relative strengths and weaknesses in different practical application scenarios.

200 citations

Journal ArticleDOI
TL;DR: In this article, a bibliometric analysis-based review is presented to investigate the evolution of process safety and risk research, and the evolution and popularity of major tools used in this field are also analyzed.

108 citations

Journal ArticleDOI
TL;DR: A review of the state of the art in this field, focusing on uncertainty handling in fault tree analysis (FTA) based risk assessment, is presented, highlighting how assessors can handle uncertainty based on the available evidence as an input to FTA.

103 citations

References
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Book
01 Aug 1996
TL;DR: A separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.
Abstract: A fuzzy set is a class of objects with a continuum of grades of membership. Such a set is characterized by a membership (characteristic) function which assigns to each object a grade of membership ranging between zero and one. The notions of inclusion, union, intersection, complement, relation, convexity, etc., are extended to such sets, and various properties of these notions in the context of fuzzy sets are established. In particular, a separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.

52,705 citations

Journal ArticleDOI
TL;DR: Much of what constitutes the core of scientific knowledge may be regarded as a reservoir of concepts and techniques which can be drawn upon to construct mathematical models of various types of systems and thereby yield quantitative information concerning their behavior.

12,530 citations

Journal ArticleDOI
TL;DR: The theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable.

8,918 citations

Journal ArticleDOI
01 Jan 1973
TL;DR: By relying on the use of linguistic variables and fuzzy algorithms, the approach provides an approximate and yet effective means of describing the behavior of systems which are too complex or too ill-defined to admit of precise mathematical analysis.
Abstract: The approach described in this paper represents a substantive departure from the conventional quantitative techniques of system analysis. It has three main distinguishing features: 1) use of so-called ``linguistic'' variables in place of or in addition to numerical variables; 2) characterization of simple relations between variables by fuzzy conditional statements; and 3) characterization of complex relations by fuzzy algorithms. A linguistic variable is defined as a variable whose values are sentences in a natural or artificial language. Thus, if tall, not tall, very tall, very very tall, etc. are values of height, then height is a linguistic variable. Fuzzy conditional statements are expressions of the form IF A THEN B, where A and B have fuzzy meaning, e.g., IF x is small THEN y is large, where small and large are viewed as labels of fuzzy sets. A fuzzy algorithm is an ordered sequence of instructions which may contain fuzzy assignment and conditional statements, e.g., x = very small, IF x is small THEN Y is large. The execution of such instructions is governed by the compositional rule of inference and the rule of the preponderant alternative. By relying on the use of linguistic variables and fuzzy algorithms, the approach provides an approximate and yet effective means of describing the behavior of systems which are too complex or too ill-defined to admit of precise mathematical analysis.

8,547 citations

Book
31 Jul 1985
TL;DR: The book updates the research agenda with chapters on possibility theory, fuzzy logic and approximate reasoning, expert systems, fuzzy control, fuzzy data analysis, decision making and fuzzy set models in operations research.
Abstract: Fuzzy Set Theory - And Its Applications, Third Edition is a textbook for courses in fuzzy set theory. It can also be used as an introduction to the subject. The character of a textbook is balanced with the dynamic nature of the research in the field by including many useful references to develop a deeper understanding among interested readers. The book updates the research agenda (which has witnessed profound and startling advances since its inception some 30 years ago) with chapters on possibility theory, fuzzy logic and approximate reasoning, expert systems, fuzzy control, fuzzy data analysis, decision making and fuzzy set models in operations research. All chapters have been updated. Exercises are included.

7,877 citations

Frequently Asked Questions (2)
Q1. What have the authors contributed in "A review of applications of fuzzy sets to safety and reliability engineering" ?

This paper presents a review of fuzzy set theory based methodologies applied to safety and reliability engineering, which include fuzzy FTA, fuzzy FMEA, fuzzy ETA, fuzzy Bayesian networks, fuzzy Markov chains, and fuzzy Petri nets. Firstly, the authors describe relevant fundamentals of fuzzy set theory and then they review applications of fuzzy set theory to system safety and reliability analysis. The review shows the context in which each technique may be more appropriate and highlights the overall potential usefulness of fuzzy set theory in addressing uncertainty in safety and reliability engineering. 

Some issues therefore require further research. In addition, further research need to be performed to evaluate fuzzy reliability of concurrent and multi-state systems. Therefore, in the future, it is worth taking repairability of the systems into account during fuzzy FTA. Considering the multiple advantages provided by the BNs, it is worth exploring further the use of fuzzy set theory with BNs.