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The selection of optimal scale has always been the essential problem of multi-scale system. However, most of the current studies only consider the consistency of the system, and ignore the cost information. Therefore, based on the ranking methods of single-valued neutrosophic number, this paper constructs a multi-scale dominant single-valued neutrosophic system. Furthermore, the test cost is defined according to the relative distance preference degree, and the risk cost of Bayesian theory introduced by decision-theoretic rough set is used as the decision cost of accepting, delaying and rejecting decisions. Therefore, we establish a multi-scale dominant single-valued neutrosophic decision-theoretic rough set based on test and decision cost. In addition, we also propose a scale updating algorithm to find out all consistent scales. Afterwards, we further raise an optimal scale selection algorithm based on the minimum total cost criterion. Finally, the algorithm is verified and analyzed by UCI data sets. The algorithm and model proposed in this paper further expand the application of single-valued neutrosophic rough set in multi-scale system, and provide a reference for subsequent research in this field. [ABSTRACT FROM AUTHOR]

We discuss the three-way rough set based approach for approximation of decision granules in Intelligent Systems (IS's). The novelty of the approach is in presenting a new concept of approximation space which is based on advanced reasoning tools. Many generalisations of the rough set approaches developed over the years are mainly concentrated around reasoning concerning (partial) inclusion of sets. However, such approximation spaces are not satisfactory to deal with important aspects of approximate reasoning by IS's aiming to construct of the high quality approximations of compound decision granules. We demonstrate a number of examples supporting this claim. In particular, in solving the considered in the paper problems are involved complex algorithmic optimization processes directed by reasoning tools supporting searching for (semi-)optimal approximations of decision granules in huge spaces. This paper is a step toward developing tools for derivation of granules supporting IS's in perceiving situations to a degree satisfactory for making the right decisions. [ABSTRACT FROM AUTHOR]

This paper addresses the preservation of numerous essential properties of a residuated lattice structure in extended algebras for partial fuzzy set theory and partial fuzzy logics. The preservation includes the residuated lattice axioms, the identities narrowing the classes of the residuated lattices, and some well-known additional properties. In this paper, we consider nine algebras for partial fuzzy logics which incorporate handling undefined values in a bit different way. In particular, we consider the Bochvar, the Bochvar external, the Sobociński, the Kleene, the McCarthy, the Nelson, and the Łukasiewicz algebras, and two recently developed ones, namely the Lower estimation and the Dragonfly algebras. We summarize the obtained results in a comprehensible form which allows readers to easily check the information for the preserved and non-preserved properties in a certain partial algebraic structure. The resulting shape of the contribution is a sort of "atlas book" that aims at providing researchers with a comfortable and comprehensible form of an overview of the (non)preservation of fundamental properties of residuated structures. [ABSTRACT FROM AUTHOR]

This paper investigates rules of proof for maximal entropy inference. It provides the first study of rules of proof for maximal entropy inference on infinite predicate languages. The main result of this paper is the construction of a set of rules, in which all rules are sound for maximal entropy inference on finite domains but are not sound for Williamson's Maximal Entropy Approach on infinite predicate languages. This elucidates differences between explications of the Maximum Entropy Principle on finite domains and on infinite predicate languages. [ABSTRACT FROM AUTHOR]

As a kind of emerging binary continuous aggregation operator that has been successfully applied in many practical application problems, overlap functions on the unit closed interval have been considered by scholars on different truth values sets lately. At the same time, studying aggregation operators on finite chains, especially for commonly used binary aggregation operators, is a meaningful and hot topic in the research field of aggregation operators. In this paper, we pay attention to overlap functions on finite chains, which are called discrete overlap functions. Specifically, first, we introduce the notions of discrete overlap functions on the finite chain L with n + 2 elements and its arbitrary subchains along with an extended form of them. Second, we study some basic properties of discrete overlap functions on L , especially for the idempotent property, Archimedean property and cancellation law. In particular, we obtain some new properties which are different from those of the overlap functions on other truth values sets, for instance, every discrete overlap function on L takes the greatest element on L as the neutral element. Third, we discuss the construction methods of discrete overlap functions on L. Finally, it is worth mentioning that the results obtained in this paper provide a theoretical basis and more possibilities for the potential applications of overlap functions in other fields besides their known applications, especially for the situation of that the reasoning of experts are described by linguistic terms or labels, such as in expert systems, fuzzy control and etc. [ABSTRACT FROM AUTHOR]

The aim of this paper is to extend closure systems from being crisp sets with certain fuzzy properties to proper fuzzy sets. The presentation of the paper shows a thorough discussion on the different alternatives that could be taken to define the desired fuzzy closure systems. These plausible alternatives are discarded if they are proven impossible to be in a bijective correspondence with closure operators. Finally, a definition of fuzzy closure system is established and a one-to-one relation with closure operators is proved. [ABSTRACT FROM AUTHOR]

Multidimensional fuzzy sets (MFS) is a new extension of fuzzy sets on which the membership values of an element in the discourse universe are increasingly ordered vectors on the set of real numbers in the interval [ 0 , 1 ]. This paper aims to investigate fuzzy negations and, mainly, fuzzy implications on the set of increasingly ordered vectors on [ 0 , 1 ] , i.e. on L ∞ ([ 0 , 1 ]) , MFN and MFI in short, with respect to some partial order. In this paper we study partial orders, giving special attention to admissible orders on L ∞ ([ 0 , 1 ]). In addition, some properties and methods to construct such operators from fuzzy negations and fuzzy implications, respectively, are provided and we demonstrate that the action of the group of automorphisms on fuzzy implications on L ∞ ([ 0 , 1 ]) preserves several original properties of the implication. Finally, through a specific type of representable MFI, we are able to generate a class of MFN called natural m-negations. [ABSTRACT FROM AUTHOR]

Let A be a pairwise comparison matrix obtained from a consistent one by perturbing three entries above the main diagonal, x , y , z , and the corresponding reciprocal entries, in a way that there is a submatrix of size 2 containing the three perturbed entries and not containing a diagonal entry. In this paper we describe the relations among x , y , z with which A always has its principal right eigenvector efficient. Previously, and only for a few cases of this problem, R. Fernandes and S. Furtado (2022) proved the efficiency of the principal right eigenvector of A. In this paper, we continue to use the strong connectivity of a certain digraph associated with A and its principal right eigenvector to characterize the vector efficiency. For completeness, we show that the existence of a sink in this digraph is equivalent to the inefficiency of the principal right eigenvector of A. [ABSTRACT FROM AUTHOR]

This paper proposes a model for imprecise probability information based on bounds on probability ratios, instead of bounds on events. This model is studied in the language of coherent sets of desirable gambles, which provides an elegant mathematical formulation and a more expressive power. The paper provides methods to check avoiding sure loss and coherence, and to compute the natural extension. The relationships with other formalisms such as imprecise multiplicative preferences, the constant odd ratio model, or comparative probability are analyzed. [ABSTRACT FROM AUTHOR]

Multidimensional fuzzy sets (MFS) is a new extension of fuzzy sets on which the membership values of an element in the universe of discourse are increasingly ordered vectors on the set of real numbers in the interval [ 0 , 1 ]. This paper aims to investigate fuzzy negations on the set of increasingly ordered vectors on [ 0 , 1 ] , i.e. on L ∞ ([ 0 , 1 ]) , MFN in short, with respect to some partial order. In this paper we study partial orders, giving special attention to admissible orders on L n ([ 0 , 1 ]) and L ∞ ([ 0 , 1 ]). In addition, we study the possibility of existence of strong multidimensional fuzzy negations and some properties and methods to construct such operators. In particular, we define the ordinal sums of n-dimensional negations and ordinal sums of multidimensional fuzzy negations on a multidimensional product order. A multi-attribute group decision making algorithm is presented. [ABSTRACT FROM AUTHOR]

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 degree in the plane, to estimate the extent of the explored region. In addition, we extend the approach to uncertain coverage measure values using interval analysis. This last contribution allows for a guaranteed characterization of the explored area, essential considering the often critical character of area-covering missions. Finally, this paper also proposes a novel algorithm for computing the topological degree in the 2-dimensional plane, for all the points inside an area of interest, which differs from existing solutions that compute the topological degree for single points. The applicability of the method is evaluated through a real-world experiment. [ABSTRACT FROM AUTHOR]

Data quality is an important consideration in many engineering applications and projects. Data collection procedures do not always involve careful utilization of the most precise instruments and strictest protocols. As a consequence, data are invariably affected by imprecision and sometimes sharply varying levels of quality of the data. Different mathematical representations of imprecision have been suggested, including a classical approach to censored data which is considered optimal when the proposed error model is correct, and a weaker approach called interval statistics based on partial identification that makes fewer assumptions. Maximizing the quality of statistical results is often crucial to the success of many engineering projects, and a natural question that arises is whether data of differing qualities should be pooled together or we should include only precise measurements and disregard imprecise data. Some worry that combining precise and imprecise measurements can depreciate the overall quality of the pooled data. Some fear that excluding data of lesser precision can increase their overall uncertainty about results because lower sample size implies more sampling uncertainty. This paper explores these concerns and describes simulation results that show when it is advisable to combine fairly precise data with rather imprecise data by comparing analyses using different mathematical representations of imprecision. Pooling data sets is preferred when the low-quality data set does not exceed a certain level of uncertainty. However, so long as the data are random, it may be legitimate to reject the low-quality data if its reduction of sampling uncertainty does not counterbalance the effect of its imprecision on the overall uncertainty. [ABSTRACT FROM AUTHOR]

AI systems often need to deal with inconsistencies. One way of getting information about inconsistencies is by measuring the amount of information in the knowledgebase. In the past 20 years numerous inconsistency measures have been proposed. Many of these measures are syntactic measures, that is, they are based in some way on the minimal inconsistent subsets of the knowledgebase. Very little attention has been given to semantic inconsistency measures, that is, ones that are based on the models of the knowledgebase where the notion of a model is generalized to allow an atom to be assigned a truth value that denotes contradiction. In fact, only one nontrivial semantic inconsistency measure, the contension measure, has been in wide use. The purpose of this paper is to define a class of semantic inconsistency measures based on 3-valued logics. First, we show which 3-valued logics are useful for this purpose. Then we show that the class of semantic inconsistency measures can be developed using a graphical framework similar to the way that syntactic inconsistency measures have been studied. We give several examples of semantic inconsistency measures and show how they apply to three useful 3-valued logics. We also investigate the properties of these inconsistency measures and show their computation for several knowledgebases. [ABSTRACT FROM AUTHOR]

We present a unified framework involved to the extensions of a t-seminorm, a t-semiconorm and a semi-uninorm in the lattice-valued setting through the use of the particular uplift and downlift of a binary operation linked by a behaviour operation. We also investigate the preservations of the left- and right-conjunctive of semi-uninorms as well as the left- and right-disjunctive of semi-uninorms under the extension approach studied in this paper. Moreover, for the extensions of t-seminorms, t-semiconorms and semi-uninorms, we provide their corresponding characterizations that depend on behaviour operations in terms of connected points. Finally, we summarize the dual results with respect to a unified way to investigations of t-seminorms, t-semiconorms and semi-uninorms. [ABSTRACT FROM AUTHOR]

Imbalanced classification refers to problems in which there are significantly more instances available for some classes than for others. Such scenarios require special attention because traditional classifiers tend to be biased towards the majority class which has a large number of examples. Different strategies, such as re-sampling, have been suggested to improve imbalanced learning. Ensemble methods have also been proven to yield promising results in the presence of class-imbalance. However, most of them only deal with binary imbalanced datasets. In this paper, we propose a re-sampling approach based on belief function theory and ensemble learning for dealing with class imbalance in the multi-class setting. This technique assigns soft evidential labels to each instance. This evidential modeling provides more information about each object's region, which improves the selection of objects in both undersampling and oversampling. Our approach firstly selects ambiguous majority instances for undersampling, then oversamples minority objects through the generation of synthetic examples in borderline regions to better improve minority class borders. Finally, to improve the induced results, the proposed re-sampling approach is incorporated into an evidential classifier-independent fusion-based ensemble. The comparative study against well-known ensemble methods reveals that our method is efficient according to the G-Mean and F1-score measures, independently from the chosen classifier. [ABSTRACT FROM AUTHOR]

Fuzzy and intuitionistic fuzzy β covering has attracted the interest of many researchers recently. However, some of the factors namely 1. the lack of inclusion relationship between lower and upper approximation, 2. Inability to fit real valued dataset i.e. misclassification, hinder its application in decision making. Also, majority of these approaches are affected by noise. All these factors have created the need for a robust model. This paper proposes a novel intutitionistic fuzzy β covering model which is robust, combining intuitionistic fuzzy set, β covering and multigranulation rough sets. A new intuitionistic fuzzy β covering based multigranulation model is proposed which satisfies inclusion relationship between two approximations. This robust model is used to formulate dependency degree, which is evaluated at various granularity levels and is thereby employed for feature subset selection. Series of experiments are conducted on real valued datasets to illustrate the robustness and effectiveness of the underlying model. Furthermore, a comparative analysis with state of art approaches followed by statistical test lays down the superiority of the proposed model. [ABSTRACT FROM AUTHOR]

Three-way decision (3WD) is a widely used and studied mathematical theory that generalizes the thinking norm of tri-level in cognitive learning, problem solving, and information processing. By utilizing the negative information contained in data, three-way concept lattice (3WCL) developed 3WD in Formal Concept Analysis and has been applied in various applications such as conflict analysis, role based access control, knowledge discovery, concept learning, and medical diagnose. However, the connections between 3WCL and classical concept lattices have not received its deserved attention. To this end, first, this paper proved that 3WCL is exactly the minimal closure system containing both concept lattice and complementary concept lattice, and classified three-way concepts into four categories. Second, this paper proved the structure theorem of 3WCL that characterizes mathematically the relationships between concept lattice, complementary concept lattice and 3WCL as two isomorphisms. Third, this paper presented several applications of the structure theorem to reveal its essentiality in discussing the properties of 3WCL. Finally, some problems that are not involved in the structure theorem are also discussed. [ABSTRACT FROM AUTHOR]

Elementary formulas for propagating information about means and variances through mathematical expressions have long been used by analysts. Yet the precise implications of such information are rarely articulated. This paper explores distribution-free techniques for risk analysis that do not require simulation, sampling or approximation of any kind. We describe best-possible bounds on risks that can be inferred given only information about the range, mean and variance of a random variable. These bounds generalise the classical Chebyshev inequality in an obvious way. We also collect in convenient tables several formulas for propagating range and moment information through calculations involving 7 binary convolutions (addition, subtraction, multiplication, division, powers, minimum, and maximum) and 9 unary transformations (scalar multiplication, scalar translation, exponentiation, natural and common logarithms, reciprocal, square, square root and absolute value) commonly encountered in risk expressions. These formulas are rigorous rather than approximate, and in most cases are either exact or mathematically best-possible. The formulas can be used effectively even when only interval estimates of the moments are available. Although most discussions of moment propagation assume stochastic independence among variables, this paper shows the assumption to be unnecessary and generalises formulas for the case when no assumptions are made about dependence, and when correlations are partially known. Along with partial means and variances, we show how interval covariances may be propagated and tracked through expressions. [ABSTRACT FROM AUTHOR]

In rough set theory, upper and lower approximation operators are two crucial concepts. The study of these two approximation operators in the framework of lattice theory is an important generalization from the mathematical point of view. On the other hand, overlap and grouping functions, as two types of not necessarily associative binary aggregation functions different from the common binary aggregation functions triangular norms and triangular conorms, have not only rich theoretical results but also a wide range of practical applications. Therefore, based on overlap and grouping functions over complete lattices, this paper is devoted to proposing (O , G) -fuzzy rough sets as a further generalization of the notion of rough sets. Firstly, we define a pair of O -upper and G -lower L -fuzzy rough approximation operators and investigate basic properties of them. Then, the characterizations of (O , G) -fuzzy rough approximation operators are discussed by using different kinds of L -fuzzy relations. Meanwhile, we investigate the topological properties of (O , G) -fuzzy rough sets. Furthermore, we show a brief comparison of the (O , G) -fuzzy rough sets with other common rough set models. At the end of this paper, we further propose multigranulation (O , G) -fuzzy rough sets over complete lattices from the viewpoint of multigranulation structure. [ABSTRACT FROM AUTHOR]

Granular computing and three-way decision are two very important methods in the field of knowledge discovery and data mining. In this paper, based on the idea of three-way decision, all attributes in the information table first are divided into three disjoint parts named indispensable attributes, rejected attributes and neutral attributes, respectively. According to the three parts of attributes, many basic and important information granules and granular structures can be induced from the information table. Then a novel granular computing model is proposed by the description operator. On the one hand, many mathematical properties related to the model proposed in this paper are systematically discussed. On the other hand, we make a preliminary and meaningful attempt to deal with network security by using this model. In addition, in order to apply the model more conveniently, two algorithms for computing description set, description degree, attribute reduction and reduction degree are developed. Finally, through numerical experiments, the validity of the algorithms and the related factors that affect the effectiveness of the algorithms are discussed in detail. [ABSTRACT FROM AUTHOR]

Three-way decision (3WD) and rough set are two influential theories of study knowledge discovery and uncertain artificial intelligence. A central notion of 3WD is a tri-level thinking paradigm consisting of trisecting, acting, and outcome (i.e., TAO model). As is well known, movement-based on three-way decision (M-3WD) and change-based TAO model, mainly started from the perspective of effectiveness measure, are two outcome evolution studies about the three-way decision, which could lead to some limitations in application. This paper builds a change-based three-way decision (C-3WD) based on confidence level, and an application to rough set is also discussed. Furthermore, the (α , β) -approximate probability regions of rough set are re-decided by the change model, and a medical decision example is introduced to explain how to make C-3WD in the classification of rough set. By comparing the effectiveness of the traditional three-way decision method with ours, it is again verified from the two aspects of cost and earns and concludes that the model in this paper is more suitable for the decision process that includes trisecting and acting. Some experiments on various datasets to demonstrate the effectiveness of our methods. [ABSTRACT FROM AUTHOR]

Recently, many learning-based methods have explored logic learning task in the assumption that the training set and testing set are from the consistent distribution, achieving good performance. But, in most cases, this assumption does not hold. In this paper, we explore this topic on the open-set logic reasoning task where the digit length and the sequence length of the training set and testing set are from inconsistent distributions. To address this issue, inspired by multigranulation studies in granular computing, we propose a granulation logic reasoning machine, namely GLRM. In this method, this open-set task is granulated into a series of sub-tasks from two dimensions: the digit length and the sequence length, and then these sub-tasks are conquered one by one. Finally, the results of the sub-tasks are organized into the final result. The effectiveness of GLRM is demonstrated by experiments on the open-set Fashion-Logic data set and the open-set Fashion-Logic task proposed in this paper. This study provides a novel view for solving open-set logic reasoning tasks and promotes the research of data-driven logic learning. [ABSTRACT FROM AUTHOR]

In this paper, we study structures such as distributive lattices, distributive semilattices, and median graphs from an algorithmic point of view. Such structures are very useful in classification and phylogeny for representing lineage relationships for example. A distributive lattice can be considered as a median graph while a distributive ∨-semilattice can be considered as a median graph provided that some conditions holding on triple of elements are satisfied. Starting from a lattice structure with different representations, we study the problem of building a median graph from such structures. We make precise and propose algorithms for checking how a lattice can be distributive and can be a median graph. Then, we adapt the problem to semilattices as a lattice where the bottom element is removed is a ∨-semilattice. We also state the problem in terms of Formal Concept Analysis and the representation of a lattice as a formal context, i.e., a binary table. Moreover, we also propose as input a system of implications such as the Duquenne-Guigues basis of a lattice, and we study how to compute such a basis for a distributive semilattice. In the paper, we provide algorithms and examples which illustrate the difficulties related to these different classification tasks. In particular, the minimality of the output lattices is a condition which is hard to ensure and which cannot be always achieved. [ABSTRACT FROM AUTHOR]

The combination of fuzzy set theory and rough set theory has been discussed in a lot of research papers over the years. In this paper, we examine one such combination, namely the notion of rough L -fuzzy sets. We provide a representation theorem that determines when a pair of L -fuzzy sets is a rough L -fuzzy set, and we establish a connection between the lattice of rough fuzzy sets and the lattice of rough relations. Furthermore, we investigate the properties of the lattice of rough L -fuzzy sets and characterize the case when a three-valued Łukasiewicz-algebra can be defined on it. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel approach for sentiment analysis that uses Formal Concept Analysis (FCA) to create dictionaries for classification. Unlike other methods that rely on pre-defined lexicons, our approach allows for the creation of customised dictionaries that are tailored to the specific data and tasks. By using a dataset of tweets categorised into positive and negative polarity, we show that our approach achieves a better performance than other standard dictionaries. [ABSTRACT FROM AUTHOR]

Explaining black-box classification models is a hot topic in AI, with the overall goal of improving trust in decisions made by such models. Several works have been done and diverse functions have been proposed. However, their formal properties and links have not been sufficiently studied. This paper presents four contributions: The first consists of investigating global explanations of black-box classifiers. We provide a formal and unifying framework in which such explanations are defined from the whole feature space. The framework is based on two concepts, which are seen as two types of global explanations: arguments in favour of (or pro) predictions and arguments against (or con) predictions. The second contribution consists of defining various types of local explanations (abductive explanations, counterfactuals, contrastive explanations) from the whole feature space, investigating their properties, links and differences, and showing how they relate to global explanations. The third contribution consists of analysing and defining explanation functions that generate (global, local) abductive explanations from incomplete information (i.e., from a subset of the feature space). We start by proposing two desirable properties that an explainer would satisfy, namely success and coherence. The former ensures the existence of explanations while the latter ensures their correctness. We show that in the incomplete case, the two properties cannot be satisfied together. The fourth contribution consists of proposing two functions that generate abductive explanations and which satisfy coherence at the expense of success. [ABSTRACT FROM AUTHOR]

The reasoning with qualitative uncertainty measures involves comparative statements about events in terms of their likeliness without necessarily assigning an exact numerical value to these events. The paper is divided into two parts. In the first part, we formalise reasoning with the qualitative counterparts of capacities, belief functions, and probabilities, within the framework of two-layered logics. Namely, we provide two-layered logics built over the classical propositional logic using a unary belief modality B that connects the inner layer to the outer one where the reasoning is formalised by means of Gödel logic. We design their Hilbert-style axiomatisations and prove their completeness. In the second part, we discuss the paraconsistent generalisations of the logics for qualitative uncertainty that take into account the case of the available information being contradictory or inconclusive. [ABSTRACT FROM AUTHOR]

With the rapid increase of large-scale, real-world datasets, it becomes critical to address the problem of partially labeled heterogeneous feature selection (i.e., some samples, which own numerical and categorical features, have no labels). Existing solutions typically adopt linear correlations between features. In this paper, three different monotonic uncertainty measures are defined on equivalence classes and neighborhood classes to study the partially labeled heterogeneous feature selection by exploring the nonlinear correlations. First, consistent entropy and monotonic neighborhood entropy, based on classical rough set theory and neighborhood rough set theory, are proposed to construct a uniform measure for feature selection in heterogeneous datasets. Furthermore, a maximal neighborhood entropy strategy is developed by considering the inconsistency of neighborhood classes described by the features and partial labels. Finally, two feature selection algorithms are presented by three novel monotonic uncertainty measures. The comparative experiments demonstrate the effectiveness and superiority of the newly proposed feature selection measures. [ABSTRACT FROM AUTHOR]

Existing graph neural networks (GNNs) associate nodes in networks with specific samples in datasets, and thus ignore the conceptual information hidden in object-attribute clusters in datasets. Besides, processing data without structural information is a problem for GNNs since structural information is the input of networks. In this paper, we aim to integrate conceptual information into the message passing of GNNs. To this end, concept lattice theory is fused into existing GNNs. A concept lattice is a powerful tool for describing generalization and specialization relations between formal concepts. And formal concepts, basic elements of concept lattices, effectively explain dependencies between features and samples. On this basis, we propose a new GNN framework induced by a concept lattice to overcome the intrinsic limitations of GNNs. And the novel GNN framework not only joins conceptual information into the message passing but also enables a GNN to process data with or without structural information. Furthermore, the proposed framework is validated under transductive and inductive learning conditions, respectively. The experimental results show that GNNs induced by concept lattices can handle the information hidden in datasets effectively and improve classification accuracies on most benchmark datasets over previous methods. [ABSTRACT FROM AUTHOR]

In many practical applications of machine learning, there are a large number of partially labeled categorical data due to the high cost of labeling data. The semi-supervised learning algorithm is needed to deal with such data. This paper studies the label prediction of partially labeled categorical data and considers semi-supervised attribute reduction in a partially labeled categorical decision information system (p-CDIS) with predicted labels. The labels of unlabeled data are first predicted by means of the conditional probability. Then, uncertainty measurement for a p-CDIS with predicted labels is studied, and the dependence and conditional information entropy (CIE) are defined. Next, based on the dependence and CIE, two attribute reduction algorithms are designed. In addition, the effect of label deletion rate (LDR) on the dependence, CIE and reduction results are also studied. Finally, the results of experiments and statistical tests on 16 categorical UCI datasets show that the designed algorithms are statistically better than some state-of-the-art algorithms in classification accuracy. [ABSTRACT FROM AUTHOR]

Conflict occurs in all aspects of life, and people tend to consider a variety of factors in the face of it and hesitate to make decisions among multiple choices. This paper performs a three-way conflict analysis in the dual hesitant fuzzy case. Firstly, we propose the concept of dual hesitant fuzzy situation tables (DHFSTs). Subsequently, we trisect the pairs of agents and objectively calculate issue weights by CRITIC method rather than subjective assignments. According to Bayesian minimum risk theory, we derive trisection of agents, in which the state set is calculated objectively. Then, we analyze three issue sets through the conflicting characters of issues, which provides a new way to consider the trisection of issues. In addition, we put forward the definition of maximal coalitions in DHFSTs and give an effective calculation method. Finally, we illustrate the feasibility of the proposed model by analyzing the development plan in Gansu Province, and conduct a brief comparative analysis. [ABSTRACT FROM AUTHOR]

In this short paper, we introduce and discuss the extended Choquet-Sugeno-like operator. It generalizes most of modifications of the Choquet integral on a finite set known in the literature providing a partially positive answer to the question posed by H. Bustince et al. in 2021. It also includes unknown Choquet-like and Sugeno-like operators. The standard optimization problem in cluster analysis is formulated using multivariable extension of the new operator. [ABSTRACT FROM AUTHOR]

In this paper, knowledge acquisition in the sense of deriving IF-THEN rules in multi-scale information systems with multi-scale decision attributes is investigated. Specifically, the concept of a generalized multi-scale information system with a multi-scale decision attribute, called generalized multi-scale decision information table (GMDIT for short), is first introduced. Such a system is a multi-scale decision table in which each condition or decision attribute at each object can take different values under different scales. The notion of scale selections for a GMDIT, which is mainly used to determine individual decision tables, is then defined. Information granules and their properties with different scale selections in GMDITs are also described. Optimal scale selections which are used to determine proper decision tables for final decision in inconsistent GMDITs are further formulated. Local optimal scale selections to obtain more concise decision rules for different objects are presented. Finally, attribute reducts based on optimal scale selections are derived and decision rules hidden in inconsistent GMDITs are unraveled. [ABSTRACT FROM AUTHOR]

Trackers based on Siamese network have achieved positive performance in recent days. However, most of the existing siamese single object trackers only consider the spatial information in the template which was given in the first frame of the video but do not extract the affluent temporal information. In this paper, we propose a novel tracking framework based on a spatial-temporal network. Specifically, we introduce three-way decision theory into object tracking to avoid interference from complex situations such as occlusions, fast motions, and non-rigid deformation. Furthermore, our proposed method can generate more precise tracking results due to the discriminative correlation filters (DCF). Extensive tests and comparisons with numerous competitive trackers on demanding large-scale benchmarks, including OTB-2015, GOT-10k, LaSOT and VOT2018, TrackingNet, demonstrate that our tracker outperforms many state-of-the-art real-time techniques while operating at 22 frames per second. [ABSTRACT FROM AUTHOR]

Density Peaks Clustering (DPC) is a classic density-based clustering algorithm that has been successfully applied in various areas. However, it assigns samples based on their nearest neighbors with higher density which may lead to an error propagation problem. Besides, it can not detect fringe and overlapping samples. To handle these defects, we improve the density measurement of DPC to make it more adaptive to different shapes and varying densities. Furthermore, we extend DPC to three-way clustering which means a sample in the positive region certainly belongs to the cluster, a sample in the boundary region belongs to the cluster partially and a sample in the negative region certainly does not belong to the cluster. In this paper, we propose a three-way clustering method called TW-RDPC. It mainly consists of three steps: (1) Identify cluster centers and assign other samples based on relative Cauchy kernel density to get initial clusters. (2) Detect potential boundary samples through boundary detection graph. (3) Determine whether potential boundary samples belong to multiple clusters based on the subordinate relationship to their k nearest neighbors. In order to validate TW-RDPC, we compare it to 7 algorithms on 10 synthetic datasets and 8 real-world datasets. Experimental results indicate that TW-RDPC is competitive with the compared 7 algorithms. [ABSTRACT FROM AUTHOR]

Shadowed sets, as a three-way approximation of fuzzy sets, employ two thresholds (α , β) to maintain the essence of fuzzy sets with reduced computing complexity and simpler semantic interpretation by allowing quantification of numeric membership grades into three parts: core, total exclusion, and complete uncertainty. An essential issue in inducing shadowed sets is determining the thresholds (α , β) and maintaining the consistency in fuzziness. However, it is found that the existing interval shadowed sets (ISS) have a significant fuzziness loss. In addition, the algorithm used to obtain the threshold pairs in ISS need to be further optimized. To this end, a novel method to induce interval shadowed sets based on a new objective function is proposed in this paper. Firstly, the shortcomings of the objective function and fuzziness loss of ISS are analyzed. Then, a new objective function is given, and interval shadowed sets with less fuzziness loss are induced based on this objective function. Afterwards, a fast algorithm is developed to obtain interval shadowed sets quickly. Finally, the rationality and validity of the proposed method are verified by experimental results. [ABSTRACT FROM AUTHOR]

Little attention has been devoted to the long memory among the different data features considered for clustering time series. Following previous literature, we measure the long memory of a time series through the estimated Hurst exponent. However, we exploit the fact that a constant value for the Hurst exponent h is unrealistic in many practical examples. In this paper, assuming that the time series follows a multifractional Brownian motion, we estimate a time-varying Hurst exponent used as the input for a fuzzy clustering procedure. Motivated by the relevance of long memory in finance, the usefulness of the proposed clustering procedure is shown with an application to stock prices. [ABSTRACT FROM AUTHOR]

In many real applications, the data are always collected from different types and they are subjected to obtain partial labeling information of objects. Such data are referred to as partially labeled mixed-type data. There is currently few work on feature selection approaches for these data. Motivated by this issue, this paper aims at selecting the informative feature subset from partially labeled mixed-type data. At first, to improve the classification performance, an improved label propagation algorithm based on K-nearest neighbor is proposed, which marks the decision labels of unlabeled objects by making use of the information between unlabeled objects and labeled objects. On this basis, a feature multi-criteria measure based on the dependency, information entropy and information granulation is proposed for selecting candidate features. Finally, the corresponding semi-supervised feature selection algorithm is developed to select the feature subset for the partially labeled mixed-type data. Experimental results on UCI data sets demonstrate the effectiveness of the proposed feature selection algorithm and the superiority in terms of the classification accuracy compared with other algorithms. [ABSTRACT FROM AUTHOR]

Path planning is a popular topic in research on mobile robots. In this paper, we apply the concept lattice to the path planning problem for the first time in the literature to propose a static path planning algorithm. The given grid map is first transformed into the formal context of the grid, and locational relations between rectangular regions are mapped into partial-order relations in the graph of rectangular regions based on a lattice of region concepts. Following this, the path planning problem on the original grid map is transformed into a path searching problem in the graph of rectangular regions. The graph derived from the sublattice of region concepts is used to avoid the high time complexity of applying the complete concept lattice. Finally, a novel path planning algorithm that can generate a path consisting of rectangular regions is constructed. This path can also be converted into the path consisting of inflection points. The results of simulations verified the effectiveness of the proposed method. It can generate a path with significantly fewer inflection points than the A* algorithm for a four-direction (left, right, front, back) mobile robot. [ABSTRACT FROM AUTHOR]

We first make a great improvement on the early definition of a reducible element of a covering approximation space and formulate the definition of a reduction of the covering. Then the crucial links between the two concepts are established and a method for obtaining an optimal reduction of the covering is proposed. More importantly, we introduce the representation matrix for a finite covering approximation space and define a new type of operation on matrices. To obtain a reduction of the covering, we need only to deal with the representation matrix, so that the reduction of the covering can be executed on computers. The concept of the product of two covering approximation spaces is defined in this paper and we explore the connections between the reductions of the covering of the product space and those of the coverings of the factor spaces. Furthermore, we deal with the connections from the standpoint of algebra. A new type of matrix product is defined and the property of the product is explored. Drawing on the product, we can research the reduction of the product space. [ABSTRACT FROM AUTHOR]

In decision support systems the motivation and justification of the system's diagnosis or classification is crucial for the acceptance of the system by the human user. In Bayesian networks a diagnosis or classification is typically formalized as the computation of the most probable joint value assignment to the hypothesis variables, given the observed values of the evidence variables (generally known as the MAP problem). While solving the MAP problem gives the most probable explanation of the evidence, the computation is a black box as far as the human user is concerned and it does not give additional insights that allow the user to appreciate and accept the decision. For example, a user might want to know to whether an unobserved variable could potentially (upon observation) impact the explanation, or whether it is irrelevant in this aspect. In this paper we introduce a new concept, MAP-independence, which tries to capture this notion of relevance, and explore its role towards a potential justification of an inference to the best explanation. We formalize several computational problems based on this concept and assess their computational complexity. [ABSTRACT FROM AUTHOR]

Yager's f -generated implication is one important class of fuzzy implication, which is based on additive generators of continuous Archimedean t-norms. Considering the related interval extension, this paper presents an analysis of interval fuzzy implications derived from interval additive generators of interval t-norms, called F -generated interval fuzzy implications. The relationship between Yager's f -generated implications and F -generated interval fuzzy implications is discussed. Then We study the basic properties of F -generated interval fuzzy implications and discuss some general forms of classical logic tautologies (i.e. law of importation, contrapositive symmetry, and distributivity over interval t-norms or interval t-conorms). Meanwhile, the relationships between F -generated interval fuzzy implications and several families of interval fuzzy implications are obtained. [ABSTRACT FROM AUTHOR]

The notion of context awareness and the challenge of reasoning with partially reliable sources are two important aspects within Information Fusion. Context is the information relevant to, but not directly affecting, the problem at hand and can be broadly categorised into either context-for or context-of , referring either to the information related to some situation or to the environment induced by some situation, respectively. In evidence theory, the Behaviour-Based Correction (BBC) model generalises reasoning with partially reliable sources as well as contextual belief correction. In this paper, we propose a model for contextual reasoning framed into evidence theory, which captures both the notions of context-for and context-of. We rephrase the BBC model to explicitly account for variation of metaknowledge regarding source behaviour, and subsequently include within it the variables defining the context-for the problem and the context-for the source. The benefit is two-fold: on the one hand, the explicit inclusion of context in the reasoning provides a better insight into the problem and on the other hand, it can improve the expressiveness of the model. This is illustrated on a case of maritime surveillance involving a missing vessel, where it is shown that this model is not only more expressive than the simple fusion of sources model but also more interpretable. [ABSTRACT FROM AUTHOR]

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 computing paradigm which can help to design IS's and DS's more close to the prototypes of real life decision making. In this regard, the paper brings to the fore different experiences faced during designing other medical IS's or DS's.As a starting step, the paper considers the experience of developing the OvuFriend platform and outlines some possible extension of it in the framework of the proposed architecture on the basis of Interactive Granular Computing (IGrC) model. Specifically, our attempt is to analyze a scheme, which is being used in the platform of OvuFriend for determining health risks and possibilities of a woman to conceive a child, from the perspective of IGrC. The target of the paper is two fold. Firstly, to show how the underlying AI algorithm of this scheme can be related with the notion of computing in the context of IGrC. Secondly, to identify possible extensions of the existing scheme so that it becomes more dynamic, interactive, and close to personalized medicine. [ABSTRACT FROM AUTHOR]

The concept of three-way decision, interpreted and described as thinking, problem solving, and information processing in "threes", has been widely studied and applied in machine learning and data engineering in recent years. In open-world environment, the connection and interaction of dynamic and uncertainty by multi-granularity learning gives more vitality to three-way decision. In this paper, we investigate and summarize the initial and development models of three-way decision. Then we revisit the historical line of sequential three-way decision from rough set to granular computing. Besides, we focus on exploring a unified framework of three-way multi-granularity learning with four crucial problems on mining uncertain region continually. Finally, we give some proposals on three-way decision associated with open-continual learning. [ABSTRACT FROM AUTHOR]

Comparing several normal variances with a control group is very important in many fields. In this paper, we propose a new inferential model-based test for the homogeneity of several variances against tree-ordered alternatives. Simulation studies demonstrate that our new solution provides a competitive alternative to existing methods. Furthermore, our IM test is the only one that works in scenarios where the sample sizes are unequal. A real numerical example is presented to illustrate the flexibility of the proposed method. [ABSTRACT FROM AUTHOR]

Pawlak conflict analysis focuses on three-valued ratings of a set of agents on a set of issues, in which the three values +, 0, and − indicate, respectively, that an agent is positive, neutral, and negative about an issue. According to their shared ratings, we can form different types of agent coalitions and, similarly, different types of issue bundles (i.e., families of issues to be considered together). The main objective of this paper is to introduce and investigate connections of agent coalitions and issue bundles from Wille formal concept analysis perspectives. By interpreting a three-valued rating table as four different formal contexts, we introduce four types of agent coalitions, namely, support, non-opposition, opposition, and non-support coalitions, the corresponding four types of issue bundles, and four lattices of coalition-bundle couplings. The lattices reveal structural information of agents and issues in a conflict situation. To demonstrate the usefulness of the proposed model, we analyze the problem of development planning of the Gansu Province of China. [ABSTRACT FROM AUTHOR]

Recently the useful redefinition of the intuitionistic and interval-valued intuitionistic fuzzy set theories (A − I F S , A − I V I F S) based on the Dempster-Shafer theory of evidence (DST) was developed. It was named the "Belief-Plausibility" (BP) approach as only the basic mathematical tools of the DST were used for its foundation. In this paper, a new approach to compare the real, interval and fuzzy-valued intuitionistic fuzzy and BP numbers is proposed. Among known approaches to compare intuitionistic fuzzy objects, most justified and used in applications are those based on the so-called score and accuracy functions. The observed multiplicity of these functions treatments and modifications indicates that the source of such a divergence is the impossibility to solve this problem exclusively in the framework of the A − I F S. Therefore, to develop the reliable methods for the considered types of comparison, a redefinition of this problem based on the BP approach is proposed. This redefinition allows us to develop new two and three criteria methods for comparison of real, interval and fuzzy-valued intuitionistic fuzzy and BP numbers, based on the local criteria with transparent interpretation in the framework of the BP approach. [ABSTRACT FROM AUTHOR]

The problem of optimal scale selection for multi-scale decision information systems is an important issue in the field of granular computing research, especially when data are dynamically updated. Determining the changes of the optimal scale for dynamic data is a goal that has drawn increasing attention from scholars in related fields. For the case of object updating, solving this problem requires finding which characteristic conditions should be satisfied by newly added objects when different cases of the optimal scale occur. However, existing studies only include the sufficient and necessary condition of the optimal scale becoming smaller for dynamically updating objects. Therefore, to complete the theory regarding how the optimal scale will be changed when objects are dynamically updated, it is still necessary to explore the sufficient and necessary conditions for the optimal scale being unchanged or becoming larger. In this paper, we use three-way decision theory to study this problem. Concretely speaking, the uncertain region of three-way decision is used to reveal the change of knowledge at different scales. That is, the obtained results, combined with existing work, provide a nice solution to the problem of finding the changing laws of the optimal scale for object updating in multi-scale decision information systems. [ABSTRACT FROM AUTHOR]