A pure probabilistic interpretation of possibilistic expected value, variance, covariance and correlation

In this work we shall give a pure probabilistic interpretation of possibilistic expected value, variance, covariance and correlation

A short survey of normative properties of possibility distributions

In 2001 Carlsson and Full´er [1] introduced the possibilistic mean value, variance and covariance of fuzzy numbers. In 2003 Full´er and Majlender [4] introduced the notations of crisp weighted possibilistic mean value, variance and covariance of fuzzy numbers, which are consistent with the extension principle. In 2003 Carlsson, Full´er and Majlender [2] proved the possibilisticCauc hy-Schwartz inequality. Drawing heavily on [1, 2, 3, 4, 5] we will summarize some normative properties of possibility distributions

On additions of interactive fuzzy numbers

In this paper we will summarize some properties of the extended addition operator on fuzzy numbers, where the interactivity relation between fuzzy numbers is given by their joint possibility distributio

An Efficient Representation Format for Fuzzy Intervals Based on Symmetric Membership Functions

International audienceThis paper proposes a novel implementation of fuzzy arithmetics that exploits both fuzzy intervals and hardware specificities. First, we propose and evaluate the benefit of an alternative representation format to the traditional lower-upper and midpoint-radius representation formats for intervals. Thanks to the proposed formats, we show that it is possible to halve the number of operations and memory requirements compared to conventional methods. Then, we show that operations on fuzzy intervals are sensitive to hardware specificities of accelerators such as GPU. These include static rounding, memory usage, instruction level parallelism (ILP) and thread-level parallelism (TLP). We develop a library of fuzzy arithmetic operations in CUDA and C++ over several formats. The proposed library is evaluated using compute-bound and memory-bound benchmarks on Nvidia GPUs, and shows a performance gain of 2 to 20 over traditional approaches

Some applications of possibilistic mean value, variance, covariance and correlation

In 2001 we introduced the notions of possibilistic mean value and variance of fuzzy numbers. In this paper we list some works that use these notions. We shall mention some application areas as wel

A rigorous possibility approach for the geotechnical reliability assessment supported by external database and local experience

Reliability analyses based on probability theory are widely applied in geotechnical engineering, and several analytical or numerical methods have been built upon the concept of failure occurrence. Nevertheless, common geotechnical engineering real-world problems deal with scarce or sparse information where experimental data are not always available to a sufficient extent and quality to infer a reliable probability distribution function. This paper rigorously combines Fuzzy Clustering and Possibility Theory for deriving a data-driven, quantitative, reliability approach, in addition to fully probability-oriented assessments, when useful but heterogeneous sources of information are available. The proposed non-probabilistic approach is mathematically consistent with the failure probability, when ideal random data are considered. Additionally, it provides a robust tool to account for epistemic uncertainties when data are uncertain, scarce, and sparse. The Average Cumulative Function transformation is used to obtain possibility distributions inferred from the fuzzy clustering of an indirect database. Target Reliability Index Values, consistent with the prescribed values provided by Eurocode 0, are established. Moreover, a Degree of Understanding tier system based on the practitioner’s local experience is also proposed. The proposed methodology is detailed and discussed for two numerical examples using national-scale databases, highlighting the potential benefits compared to traditional probabilistic approaches

A rigorous possibility approach for the geotechnical reliability assessment supported by external database and local experience

This is the final version. Available on open access from Elsevier via the DOI in this recordData availability: Data will be made available on request.Reliability analyses based on probability theory are widely applied in geotechnical engineering, and several analytical or numerical methods have been built upon the concept of failure occurrence. Nevertheless, common geotechnical engineering real-world problems deal with scarce or sparse information where experimental data are not always available to a sufficient extent and quality to infer a reliable probability distribution function. This paper rigorously combines Fuzzy Clustering and Possibility Theory for deriving a data-driven, quantitative, reliability approach, in addition to fully probability-oriented assessments, when useful but heterogeneous sources of information are available. The proposed non-probabilistic approach is mathematically consistent with the failure probability, when ideal random data are considered. Additionally, it provides a robust tool to account for epistemic uncertainties when data are uncertain, scarce, and sparse. The Average Cumulative Function transformation is used to obtain possibility distributions inferred from the fuzzy clustering of an indirect database. Target Reliability Index Values, consistent with the prescribed values provided by Eurocode 0, are established. Moreover, a Degree of Understanding tier system based on the practitioner’s local experience is also proposed. The proposed methodology is detailed and discussed for two numerical examples using national-scale databases, highlighting the potential benefits compared to traditional probabilistic approaches.Engineering and Physical Sciences Research Council (EPSRC