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Application of Tropical Optimization for Solving Multicriteria Problems of Pairwise Comparisons Using Log-Chebyshev Approximation Int. J. Approx. Reason. (IF 3.9) Pub Date : 2024-03-16 Nikolai Krivulin
We consider a decision-making problem to find absolute ratings of alternatives that are compared in pairs under multiple criteria, subject to constraints in the form of two-sided bounds on ratios between the ratings. Given matrices of pairwise comparisons made according to the criteria, the problem is formulated as the log-Chebyshev approximation of these matrices by a common consistent matrix (a symmetrically
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A study of rough inclusion on algebras with quasi-Boolean base Int. J. Approx. Reason. (IF 3.9) Pub Date : 2024-03-15 Anirban Saha, Jayanta Sen, Mihir Kumar Chakraborty
Pre-rough algebra has emerged from the rough set theory, which is a quasi-Boolean algebra with a few additional axioms. Four types of abstract rough inclusion are defined in pre-rough algebra which give rise to four different implication operators within this algebra. Properties of these four implications are studied from the angle of residuation. Logics of pre-rough algebra with respect to different
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A probabilistic modal logic for context-aware trust based on evidence Int. J. Approx. Reason. (IF 3.9) Pub Date : 2024-03-15 Alessandro Aldini, Gianluca Curzi, Pierluigi Graziani, Mirko Tagliaferri
Trust is an extremely helpful construct when reasoning under uncertainty. Thus, being able to logically formalize the concept in a suitable language is important. However, doing so is problematic for three reasons. First, in order to keep track of the contextual nature of trust, situation trackers are required inside the language. Second, in order to produce trust estimations, agents rely on evidence
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Overlap function-based fuzzy β-covering relations and fuzzy β-covering rough set models Int. J. Approx. Reason. (IF 3.9) Pub Date : 2024-03-13 Yaoyao Fan, Xiaohong Zhang, Jingqian Wang
As an extension of the fuzzy covering, fuzzy -covering has garnered significant scholarly concern. However, certain limitations impede its practical application. To address the issue of inaccurate characterization of object relationships caused by the current fuzzy -neighborhood operator, four new operators were developed, which exhibit both symmetry and reflexivity through the utilization of established
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An Auto-weighted Enhanced Horizontal Collaborative Fuzzy Clustering Algorithm with Knowledge Adaption Mechanism Int. J. Approx. Reason. (IF 3.9) Pub Date : 2024-03-12 Huilin Yang, Fusheng Yu, Witold Pedrycz, IEEE Life Fellow, Zonglin Yang, Jiaqi Chang, Jiayin Wang
Among the multi-source data clustering tasks, there is a kind of frequently encountered tasks where only one of the multi-source datasets is available for sake of privacy and other reasons. The only available dataset is called local dataset, and the other are called external datasets. The horizontal collaborative fuzzy clustering (HCFC) model is a typical one that can deal with such clustering tasks
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New results of (U,N)-implications satisfying I(r,I(s,t))=I(I(r,s),I(r,t)) Int. J. Approx. Reason. (IF 3.9) Pub Date : 2024-03-12 Cheng Zhang, Feng Qin
Generalized Frege's law has been extensively explored by numerous scholars in the field of fuzzy mathematics, particularly within the framework of fuzzy logic. This study aims to further investigate the -implications that satisfy this law and presents a multitude of novel findings. First, to efficiently determine the satisfiability of the generalized Frege's law for any -implication, two new necessary
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Systematic attribute reductions based on double granulation structures and three-view uncertainty measures in interval-set decision systems Int. J. Approx. Reason. (IF 3.9) Pub Date : 2024-03-08 Xin Xie, Xianyong Zhang
Attribute reductions eliminate redundant information to become valuable in data reasoning. In the data context of interval-set decision systems (ISDSs), attribute reductions rely on granulation structures and uncertainty measures; however, the current structures and measures exhibit the singleness limitations, so their enrichments imply corresponding improvements of attribute reductions. Aiming at
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Comparing Machine Learning Algorithms by Union-Free Generic Depth Int. J. Approx. Reason. (IF 3.9) Pub Date : 2024-03-07 Hannah Blocher, Georg Schollmeyer, Malte Nalenz, Christoph Jansen
We propose a framework for descriptively analyzing sets of partial orders based on the concept of depth functions. Despite intensive studies in linear and metric spaces, there is very little discussion on depth functions for non-standard data types such as partial orders. We introduce an adaptation of the well-known simplicial depth to the set of all partial orders, the depth. Moreover, we utilize
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Estimating the coverage measure and the area explored by a line-sweep sensor on the plane Int. J. Approx. Reason. (IF 3.9) Pub Date : 2024-03-01 Maria Costa Vianna, Eric Goubault, Luc Jaulin, Sylvie Putot
This paper presents a method for determining the area explored by a line-sweep sensor during an area-covering mission in a two-dimensional plane. Accurate knowledge of the explored area is crucial for various applications in robotics, such as mapping, surveillance, and coverage optimization. The proposed method leverages the concept of coverage measure of the environment and its relation to the topological
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Uncertainty quantification in logistic regression using random fuzzy sets and belief functions Int. J. Approx. Reason. (IF 3.9) Pub Date : 2024-02-29 Thierry Denœux
Evidential likelihood-based inference is a new approach to statistical inference in which the relative likelihood function is interpreted as a possibility distribution. By expressing new data as a function of the parameter and a random variable with known probability distribution, one then defines a random fuzzy set and an associated predictive belief function representing uncertain knowledge about
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Fast and robust clustering of general-shaped structures with tk-merge Int. J. Approx. Reason. (IF 3.9) Pub Date : 2024-02-27 Luca Insolia, Domenico Perrotta
In real-world applications, the group of provenance of data can be inherently uncertain, the data values can be imprecise and some of them can be wrong. We handle uncertain, imprecise and noisy data in clustering problems with general-shaped structures. We do it under very weak parametric assumptions with a two-step hybrid robust clustering algorithm based on trimmed k-means and hierarchical agglomeration
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Reprint of: Some thoughts about transfer learning. What role for the source domain? Int. J. Approx. Reason. (IF 3.9) Pub Date : 2024-02-26 A. Cornuéjols
Transfer learning is called for when the training and test data do not share the same input distributions () or/and not the same conditional ones (). In the most general case, the input spaces and/or output spaces can be different: and/or . However, most work assume that . Furthermore, a common held assumption is that it is necessary that the source hypothesis be good on the source training data and
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L-valued covering-based rough sets and corresponding decision-making applications Int. J. Approx. Reason. (IF 3.9) Pub Date : 2024-02-23 Kamal El-Saady, Amal Rashed, Ayat A. Temraz
Considering to be a complete residuated lattice, by introducing the notion of -valued covering on an -set (as a universe), and then an -valued neighborhood based on it, we present the concept of -valued covering-based rough sets. We mainly address the following issues in this paper: Firstly, we present four types of -valued neighborhood operators and study some of their respective properties. Secondly
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Fuzzy implications - A (dis)similarity perspective Int. J. Approx. Reason. (IF 3.9) Pub Date : 2024-02-22 Kavit Nanavati, Megha Gupta, Balasubramaniam Jayaram
Fuzzy implications continue to remain an important class among the fuzzy logic connectives, having found utility in contexts outside of logical inference too. Recently, fuzzy implications have been shown to be a fertile source for obtaining distance functions with very beneficial properties. In this work, we show that fuzzy implications can also be a good wellspring of fuzzy compatibility relations
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Multi-label feature selection based on fuzzy rough sets with metric learning and label enhancement Int. J. Approx. Reason. (IF 3.9) Pub Date : 2024-02-22 Mingjie Cai, Mei Yan, Pei Wang, Feng Xu
Multi-label feature selection based on fuzzy rough sets, as a key step of multi-label data preprocessing, has been widely concerned by scholars in recent years. Most of the existing multi-label feature selection algorithms directly treat labels as logical labels and use a single distance metric to describe similarity. However, the variability of label descriptions and the limitations of a single distance
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Strictly frequentist imprecise probability Int. J. Approx. Reason. (IF 3.9) Pub Date : 2024-02-21 Christian Fröhlich, Rabanus Derr, Robert C. Williamson
Strict frequentism defines probability as the limiting relative frequency in an infinite sequence. What if the limit does not exist? We present a broader theory, which is applicable also to data that exhibit diverging relative frequencies. In doing so, we develop a close connection with the theory of imprecise probability: the cluster points of relative frequencies yield a coherent upper prevision
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Three-phase multi-criteria ranking considering three-way decision framework and criterion fuzzy concept Int. J. Approx. Reason. (IF 3.9) Pub Date : 2024-02-20 Kai Zhang, Jianhua Dai
The criterion fuzzy concept refers to a fuzzy set that represents the decision-maker's subjective preference for each criterion within the universe of criteria. Addressing the challenge of ranking all alternatives based on a given criterion fuzzy concept is a novel research direction in the field of fuzzy multi-criteria ranking issues. This paper proposes a three-phase approach for multi-criteria ranking
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Extended papers from the 11th International Symposium on Imprecise Probabilities: Theories and Applications Int. J. Approx. Reason. (IF 3.9) Pub Date : 2024-02-19 Jasper De Bock, Gert de Cooman, Cassio P. de Campos
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Minimality, necessity and sufficiency for argumentation and explanation Int. J. Approx. Reason. (IF 3.9) Pub Date : 2024-02-12 AnneMarie Borg, Floris Bex
We discuss explanations for formal (abstract and structured) argumentation – the question whether and why a certain argument or claim can be accepted (or not) under various extension-based semantics. We introduce a flexible framework, which can act as the basis for many different types of explanations. For example, we can have simple or comprehensive explanations in terms of arguments for or against
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A review on declarative approaches for constrained clustering Int. J. Approx. Reason. (IF 3.9) Pub Date : 2024-02-02 Thi-Bich-Hanh Dao, Christel Vrain
Clustering is an important Machine Learning task, which aims at discovering the implicit structure of data. Applying a clustering algorithm is easy but since clustering is an unsupervised task, tuning it so that the results is appropriate to the expert expectations is much less obvious. To overcome this, expert knowledge can be integrated into a clustering process; this is generally formalized as constraints
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Paralinear distance and its algorithm for hierarchical clustering of high-dimensional discrete variables Int. J. Approx. Reason. (IF 3.9) Pub Date : 2024-01-26 Shuai Wang, Lizhu Hao, Xiaofei Wang, Jianhua Guo
Variable clustering is an important tool for mining association rules and explaining the latent mechanisms responsible for generating data. In this work, we aim to study the hierarchical variable clustering algorithm based on the paralinear distance between discrete variables. Firstly, we study the paralinear distance with the multinomial distribution, and point out that any distance with additivity
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Evaluating uncertainty with Vertical Barrier Models Int. J. Approx. Reason. (IF 3.9) Pub Date : 2024-01-26 Enrique Miranda, Renato Pelessoni, Paolo Vicig
Vertical Barrier Models (VBM) are a family of imprecise probability models that generalise a number of well known distortion/neighbourhood models (such as the Pari-Mutuel Model, the Linear-Vacuous Model, and others) while still being relatively simple. Several of their properties were established in previous works; in this paper we explore, in a finite framework, further facets of these models: their
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Constructing overlap functions on bounded posets via multiplicative generators Int. J. Approx. Reason. (IF 3.9) Pub Date : 2024-01-26 Jing Lu, Bin Zhao
Overlap functions are an important class of aggregation operators on [0,1] that have been proposed for applications in image processing, classification, etc. Later, Paiva et al. lifted overlap functions on [0,1] to complete lattices. In this paper, we continue to study overlap functions on bounded posets so as to lift the continuity in the notion of overlap functions from [0,1] to bounded posets mainly
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Graph neural networks-based preference learning method for object ranking Int. J. Approx. Reason. (IF 3.9) Pub Date : 2024-01-26 Zhenhua Meng, Rongheng Lin, Budan Wu
Preference learning refers to the task of predicting the ranking of a collection of alternatives based on observed or revealed preference information. Object ranking is a critical problem within the domain of preference learning, which can be described as learning a ranking function based on training data in a ranked form. Some existing parametric preference learning methods are difficult to balance
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Feature selection of dominance-based neighborhood rough set approach for processing hybrid ordered data Int. J. Approx. Reason. (IF 3.9) Pub Date : 2024-01-26 Jiayue Chen, Ping Zhu
Feature selection is a fundamental application of rough set theory in identifying significant features and reducing data dimensionality. For ordered data (OD), existing studies of feature selection mainly aim at ODs with specific criteria, i.e., single-valued, interval-valued, or set-valued criteria. However, these studies are inapplicable to ODs simultaneously including the three criteria, namely
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The interior of inconsistency in a knowledge base Int. J. Approx. Reason. (IF 3.9) Pub Date : 2024-01-18 Kedian Mu
Looking inside local inconsistencies arising in different parts of a knowledge base may help us better frame the inconsistency of the knowledge base. Moreover, as possible changes of the inconsistency due to removing some formulas from the knowledge base, local inconsistencies play an important role in identifying contributions of formulas to the inconsistency in the knowledge base. In this paper,
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CCN+: A Neuro-symbolic Framework for Deep Learning with Requirements Int. J. Approx. Reason. (IF 3.9) Pub Date : 2024-01-22 Eleonora Giunchiglia, Alex Tatomir, Mihaela Cătălina Stoian, Thomas Lukasiewicz
For their outstanding ability of finding hidden patterns in data, deep learning models have been extensively applied in many different domains. However, recent works have shown that, if a set of requirements expressing inherent knowledge about the problem at hand is given, then neural networks often fail to comply with them. This represents a major drawback for deep learning models, as requirements
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Semirings for Probabilistic and Neuro-Symbolic Logic Programming Int. J. Approx. Reason. (IF 3.9) Pub Date : 2024-01-22 Vincent Derkinderen, Robin Manhaeve, Pedro Zuidberg Dos Martires, Luc De Raedt
The field of probabilistic logic programming (PLP) focuses on integrating probabilistic models into programming languages based on logic. Over the past 30 years, numerous languages and frameworks have been developed for modeling, inference and learning in probabilistic logic programs. While originally PLP focused on discrete probability, more recent approaches have incorporated continuous distributions
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Enriching Interactive Explanations with Fuzzy Temporal Constraint Networks Int. J. Approx. Reason. (IF 3.9) Pub Date : 2024-01-17 Mariña Canabal-Juanatey, Jose M. Alonso-Moral, Alejandro Catala, Alberto Bugarín-Diz
Humans often use expressions with vague terms which play a fundamental role for effective communication. These expressions are successfully modeled with fuzzy technology, but they are not usually integrated yet with Natural Language Processing models and techniques. Large-scale pre-trained language models yield excellent results in many language tasks, but they have some drawbacks such as their lack
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Aggregation of random elements over bounded lattices Int. J. Approx. Reason. (IF 3.9) Pub Date : 2024-01-15 Juan Baz, Irene Díaz, Susana Montes
Aggregation functions are widely used to fuse information from different sources in a unique value. In many cases, the aggregated information is related to some experimental measure or random sampling of a population. In this direction, it is reasonable to consider aggregation of random elements. In this paper, the concept of aggregation functions of random elements over bounded lattices, which are
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New results on convergence in distribution of fuzzy random variables Int. J. Approx. Reason. (IF 3.9) Pub Date : 2024-01-17 Miriam Alonso de la Fuente
We study some properties of convergence in distribution of fuzzy random variables in the metric dp, more precisely, if this type of convergence is preserved when we apply some functions between the space of fuzzy sets and other metric spaces. In particular, we show that this convergence is preserved when we take the closed convex hull, the maximum, the minimum, the product and the quotient. Moreover
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RCAviz: Exploratory search in multi-relational datasets represented using relational concept analysis Int. J. Approx. Reason. (IF 3.9) Pub Date : 2024-01-17 Marianne Huchard, Pierre Martin, Emile Muller, Pascal Poncelet, Vincent Raveneau, Arnaud Sallaberry
The conceptual structures built with Formal Concept Analysis (FCA) and its extensions are appropriate constructs for supporting Exploratory Search (ES). FCA indeed classifies a set of objects described by Boolean attributes in a concept lattice which is prone to (intra-lattice) navigation. Relational Concept Analysis (RCA), for its part, classifies several sets of objects connected through multiple
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Moderated revision Int. J. Approx. Reason. (IF 3.9) Pub Date : 2024-01-17 Daniel Grimaldi, Maria Vanina Martinez, Ricardo O. Rodriguez
In this article, we provide a new kind of belief revision operator that we call Moderated Revision. At first glance, it is a non-prioritized operator that combines a basic classical AGM operator with a credibility-limited one. The underlying idea is this: when new observation μ is received, it is accepted but with doubts, i.e., uncertainty. We use a revision operator to model the accepted part and
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Interval R-Sheffer strokes and interval fuzzy Sheffer strokes endowed with admissible orders Int. J. Approx. Reason. (IF 3.9) Pub Date : 2024-01-11 Yifan Zhao, Hua-Wen Liu
Fuzzy Sheffer stroke is a new class of fuzzy connectives introduced by Baczyński et al., which generalizes the Sheffer stroke operation in classical logic. However, the investigation on interval extensions of fuzzy Sheffer strokes is still missing in the literature. To fill this gap, in this paper, we introduce two interval generalizations of fuzzy Sheffer strokes. Firstly, we propose the notion of
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Computing crisp bisimulations for fuzzy structures Int. J. Approx. Reason. (IF 3.9) Pub Date : 2024-01-12 Linh Anh Nguyen, Dat Xuan Tran
We present an efficient algorithm for computing the partition corresponding to the greatest crisp bisimulation of a given finite fuzzy labeled graph. Its complexity is of order O((mlogl+n)logn), where n, m and l are the number of vertices, the number of nonzero edges and the number of different fuzzy degrees of edges of the input graph, respectively. We also study a similar problem for the setting
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On the Failings of Shapley Values for Explainability Int. J. Approx. Reason. (IF 3.9) Pub Date : 2024-01-10 Xuanxiang Huang, Joao Marques-Silva
Explainable Artificial Intelligence (XAI) is widely considered to be critical for building trust into the deployment of systems that integrate the use of machine learning (ML) models. For more than two decades Shapley values have been used as the theoretical underpinning for some methods of XAI, being commonly referred to as SHAP scores. Some of these methods of XAI now rank among the most widely used
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Stochastic dominance and statistical preference for random variables coupled by arbitrary copulas Int. J. Approx. Reason. (IF 3.9) Pub Date : 2024-01-08 Inés Couso, Luciano Sánchez
Recently, results have been published showing that first order stochastic dominance implies statistical preference and diff-stochastic dominance, when the copula relating the compared variables is either Archimedean, the product copula, or one of the Fréchet-Hoeffding bounds. In the present paper, we rely on known results on multivariate stochastic orders to extend these results and simplify the proofs
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Efficient computation of counterfactual bounds Int. J. Approx. Reason. (IF 3.9) Pub Date : 2024-01-03 Marco Zaffalon, Alessandro Antonucci, Rafael Cabañas, David Huber, Dario Azzimonti
We assume to be given structural equations over discrete variables inducing a directed acyclic graph, namely, a structural causal model, together with data about its internal nodes. The question we want to answer is how can we compute bounds for partially identifiable counterfactual queries from such an input. We start by giving a map from structural casual models to credal networks. This allows us
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Some notes on possibilistic randomisation with t-norm based joint distributions in strategic-form games Int. J. Approx. Reason. (IF 3.9) Pub Date : 2024-01-02 Esther Anna Corsi, Hykel Hosni, Enrico Marchioni
This article continues the investigation started in [18] on the role of possibilistic mixed strategies in strategic-form games. In this earlier work we assumed, as standard in possibility theory, that joint possibility distributions were computed by combining possibilistic mixed strategies with the minimum t-norm. In this paper, we investigate the consequences of defining joint possibility distributions
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Stochastically ordered aggregation operators Int. J. Approx. Reason. (IF 3.9) Pub Date : 2023-12-28 Juan Baz, Franco Pellerey, Irene Díaz, Susana Montes
In aggregation theory, there exists a large number of aggregation functions that are defined in terms of rearrangements in increasing order of the arguments. Prominent examples are the Ordered Weighted Operator and the Choquet and Sugeno integrals. Following a probability approach, ordering random variables by means of stochastic orders can be also a way to define aggregations of random variables.
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Relevance, recovery and recuperation: A prelude to ring withdrawal Int. J. Approx. Reason. (IF 3.9) Pub Date : 2023-12-28 Eduardo Fermé, Marco Garapa, Abhaya Nayak, Maurício D.L. Reis
In this paper, we introduce recuperative withdrawals, belief change operators that satisfy recuperation, a postulate weaker than recovery, all the AGM postulates for contraction except recovery and another postulate which is a slightly stronger condition than conjunctive inclusion. Furthermore, we present a constructive definition for a class of operators —named ring withdrawals— which are such that
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A three-way decision approach for dynamically expandable networks Int. J. Approx. Reason. (IF 3.9) Pub Date : 2023-12-22 Usman Wajid, Muhammad Hamza, Muhammad Taimoor Khan, Nouman Azam
Conventional deep learning models are designed to work on a single task. They are required to be trained from scratch each time new tasks are added. This leads to overhead in training time. Continual deep learning models with dynamically expandable network architecture aim to handle this issue. The key idea in these models is to find a balance between the properties of stability (preserving the learned
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Some thoughts about transfer learning. What role for the source domain? Int. J. Approx. Reason. (IF 3.9) Pub Date : 2023-12-19 A. Cornuéjols
Transfer learning is called for when the training and test data do not share the same input distributions (PXS≠PXT) or/and not the same conditional ones (PY|XS≠PY|XT). In the most general case, the input spaces and/or output spaces can be different: XS≠XT and/or YS≠YT. However, most work assume that XS=XT. Furthermore, a common held assumption is that it is necessary that the source hypothesis be good
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Medical decision support in the light of interactive granular computing: Lessons from the Ovufriend project Int. J. Approx. Reason. (IF 3.9) Pub Date : 2023-12-13 Soma Dutta, Andrzej Skowron, Łukasz Sosnowski
The main aim of the paper is to discuss the architecture for the future Intelligent Systems (IS's) and Decision Support Systems (DS's) dealing with complex phenomena such as supporting medical decisions (diagnosis and therapy) and to emphasize challenges in designing such systems. More precisely, the paper presents arguments for developing a specialized computing model based on the interactive granular
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Spatial unity for the apperception engine Int. J. Approx. Reason. (IF 3.9) Pub Date : 2023-12-15 Arie Soeteman, Michiel van Lambalgen
We develop a logical approach for computational agents to spatially explore their environment, extending on the Kant-inspired logical unification methods of the Apperception Engine. Evaluating models of the Regional Connection Calculus as Alexandroff Topologies, we axiomatise connectedness and unity of space. We further define dimensionality for tolerance spaces and prove that locally verifiable properties
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An answer set programming-based implementation of epistemic probabilistic event calculus Int. J. Approx. Reason. (IF 3.9) Pub Date : 2023-12-14 Fabio Aurelio D'Asaro, Antonis Bikakis, Luke Dickens, Rob Miller
We describe a general procedure for translating Epistemic Probabilistic Event Calculus (EPEC) action language domains into Answer Set Programs (ASP), and show how the Python-driven features of the ASP solver Clingo can be used to provide efficient computation in this probabilistic setting. EPEC supports probabilistic, epistemic reasoning in domains containing narratives that include both an agent's
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Graph representation learning method based on three-way partial order structure Int. J. Approx. Reason. (IF 3.9) Pub Date : 2023-12-13 Enliang Yan, Shikuan Hao, Tao Zhang, Tianyong Hao, Qiliang Chen, Jianping Yu
In the era of big data, handling massive datasets to extract valuable information has become increasingly critical. Knowledge representation emerges as a pivotal method to address this challenge. In the domain of knowledge representation, there exist two primary approaches: symbolic representation and vector representation. The integration of symbolic and vector representations to harness their respective
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Confidence assessment in safety argument structure - Quantitative vs. qualitative approaches Int. J. Approx. Reason. (IF 3.9) Pub Date : 2023-12-12 Yassir Idmessaoud, Didier Dubois, Jérémie Guiochet
Some safety standards (e.g., ISO 26262 in automotive industry) propose the use of argument structures to justify that the high-level safety properties of a system have been ensured. The goal structuring notation (GSN) is a graphical tool used to represent these argument structures. However, this approach does not address the uncertainties that may affect the validity of the arguments. Thus, some authors
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Fuzzy rough unlearning model for feature selection Int. J. Approx. Reason. (IF 3.9) Pub Date : 2023-12-09 Yuxin Tang, Suyun Zhao, Hong Chen, Cuiping Li, Junhai Zhai, Qiangjun Zhou
In big data era, some data, becoming meaningless or illegal over time and space, need to be deleted from historical knowledge. It is a challenging problem, called machine unlearning, to efficiently forget the information of those outdated data from historical models. Some unlearning techniques have been proposed in loss-well-defined classification models, such as SVM, Random Forest, and Federated learning
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Hierarchical variable clustering via copula-based divergence measures between random vectors Int. J. Approx. Reason. (IF 3.9) Pub Date : 2023-12-06 Steven De Keyser, Irène Gijbels
This article considers rank-invariant clustering of continuous data via copula-based Φ-dependence measures. The general theoretical framework establishes dependence quantification between random vectors (groups of variables), which is used for measuring the similarity between variable clusters in an agglomerative hierarchical procedure afterwards. Special attention is devoted to meta-elliptical copulas
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Coherence and avoidance of sure loss for standardized functions and semicopulas Int. J. Approx. Reason. (IF 3.9) Pub Date : 2023-11-27 Erich Peter Klement, Damjana Kokol Bukovšek, Blaž Mojškerc, Matjaž Omladič, Susanne Saminger-Platz, Nik Stopar
We discuss avoidance of sure loss and coherence results for semicopulas and standardized functions, i.e., for grounded, 1-increasing functions with value 1 at (1,1,…,1). We characterize the existence of a k-increasing n-variate function C fulfilling A⩽C⩽B for standardized n-variate functions A,B and discuss methods for constructing such functions. Our proofs also include procedures for extending functions
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Nature of decision valuations in elimination of redundant attributes Int. J. Approx. Reason. (IF 3.9) Pub Date : 2023-11-28 Soma Dutta, Dominik Ślęzak
Information systems are the basic building blocks of the theory of rough sets which, based on information signatures of objects, develops strategies for classifying concepts and/or deriving significant information about decision attributes. During such processes of aggregating decision information, one needs to focus on the aspects of designing its representation and considering various ways for reducing
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Exploiting fuzzy rough entropy to detect anomalies Int. J. Approx. Reason. (IF 3.9) Pub Date : 2023-11-20 Sihan Wang, Zhong Yuan, Chuan Luo, Hongmei Chen, Dezhong Peng
Anomaly detection has been used in a wide range of fields. However, most of the current detection methods are only applicable to certain data, ignoring uncertain information such as fuzziness in the data. Fuzzy rough set theory, as an essential mathematical model for granular computing, provides an effective method for processing uncertain data such as fuzziness. Fuzzy rough entropy has been proposed
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A probabilistic analysis of selected notions of iterated conditioning under coherence Int. J. Approx. Reason. (IF 3.9) Pub Date : 2023-11-23 Lydia Castronovo, Giuseppe Sanfilippo
It is well known that basic conditionals satisfy some desirable basic logical and probabilistic properties, such as the compound probability theorem. However checking the validity of these becomes trickier when we switch to compound and iterated conditionals. Herein we consider de Finetti's notion of conditional both in terms of a three-valued object and as a conditional random quantity in the betting
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A direct approach to representing algebraic domains by formal contexts Int. J. Approx. Reason. (IF 3.9) Pub Date : 2023-11-17 Xiangnan Zhou, Longchun Wang, Qingguo Li
This paper is to establish closer links between domain theory and Formal Concept Analysis (FCA). We propose the notion of an optimised concept for a formal context, which has some properties similar to an intent. With the tool of optimised concepts, we show that the class of formal contexts has directly corresponded with algebraic domains. Meanwhile, two subclasses of formal contexts are identified
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Data complexity: An FCA-based approach Int. J. Approx. Reason. (IF 3.9) Pub Date : 2023-11-15 Alexey Buzmakov, Egor Dudyrev, Sergei O. Kuznetsov, Tatiana Makhalova, Amedeo Napoli
In this paper we propose different indices for measuring the complexity of a dataset in terms of Formal Concept Analysis (FCA). We extend the lines of the research about the “closure structure” and the “closure index” based on minimum generators of intents (aka closed itemsets). We would try to capture statistical properties of a dataset, not just extremal characteristics, such as the size of a passkey
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An efficient method of renewing object-induced three-way concept lattices involving decreasing attribute-granularity levels Int. J. Approx. Reason. (IF 3.9) Pub Date : 2023-11-13 Junping Xie, Jing Yang, Jinhai Li, Debby D. Wang
In three-way concept analysis, changing (decreasing or increasing) attribute-granularity levels is needed to seek desirable information. Reconstructing three-way concept lattices often requires huge computation and long elapsed time when attribute-granularity levels are changed. To avoid this problem, a good strategy is indirectly renewing three-way concept lattices. Our paper studies how to renew
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Changing behaviour under unfairness: An evolutionary model of the Ultimatum Game Int. J. Approx. Reason. (IF 3.9) Pub Date : 2023-11-08 Gianni Arioli, Roberto Lucchetti, Giovanni Valente
Experimental results on the Ultimatum Game indicate that receivers may reject non-zero offers, even though that seems irrational. The explanation is that, when players are treated unfairly, they can act against strict rationality. This paper discusses an evolutionary model of the Ultimatum Game describing how populations of players change their behaviour in time. We prove an analytical result that