Related papers: Quantile-Based Skewness for Fuzzy Numbers with Pro…
We give a geometrically motivated measure of skewness, define a mean value triangle number, and dispersion (in that order) of a fuzzy number without reference or seeking analogy to the namesake but parallel concepts in probability theory.…
In quantum mechanics, a norm squared wave function can be interpreted as the probability density that describes the likelihood of a particle to be measured in a given position or momentum. This statistical property is at the core of the…
The practice of stochastic sensitivity analysis described in the decision analysis literature is a testimonial to the need for considering deviations from precise point estimates of uncertainty. We propose the use of Bayesian fuzzy…
Possibility and probability theories are alternative and complementary ways to deal with uncertainty, which has motivated over the last years an interest for the study of ways to transform probability distributions into possibility…
We introduce and study a new class of partial differential equations (PDEs) with hybrid fuzzy-stochastic parameters, coined fuzzy-stochastic PDEs. Compared to purely stochastic PDEs or purely fuzzy PDEs, fuzzy-stochastic PDEs offer powerful…
Frailty models are often the model of choice for heterogeneous survival data. A frailty model contains both random effects and fixed effects, with the random effects accommodating for the correlation in the data. Different estimation…
Fuzzy metric spaces, grounded in t-norms and membership functions, have been widely proposed to model uncertainty in machine learning, decision systems, and artificial intelligence. Yet these frameworks treat uncertainty as an external…
A novel procedure to perform fuzzy clustering of multivariate time series generated from different dependence models is proposed. Different amounts of dissimilarity between the generating models or changes on the dynamic behaviours over…
Fuzzy data, prevalent in social sciences and other fields, capture uncertainties arising from subjective evaluations and measurement imprecision. Despite significant advancements in fuzzy statistics, a unified inferential regression-based…
Fuzzy simplicial sets have become an object of interest in dimensionality reduction and manifold learning, most prominently through their role in UMAP. However, their definition through tools from algebraic topology without a clear…
Accurate reconstruction of probability density functions (PDFs) from data is essential in engineering applications. Classical global moment-based polynomial approximations often suffer from oscillations, instability in the tails, and…
The purpose of the paper is to provide a new way of seeing the p-value in terms of a fuzzy membership function. According to the ASAs statement, we aim at removing the arbitrary choice of the significance level and at demonstrating that the…
Based on the in-depth analysis of the nature and features of vague phenomenon, this paper focuses on establishing the axiomatical foundation of the membership degree theory for vague phenomenon, presents an axiomatic system of governing…
This paper proposes a new fuzzy assessing procedure with application in management decision making. The proposed fuzzy approach build the membership functions for system characteristics of a standby repairable system. This method is used to…
This article is the first part of series of articles that aim to present the foundations for fuzzy variational calculus for functions taking values in the space of linearly correlated fuzzy numbers $\mathbb{R}_{\mathcal{F}(A)}$. Recall that…
The optimization on the structure of process of information management under uncertain environment has attracted lots of attention from researchers around the world. Nevertheless, how to obtain accurate and rational evaluation from…
In this paper, we introduce a fundamental framework to create a bridge between Probability Theory and Fuzzy Logic. Indeed, our theory formulates a random experiment of selecting crisp elements with the criterion of having a certain fuzzy…
Rigorous guarantees about the performance of predictive algorithms are necessary in order to ensure their responsible use. Previous work has largely focused on bounding the expected loss of a predictor, but this is not sufficient in many…
A statistical, data-driven method is presented that quantifies influences between variables of a dynamical system. The method is based on finding a suitable representation of points by fuzzy affiliations with respect to landmark points…
Fuzzy measures, also referred to as nonadditive measures, emerge from the foundational concept of additive measures by transforming additivity into monotonicity. In comparison to the expansive $2^n$ coefficients of fuzzy measures, additive…