International Journal of Approximate Reasoning最新文献

{"title":"Desirable gambles based on pairwise comparisons","authors":"Serafín Moral","doi":"10.1016/j.ijar.2024.109180","DOIUrl":"https://doi.org/10.1016/j.ijar.2024.109180","url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"169 ","pages":"Article 109180"},"PeriodicalIF":3.9,"publicationDate":"2024-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0888613X24000677/pdfft?md5=1b16f3b4f516e5705b5d062c10b3a2be&pid=1-s2.0-S0888613X24000677-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140308615","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Quantified neural Markov logic networks","authors":"Peter Jung ,&nbsp;Giuseppe Marra ,&nbsp;Ondřej Kuželka","doi":"10.1016/j.ijar.2024.109172","DOIUrl":"10.1016/j.ijar.2024.109172","url":null,"abstract":"<div><p>Markov Logic Networks (MLNs) are discrete generative models in the exponential family. However, specifying these rules requires considerable expertise and can pose a significant challenge. To overcome this limitation, Neural MLNs (NMLNs) have been introduced, enabling the specification of potential functions as neural networks. Thanks to the compact representation of their neural potential functions, NMLNs have shown impressive performance in modeling complex domains like molecular data. Despite the superior performance of NMLNs, their theoretical expressiveness is still equivalent to that of MLNs without quantifiers. In this paper, we propose a new class of NMLN, called Quantified NMLN, that extends the expressivity of NMLNs to the quantified setting. Furthermore, we demonstrate how to leverage the neural nature of NMLNs to employ learnable aggregation functions as quantifiers, increasing expressivity even further. We demonstrate the competitiveness of Quantified NMLNs over original NMLNs and state-of-the-art diffusion models in molecule generation experiments.</p></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"171 ","pages":"Article 109172"},"PeriodicalIF":3.9,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140283143","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Multidimensional fuzzy sets: Negations and an algorithm for multi-attribute group decision making","authors":"Landerson Santiago ,&nbsp;Benjamin Bedregal","doi":"10.1016/j.ijar.2024.109171","DOIUrl":"https://doi.org/10.1016/j.ijar.2024.109171","url":null,"abstract":"<div><p>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 <span><math><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span>. This paper aims to investigate fuzzy negations on the set of increasingly ordered vectors on <span><math><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span>, i.e. on <span><math><msub><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msub><mo>(</mo><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo><mo>)</mo></math></span>, MFN in short, with respect to some partial order. In this paper we study partial orders, giving special attention to admissible orders on <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo><mo>)</mo></math></span> and <span><math><msub><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msub><mo>(</mo><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo><mo>)</mo></math></span>. 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.</p></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"169 ","pages":"Article 109171"},"PeriodicalIF":3.9,"publicationDate":"2024-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140180509","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Application of tropical optimization for solving multicriteria problems of pairwise comparisons using log-Chebyshev approximation","authors":"Nikolai Krivulin","doi":"10.1016/j.ijar.2024.109168","DOIUrl":"10.1016/j.ijar.2024.109168","url":null,"abstract":"<div><p>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 reciprocal matrix of unit rank) to minimize the approximation errors for all matrices simultaneously. We rearrange the approximation problem as a constrained multiobjective optimization problem of finding a vector that determines the approximating consistent matrix. The problem is then represented in the framework of tropical algebra, which deals with the theory and applications of idempotent semirings and provides a formal basis for fuzzy and interval arithmetic. We apply methods and results of tropical optimization to develop a new approach for handling the multiobjective optimization problem according to various principles of optimality. New complete solutions in the sense of the max-ordering, lexicographic ordering and lexicographic max-ordering optimality are obtained, which are given in a compact vector form ready for formal analysis and efficient computation. We present numerical examples of solving multicriteria problems of rating four alternatives from pairwise comparisons to illustrate the technique and compare it with others.</p></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"169 ","pages":"Article 109168"},"PeriodicalIF":3.9,"publicationDate":"2024-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140154085","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A probabilistic modal logic for context-aware trust based on evidence","authors":"Alessandro Aldini ,&nbsp;Gianluca Curzi ,&nbsp;Pierluigi Graziani ,&nbsp;Mirko Tagliaferri","doi":"10.1016/j.ijar.2024.109167","DOIUrl":"10.1016/j.ijar.2024.109167","url":null,"abstract":"<div><p>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 personally gathered or reported by other agents; this requires elements in the language that can track which agents are used as referrals and how much weight is placed on their opinions. Finally, trust is subjective in nature, thus, personal thresholds are needed to track the trust-propensity of different evaluators. In this paper we propose an interpretation of a probabilistic modal language à la Hennessy-Milner in order to capture a context-aware quantitative notion of trust based on evidence. We also provide an axiomatization for the language and prove soundness, completeness, and decidability results.</p></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"169 ","pages":"Article 109167"},"PeriodicalIF":3.9,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0888613X24000549/pdfft?md5=4f8df3737451f342a0bf6a2d5024f1b9&pid=1-s2.0-S0888613X24000549-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140154081","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A study of rough inclusion on algebras with quasi-Boolean base","authors":"Anirban Saha ,&nbsp;Jayanta Sen ,&nbsp;Mihir Kumar Chakraborty","doi":"10.1016/j.ijar.2024.109170","DOIUrl":"10.1016/j.ijar.2024.109170","url":null,"abstract":"<div><p>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 implications are presented.</p></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"169 ","pages":"Article 109170"},"PeriodicalIF":3.9,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140154257","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Overlap function-based fuzzy β-covering relations and fuzzy β-covering rough set models","authors":"Yaoyao Fan ,&nbsp;Xiaohong Zhang ,&nbsp;Jingqian Wang","doi":"10.1016/j.ijar.2024.109164","DOIUrl":"10.1016/j.ijar.2024.109164","url":null,"abstract":"<div><p>As an extension of the fuzzy covering, fuzzy <em>β</em>-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 <em>β</em>-neighborhood operator, four new operators were developed, which exhibit both symmetry and reflexivity through the utilization of established fuzzy <em>β</em>-neighborhood operators, overlap functions and grouping functions. Furthermore, we demonstrate that these operators satisfy the fuzzy <em>β</em>-covering relation, and utilize the fuzzy <em>β</em>-covering relations on the basis of overlap functions to propose new fuzzy <em>β</em>-covering rough set model. Additionally, incorporating the attribute significance, an attribute reduction algorithm is designed. Ultimately, we substantiate the rationality and superiority of our proposed algorithm by conducting a sequence of experiments. Meanwhile, we analyze the impacts of varying overlap functions and <em>β</em> values on the algorithm's performance.</p></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"169 ","pages":"Article 109164"},"PeriodicalIF":3.9,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140154170","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An auto-weighted enhanced horizontal collaborative fuzzy clustering algorithm with knowledge adaption mechanism","authors":"Huilin Yang ,&nbsp;Fusheng Yu ,&nbsp;Witold Pedrycz ,&nbsp;Life Fellow, IEEE,&nbsp;Zonglin Yang ,&nbsp;Jiaqi Chang ,&nbsp;Jiayin Wang","doi":"10.1016/j.ijar.2024.109169","DOIUrl":"10.1016/j.ijar.2024.109169","url":null,"abstract":"<div><p>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. In HCFC, each external dataset is used through the knowledge mined from it rather than itself. The knowledge expressed as a knowledge partition matrix is fused into the clustering process of the local dataset. Reviewing the existing HCFC models, we can find three issues that need improvement. Firstly, the existing HCFC models quantify the collaboration contribution of each external knowledge by a hyperparameter at dataset-level, and moreover, do not distinguish the collaboration contributions of objects in the same external dataset. This may lead to counterintuitive clustering results. Focused on this issue, this paper proposes an enhanced HCFC (EHCFC) algorithm that extends the collaboration from dataset-level to object-level, and assigns different weights to objects based on the information amount provided by objects. Through EHCFC, a more flexible collaboration and a more intuitive clustering result can be reached. Secondly, the collaboration mechanisms of the existing HCFC models require that the dimensionalities of the partition matrices of external datasets and local dataset are the same, which makes the HCFC algorithms unable to work in many real situations. Focused on this limitation, a knowledge adaption mechanism based on relative entropy and spectral clustering is proposed resulting in a further refined EHCFC-KA algorithm, i.e., EHCFC with knowledge adaption. The proposed knowledge adaption mechanism makes both the HCFC algorithms and the EHCFC algorithm effective and successful in more application scenarios. Finally, we define two indexes in terms of consistency (the consistency of the clustering result with external knowledge) to evaluate the performance of collaborative clustering. Experiments on synthetic datasets and UCI public datasets demonstrate that the proposed EHCFC and EHCFC-KA algorithms outperform the existing HCFC algorithms and achieve significantly better intuitive collaborative clustering performance.</p></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"169 ","pages":"Article 109169"},"PeriodicalIF":3.9,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140154073","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"New results of (U,N)-implications satisfying I(r,I(s,t))=I(I(r,s),I(r,t))","authors":"Cheng Zhang ,&nbsp;Feng Qin","doi":"10.1016/j.ijar.2024.109163","DOIUrl":"10.1016/j.ijar.2024.109163","url":null,"abstract":"<div><p>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 <span><math><mo>(</mo><mi>U</mi><mo>,</mo><mi>N</mi><mo>)</mo></math></span>-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 <span><math><mo>(</mo><mi>U</mi><mo>,</mo><mi>N</mi><mo>)</mo></math></span>-implication, two new necessary conditions have been introduced that are simple and practical: for the fuzzy negation <em>N</em>, it must be noncontinuous, and its values in the interval <span><math><mo>[</mo><mn>0</mn><mo>,</mo><mi>e</mi><mo>]</mo></math></span> should remain the constant 1. Next, the necessary and sufficient conditions for any <span><math><mo>(</mo><mi>U</mi><mo>,</mo><mi>N</mi><mo>)</mo></math></span>-implication to satisfy the generalized Frege's law are provided. Several complete characterizations are described depending on the position of <em>α</em> in <span><math><mo>[</mo><mi>e</mi><mo>,</mo><mn>1</mn><mo>]</mo></math></span>. To be more specific, the full characterization is achieved when <span><math><mi>α</mi><mo>=</mo><mi>e</mi></math></span> (<span><math><mi>α</mi><mo>=</mo><mn>1</mn></math></span>) and a disjunctive uninorm with a continuous underlying t-norm (t-conorm). The necessary and sufficient conditions are presented when <span><math><mi>α</mi><mo>∈</mo><mo>]</mo><mi>e</mi><mo>,</mo><mn>1</mn><mo>[</mo></math></span> and <em>U</em> is a locally internal and disjunctive uninorm.</p></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"169 ","pages":"Article 109163"},"PeriodicalIF":3.9,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140154166","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Systematic attribute reductions based on double granulation structures and three-view uncertainty measures in interval-set decision systems","authors":"Xin Xie ,&nbsp;Xianyong Zhang","doi":"10.1016/j.ijar.2024.109165","DOIUrl":"10.1016/j.ijar.2024.109165","url":null,"abstract":"<div><p>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 ISDSs, a fuzzy-equivalent granulation structure is proposed to improve the existing similar granulation structure, dependency degrees are proposed to enrich the existing condition entropy by using algebra-information fusion, so <span><math><mn>3</mn><mo>×</mo><mn>2</mn></math></span> attribute reductions are systematically formulated to contain both a basic reduction algorithm (called CAR) and five advanced reduction algorithms. At the granulation level, the similar granulation structure is improved to the fuzzy-equivalent granulation structure by removing the granular repeatability, and two knowledge structures emerge. At the measurement level, dependency degrees are proposed from the algebra perspective to supplement the condition entropy from the information perspective, and mixed measures are generated by fusing dependency degrees and condition entropies from the algebra-information viewpoint, so three-view and three-way uncertainty measures emerge to acquire granulation monotonicity/non-monotonicity. At the reduction level, the two granulation structures and three-view uncertainty measures two-dimensionally produce <span><math><mn>3</mn><mo>×</mo><mn>2</mn></math></span> heuristic reduction algorithms based on attribute significances, and thus five new algorithms emerge to improve an old algorithm (i.e., CAR). As finally shown by data experiments, <span><math><mn>3</mn><mo>×</mo><mn>2</mn></math></span>-systematic construction measures and attribute reductions exhibit the effectiveness and development, comparative results validate the three-level improvements of granulation structures, uncertainty measures, and reduction algorithms on ISDSs. This study resorts to tri-level thinking to enrich the theory and application of three-way decision.</p></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"169 ","pages":"Article 109165"},"PeriodicalIF":3.9,"publicationDate":"2024-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140076026","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}