On the Granular Representation of Fuzzy Quantifier-Based Fuzzy Rough Sets

• URL: http://arxiv.org/abs/2312.16704v1
• Date: Wed, 27 Dec 2023 20:02:40 GMT
• Title: On the Granular Representation of Fuzzy Quantifier-Based Fuzzy Rough Sets
• Authors: Adnan Theerens and Chris Cornelis
• Abstract summary: This paper focuses on fuzzy quantifier-based fuzzy rough sets (FQFRS) It shows that Choquet-based fuzzy rough sets can be represented granularly under the same conditions as OWA-based fuzzy rough sets. This observation highlights the potential of these models for resolving data inconsistencies and managing noise.
• Score: 0.7614628596146602
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Rough set theory is a well-known mathematical framework that can deal with inconsistent data by providing lower and upper approximations of concepts. A prominent property of these approximations is their granular representation: that is, they can be written as unions of simple sets, called granules. The latter can be identified with "if. . . , then. . . " rules, which form the backbone of rough set rule induction. It has been shown previously that this property can be maintained for various fuzzy rough set models, including those based on ordered weighted average (OWA) operators. In this paper, we will focus on some instances of the general class of fuzzy quantifier-based fuzzy rough sets (FQFRS). In these models, the lower and upper approximations are evaluated using binary and unary fuzzy quantifiers, respectively. One of the main targets of this study is to examine the granular representation of different models of FQFRS. The main findings reveal that Choquet-based fuzzy rough sets can be represented granularly under the same conditions as OWA-based fuzzy rough sets, whereas Sugeno-based FRS can always be represented granularly. This observation highlights the potential of these models for resolving data inconsistencies and managing noise.

Related papers

• Random Models for Fuzzy Clustering Similarity Measures [0.0]
  The Adjusted Rand Index (ARI) is a widely used method for comparing hard clusterings. We propose a single framework for computing the ARI with three random models that are intuitive and explainable for both hard and fuzzy clusterings.
  arXiv  Detail & Related papers  (2023-12-16T00:07:04Z)
• ChiroDiff: Modelling chirographic data with Diffusion Models [132.5223191478268]
  We introduce a powerful model-class namely "Denoising Diffusion Probabilistic Models" or DDPMs for chirographic data. Our model named "ChiroDiff", being non-autoregressive, learns to capture holistic concepts and therefore remains resilient to higher temporal sampling rate.
  arXiv  Detail & Related papers  (2023-04-07T15:17:48Z)
• Fuzzy Rough Sets Based on Fuzzy Quantification [1.4213973379473654]
  We introduce fuzzy quantifier-based fuzzy rough sets (FQFRS) FQFRS is an intuitive generalization of fuzzy rough sets. We show how several existing models fit in this generalization as well as how it inspires novel ones.
  arXiv  Detail & Related papers  (2022-12-06T19:59:57Z)
• Some neighborhood-related fuzzy covering-based rough set models and their applications for decision making [8.270779659551431]
  We propose four types of fuzzy neighborhood operators based on fuzzy covering by overlap functions and their implicators. A novel fuzzy TOPSIS methodology is put forward to solve a biosynthetic nanomaterials select issue.
  arXiv  Detail & Related papers  (2022-05-13T05:02:53Z)
• Choquet-Based Fuzzy Rough Sets [2.4063592468412276]
  Fuzzy rough set theory can be used as a tool for dealing with inconsistent data when there is a gradual notion of indiscernibility between objects. To mitigate this problem, ordered weighted average (OWA) based fuzzy rough sets were introduced. We show how the OWA-based approach can be interpreted intuitively in terms of vague quantification, and then generalize it to Choquet-based fuzzy rough sets.
  arXiv  Detail & Related papers  (2022-02-22T13:10:16Z)
• Evaluating State-of-the-Art Classification Models Against Bayes Optimality [106.50867011164584]
  We show that we can compute the exact Bayes error of generative models learned using normalizing flows. We use our approach to conduct a thorough investigation of state-of-the-art classification models.
  arXiv  Detail & Related papers  (2021-06-07T06:21:20Z)
• Deconfounding Scores: Feature Representations for Causal Effect Estimation with Weak Overlap [140.98628848491146]
  We introduce deconfounding scores, which induce better overlap without biasing the target of estimation. We show that deconfounding scores satisfy a zero-covariance condition that is identifiable in observed data. In particular, we show that this technique could be an attractive alternative to standard regularizations.
  arXiv  Detail & Related papers  (2021-04-12T18:50:11Z)
• Stochastic Aggregation in Graph Neural Networks [9.551282469099887]
  Graph neural networks (GNNs) manifest pathologies including over-smoothing and limited power discriminating. We present a unifying framework for aggregation (STAG) in GNNs, where noise is (adaptively) injected into the aggregation process from the neighborhood to form node embeddings.
  arXiv  Detail & Related papers  (2021-02-25T02:52:03Z)
• Structural Causal Models Are (Solvable by) Credal Networks [70.45873402967297]
  Causal inferences can be obtained by standard algorithms for the updating of credal nets. This contribution should be regarded as a systematic approach to represent structural causal models by credal networks. Experiments show that approximate algorithms for credal networks can immediately be used to do causal inference in real-size problems.
  arXiv  Detail & Related papers  (2020-08-02T11:19:36Z)
• Explainable Matrix -- Visualization for Global and Local Interpretability of Random Forest Classification Ensembles [78.6363825307044]
  We propose Explainable Matrix (ExMatrix), a novel visualization method for Random Forest (RF) interpretability. It employs a simple yet powerful matrix-like visual metaphor, where rows are rules, columns are features, and cells are rules predicates. ExMatrix applicability is confirmed via different examples, showing how it can be used in practice to promote RF models interpretability.
  arXiv  Detail & Related papers  (2020-05-08T21:03:48Z)
• Fast and Robust Rank Aggregation against Model Misspecification [105.54181634234266]
  In rank aggregation (RA), a collection of preferences from different users are summarized into a total order under the assumption of homogeneity of users. Model misspecification in RA arises since the homogeneity assumption fails to be satisfied in the complex real-world situation. We propose CoarsenRank, which possesses robustness against model misspecification.
  arXiv  Detail & Related papers  (2019-05-29T11:35:28Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.