Belief functions induced by random fuzzy sets: A general framework for representing uncertain and fuzzy evidence
Université de technologie de Compiègne（贡比涅技术大学）；CNRS UMR 7253 Heudiasyc（法国国家科学研究中心联合研究单位7253 赫迪亚西克实验室）；Shanghai University（上海大学）；UTSEUS（上海大学中欧工程技术学院）；Institut universitaire de France（法兰西大学研究院）
Thierry Denoeux
发表信息：
Fuzzy Sets and Systems, Volume 424, 2021, Pages 63-91
We revisit Zadeh's notion of "evidence of the second kind" and show that it provides the foundation for a general theory of epistemic random fuzzy sets, which generalizes both the Dempster-Shafer theory of belief functions and possibility theory. In this perspective, Dempster-Shafer theory deals with belief functions generated by random sets, while possibility theory deals with belief functions induced by fuzzy sets. The more general theory allows us to represent and combine evidence that is both uncertain and fuzzy. We demonstrate the application of this formalism to statistical inference, and show that it makes it possible to reconcile the possibilistic interpretation of likelihood with Bayesian inference.
In this paper, a new interval type-2 fuzzy neural network able to construct non-separable fuzzy rules with adaptive shapes is introduced. To reflect the uncertainty, the shape of fuzzy sets considered to be uncertain. Therefore, a new form of interval type-2 fuzzy sets based on a general Gaussian model able to construct different shapes (including triangular, bell-shaped, trapezoidal) is proposed. To consider the interactions among input variables, input vectors are transformed to new feature spaces with uncorrelated variables proper for defining each fuzzy rule. Next, the new features are fed…
Quchan University of Technology（库昌理工大学）；University of Melbourne（墨尔本大学）
This contribution reviews critically the existing entropy measures for probabilistic hesitant fuzzy sets (PHFSs), and demonstrates that these entropy measures fail to effectively distinguish a variety of different PHFSs in some cases. In the sequel, we develop a new axiomatic framework of entropy measures for probabilistic hesitant fuzzy elements (PHFEs) by considering two facets of uncertainty associated with PHFEs which are known as fuzziness and nonspecificity. Respect to each kind of uncertainty, a number of formulae are derived to permit flexible selection of PHFE entropy measures. Moreov…
A Class Inference Scheme With Dempster-Shafer Theory for Learning Fuzzy-Classifier Systems
Faculty of Engineering（工学部）；Yokohama National University（Yokohama国立大学）；Department of Computer Science and Engineering（计算机科学与工程系）；Southern University of Science and Technology（南方科技大学）
Univ Rennes（雷恩大学）；IRISA（法国国家信息与自动化研究所雷恩分院（雷恩信息系统与随机过程研究所））；IUT de Lannion（拉尼翁大学技术学院）
Most questionnaires offer ordered responses whose order is poorly studied via belief functions. In this paper, we study the consequences of a frame of discernment consisting of ordered elements on belief functions. This leads us to redefine the power space and the union of ordered elements for the disjunctive combination. We also study distances on ordered elements and their use. In particular, from a membership function, we redefine the cardinality of the intersection of ordered elements, considering them fuzzy.
On modeling vagueness and uncertainty in data-to-text systems through fuzzy sets
Centro Singular en Investigación en Tecnoloxías da Información (CiTIUS), Universidade de Santiago de Compostela（圣地亚哥-德孔波斯特拉大学信息技术研究中心）；University of Aberdeen（阿伯丁大学）；Universidade de Santiago de Compostela（圣地亚哥-德孔波斯特拉大学）；University of Dundee（邓迪大学）
Beginning with a simple semantics for propositions, based on counting observations, it is shown that probabilistic and fuzzy logic correspond to two different heuristic assumptions regarding the combination of propositions whose evidence bases are not currently available. These two different heuristic assumptions lead to two different sets of formulas for propagating quantitative truth values through lattice operations. It is shown that these two sets of formulas provide a natural grounding for the multiplicative and additive operator-sets in linear logic. The standard rules of linear logic th…
This paper proposes a new generative model called neural belief reasoner (NBR). It differs from previous models in that it specifies a belief function rather than a probability distribution. Its implementation consists of neural networks, fuzzy-set operations and belief-function operations, and query-answering, sample-generation and training algorithms are presented. This paper studies NBR in two tasks. The first is a synthetic unsupervised-learning task, which demonstrates NBR's ability to perform multi-hop reasoning, reasoning with uncertainty and reasoning about conflicting information. The…
Parameter estimation based on interval-valued belief structures
Southwest University（西南大学）；Guangdong University of Foreign Studies（广东外语外贸大学）；Sun Yat-Sen University（中山大学）；Hong Kong Polytechnic University（香港理工大学）；Vanderbilt University（范德堡大学）
An Uncertainty-Aware Loss Function Incorporating Fuzzy Logic: Application to MRI Brain Image Segmentation
Department of Mathematics, Bareilly College, Bareilly (MJP Rohilkhand University), Uttar Pradesh（巴里利学院数学系，巴里利（MJP罗希尔坎德大学），乌塔尔 Pradesh）；CSIR-Central Electronics Engineering Research Institute, Pilani, Rajasthan（CSIR-中央电子工程研究机构，比兰蒂，拉贾斯坦）；CICMR, Regional Medical Research Center, Dibrugarh, India（CICMR，迪布格尔中心医学研究中心，印度）；Department of Statistics, Bareilly College, Bareilly, Uttar Pradesh（巴里利学院统计系，巴里利，乌塔尔 Pradesh）
University of Michigan（密歇根大学）；DEVCOM Army Research Laboratory（DEVCOM陆军研究实验室）；BI Norwegian Business School（BI挪威商学院）；University of Brescia（布雷西亚大学）
In second-order uncertain Bayesian networks, the conditional probabilities are only known within distributions, i.e., probabilities over probabilities. The delta-method has been applied to extend exact first-order inference methods to propagate both means and variances through sum-product networks derived from Bayesian networks, thereby characterizing epistemic uncertainty, or the uncertainty in the model itself. Alternatively, second-order belief propagation has been demonstrated for polytrees but not for general directed acyclic graph structures. In this work, we extend Loopy Belief Propagat…
IBM Research（IBM研究院）；University of Sao Paulo（圣保罗大学）；INSA de Rouen（鲁昂国立应用科学学院）
本文引入模糊集上的核的概念，作为$[0,1]$值函数的相似性度量，也称为模糊集上的核。\emph{membership functions of fuzzy sets}。我们定义了以下几类核：模糊集上的叉积核、交集核、非单点核和基于距离的核。这些内核适用于机器学习和数据科学任务，其中数据中的不确定性具有本体或认识论解释。
