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Project risk management using fuzzy theory
Published in Stephen O. Ogunlana, Prasanta Kumar Dey, Risk Management in Engineering and Construction, 2019
Daniel Wright, Prasanta Kumar Dey
Fuzzy logic is a contemporary risk management method, but the underpinning theory has existed since Lotfi Zadeh’s work in the 1960s. Fuzzy theory, sometimes referred to as possibility theory, is one of a restricted number of techniques well suited to risk analysis. This branch of modern mathematics has proven itself as an effective method of converting human perception and logic into intuitive control and decision-supporting tools. By mimicking human cognition and approximate reasoning with, often, partial information, this contemporary method represented a paradigm shift in the scientific community – a paradigm shift that they were initially not willing to accept. By utilising symbolic heuristic-based logic and moving away from the traditional numerical algorithmic logic, fuzzy logic is able to better accommodate particular problems. Zadeh (1973) argued that with this new approach “ . . . we acquire a capability to deal with systems which are much too complex to be susceptible to analysis in conventional mathematical terms”.
Introduction
Published in Umberto Straccia, Foundations of Fuzzy Logic and Semantic Web Languages, 2016
As for the main differences between probability and possibility theory, the probability of an event is the sum of the probabilities of all worlds that satisfy this event, whereas the possibility of an event is the maximum of the possibilities of all worlds that satisfy the event. Intuitively, the probability of an event aggregates the probabilities of all worlds that satisfy this event, whereas the possibility of an event is simply the possibility of the “most optimistic” world that satisfies the event. Hence, although both probability and possibility theory allow for quantifying degrees of uncertainty, they are conceptually quite different from each other. That is, probability and possibility theory represent different facets of uncertainty.
Handling Uncertainty: Probability and Fuzzy Logic
Published in Adrian A. Hopgood, Intelligent Systems for Engineers and Scientists, 2021
This chapter will review some of the commonly used techniques for reasoning with uncertainty. Bayesian updating has a rigorous derivation based upon probability theory, but its underlying assumptions, for example, the statistical independence of multiple pieces of evidence, may not be true in practical situations. Certainty theory does not have a rigorous mathematical basis but has been devised as a practical way of overcoming some of the limitations of Bayesian updating. Possibility theory, or fuzzy logic, allows the third form of uncertainty, that is, vague language, to be used in a precise manner. The assumptions and arbitrariness of some of the techniques have meant that reasoning under uncertainty remains a controversial topic.
Modeling interdependent effects of infrastructure failures using imprecise dependency information
Published in Sustainable and Resilient Infrastructure, 2022
Srijith Balakrishnan, Zhanmin Zhang
Possibility theory was introduced by Zadeh (1999) in order to handle the imprecision intrinsic to the natural language. Possibility theory is based on set functions, which makes it comparable to probability theory. However, possibility theory introduces a pair of dual set functions, namely possibility and necessity measures, to represent real-world scenarios using partial information. The possibility distribution is a mapping of to a real number in the interval [0,1]. If , the state is totally possible, and if , the state is impossible. Possibility theory assumes that unless there is evidence to reject a hypothesis, it is still possible. The possibility and necessity measures, denoted by and , can be derived from possibility distribution as follows:
Possibilistic Pareto-dominance approach to support technical bid selection under imprecision and uncertainty in engineer-to-order bidding process
Published in International Journal of Production Research, 2021
Abdourahim Sylla, Thierry Coudert, Elise Vareilles, Laurent Geneste, Michel Aldanondo
The possibility theory together with the confidence indicators offer a good opportunity to model the uncertain and imprecise values of the decision criteria by possibility distributions. For a solution , the possibility distribution corresponding to the possible values of the decision criterion k, is characterised with five parameters: a, b, c, d and e (see Figure 1). Moreover, it can be formally defined by Equation (1). For every value of the criterion k for the solution i (noted ), () is the possibility of the value .
Global sensitivity analysis for fuzzy inputs based on the decomposition of fuzzy output entropy
Published in Engineering Optimization, 2018
Yan Shi, Zhenzhou Lu, Yicheng Zhou
The GSA methods introduced in the previous paragraph consider only random inputs described by certain probability distributions. However, the probability distributions of the inputs cannot always be obtained because of poor information in engineering, and the input uncertainty may be described by non-probabilistic uncertainty. Many non-probabilistic methods have been developed to measure non-probabilistic uncertainty, such as convex modelling analysis (Ben-Haim and Elishakoff 1990; Elishakoff 1995; Qiu 2005), interval analysis (Moore 1966; Alefeld and Herzberger 1983; Hu and Qiu 2010) and possibility theory (Shafer 1976; Zadeh 1978; Dubois and Prade 1988, 1997; Tang, Lu, and Hu 2014). Among these non-probabilistic methods, possibility theory has proved to be an effective method for measuring fuzzy uncertainty. Fuzzy number theory, which describes fuzzy uncertainty by the membership function, is a highly useful tool in possibility theory. Several GSA approaches for fuzzy variables (Gauger, Turrin, and Hanss 2008; Song, Lu, and Cui 2012; Giannini and Hanss 2008) have been developed to measure the effect of fuzzy inputs on the response of models. To measure the effect of uncertainty of mixed inputs involving both randomness and fuzziness on the structural response, many uncertainty importance measures (Song, Lu, and Li 2014; Li, Lu, and Li 2011; Tang et al. 2012) have been provided. Among these uncertainty importance measures, entropy-based GSA (Tang et al. 2012) can identify the effect of fuzzy inputs based on the entropy of fuzzy variables (Liu 2007).