The posterity of Zadeh's 50-year-old paper: A retrospective in 101 Easy Pieces – and a Few More

International audienceThis article was commissioned by the 22nd IEEE International Conference of Fuzzy Systems (FUZZ-IEEE) to celebrate the 50th Anniversary of Lotfi Zadeh's seminal 1965 paper on fuzzy sets. In addition to Lotfi's original paper, this note itemizes 100 citations of books and papers deemed “important (significant, seminal, etc.)” by 20 of the 21 living IEEE CIS Fuzzy Systems pioneers. Each of the 20 contributors supplied 5 citations, and Lotfi's paper makes the overall list a tidy 101, as in “Fuzzy Sets 101”. This note is not a survey in any real sense of the word, but the contributors did offer short remarks to indicate the reason for inclusion (e.g., historical, topical, seminal, etc.) of each citation. Citation statistics are easy to find and notoriously erroneous, so we refrain from reporting them - almost. The exception is that according to Google scholar on April 9, 2015, Lotfi's 1965 paper has been cited 55,479 times

ISIPTA'07: Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications

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

Safety and reliability are rigorously assessed during the design of dependable systems. Probabilistic risk assessment (PRA) processes are comprehensive, structured and logical methods widely used for this purpose. PRA approaches include, but not limited to Fault Tree Analysis (FTA), Failure Mode and Effects Analysis (FMEA), and Event Tree Analysis (ETA). In conventional PRA, failure data about components is required for the purposes of quantitative analysis. In practice, it is not always possible to fully obtain this data due to unavailability of primary observations and consequent scarcity of statistical data about the failure of components. To handle such situations, fuzzy set theory has been successfully used in novel PRA approaches for safety and reliability evaluation under conditions of uncertainty. 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, we describe relevant fundamentals of fuzzy set theory and then we 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

DAG-Based Attack and Defense Modeling: Don't Miss the Forest for the Attack Trees

This paper presents the current state of the art on attack and defense modeling approaches that are based on directed acyclic graphs (DAGs). DAGs allow for a hierarchical decomposition of complex scenarios into simple, easily understandable and quantifiable actions. Methods based on threat trees and Bayesian networks are two well-known approaches to security modeling. However there exist more than 30 DAG-based methodologies, each having different features and goals. The objective of this survey is to present a complete overview of graphical attack and defense modeling techniques based on DAGs. This consists of summarizing the existing methodologies, comparing their features and proposing a taxonomy of the described formalisms. This article also supports the selection of an adequate modeling technique depending on user requirements

Applications of Fuzzy Set Theory, Fuzzy Measure Theory and Fuzzy Differential Calculus

This research tackles the issue of uncertainty due to lack of information, alternatively known as Knightian Uncertainty, and its impact on option pricing. In the presence of such uncertainty, Probability Theory becomes restrictive and alternative tools are called for. In this research, we consider tools of Fuzzy Theory. We introduce three Option Pricing Models the first of which is a fuzzy binomial model based on the standard CRR binomial model. The model performs option pricing in a fuzzy world characterized by blurred prices. In such a world, it is no longer possible to price by replication. So we introduce a fuzzy pricing approach that employs Sugeno integration and fuzzy measures, and generates bounds on the possible option price. The second model is a fuzzy Black-Scholes model, which prices options in the presence of uncertain or fuzzy volatility. We model such volatility by establishing bounds on the corresponding fuzzy values thereby generating fuzzy bounds on the possible option price. Finally, the third model is an extension on an existing one period fuzzy binomial model that prices options when the underlying price is characterized by opacity. The option price returned by this model is dependent on a market parameter that summarizes its completeness. However, it is possible to defuzzify the last two models to obtain one crisp price that summarizes market information. The last two models outperform their standard counterparts