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33 pages, 5060 KiB

Open AccessFeature PaperArticle

The Extreme Value Support Measure Machine for Group Anomaly Detection

by Lixuan An, Bernard De Baets and Stijn Luca

Mathematics 2025, 13(11), 1813; https://doi.org/10.3390/math13111813 - 29 May 2025

Viewed by 362

Group anomaly detection is a subfield of pattern recognition that aims at detecting anomalous groups rather than individual anomalous points. However, existing approaches mainly target the unusual aggregate of points in high-density regions. In this way, unusual group behavior with a number of [...] Read more.

Group anomaly detection is a subfield of pattern recognition that aims at detecting anomalous groups rather than individual anomalous points. However, existing approaches mainly target the unusual aggregate of points in high-density regions. In this way, unusual group behavior with a number of points located in low-density regions is not fully detected. In this paper, we propose a systematic approach based on extreme value theory (EVT), a field of statistics adept at modeling the tails of a distribution where data are sparse, and one-class support measure machines (OCSMMs) to quantify anomalous group behavior comprehensively. First, by applying EVT to a point process model, we construct an analytical model describing the likelihood of an aggregate within a group with respect to low-density regions, aimed at capturing anomalous group behavior in such regions. This model is then combined with a calibrated OCSMM, which provides probabilistic outputs to characterize anomalous group behavior in high-density regions, enabling improved assessment of overall anomalous group behavior. Extensive experiments on simulated and real-world data demonstrate that our method outperforms existing group anomaly detectors across diverse scenarios, showing its effectiveness in quantifying and interpreting various types of anomalous group behavior. Full article

(This article belongs to the Section D1: Probability and Statistics)

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20 pages, 3731 KiB

Open AccessArticle

Fuzzy Clustering with Uninorm-Based Distance Measure

by Evgeny Kagan, Alexander Novoselsky and Alexander Rybalov

Mathematics 2025, 13(10), 1661; https://doi.org/10.3390/math13101661 - 19 May 2025

Viewed by 367

Abstract

In this paper, we suggest an algorithm of fuzzy clustering with a uninorm-based distance measure. The algorithm follows a general scheme of fuzzy c-means (FCM) clustering, but in contrast to the existing algorithm, it implements logical distance between data instances. The centers [...] Read more.

In this paper, we suggest an algorithm of fuzzy clustering with a uninorm-based distance measure. The algorithm follows a general scheme of fuzzy c-means (FCM) clustering, but in contrast to the existing algorithm, it implements logical distance between data instances. The centers of the clusters calculated by the algorithm are less dispersed and are concentrated in the areas of the actual centers of the clusters that result in the more accurate recognition of the number of clusters and of data structure. Full article

(This article belongs to the Special Issue Advances in Multi-Criteria Decision Making Methods with Applications)

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22 pages, 1134 KiB

Open AccessArticle

A Quantitative Group Decision-Making Methodology for Structural Eco-Materials Selection Based on Qualitative Sustainability Attributes

by Majdi Al Shdifat, María L. Jalón, Esther Puertas and Juan Chiachío

Appl. Sci. 2023, 13(22), 12310; https://doi.org/10.3390/app132212310 - 14 Nov 2023

Cited by 3 | Viewed by 2444

Abstract

In response to escalating global environmental challenges, developed countries have embarked on an ecological transition across a range of sectors. Among these, the construction industry plays a key role due to its extensive use of raw materials and energy resources. In particular, research [...] Read more.

In response to escalating global environmental challenges, developed countries have embarked on an ecological transition across a range of sectors. Among these, the construction industry plays a key role due to its extensive use of raw materials and energy resources. In particular, research into sustainable construction materials, here named eco-materials, has seen a boost in recent years because of their potential to replace less environmentally friendly materials such as concrete and steel. This paper proposes a large-scale group decision-making methodology to select among a set of candidate structural eco-materials based on sustainability considerations. The proposed approach is based on a novel quantitative SWOT analysis using survey data from a diverse group of experts, considering not only the technical aspects of the materials but also their impact in the context of the United Nations’ Sustainable Development Goals. As a result, a range of eco-materials are probabilistically assessed and ranked, taking into account the variability and uncertainty in the survey data. The results of this research demonstrate the suitability of the proposed methodology for eco-material selection based on sustainability criteria, but also provide a new generic methodology for group decision assessment considering the uncertainty in the survey data, which can be extended to multiple applications. Full article

(This article belongs to the Special Issue Sustainability and Resilience of Engineering Assets)

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17 pages, 5016 KiB

Open AccessArticle

Non-Commutative Logic for Collective Decision-Making with Perception Bias

by Evgeny Kagan, Alexander Novoselsky, Daria Ramon and Alexander Rybalov

Robotics 2023, 12(3), 76; https://doi.org/10.3390/robotics12030076 - 22 May 2023

Cited by 3 | Viewed by 2097

Abstract

In this paper, we suggest an implementation of non-commutative logic and apply its operators for decision-making in a group of autonomous agents. The suggested operators extend the uninorm and absorbing norm aggregators and use an additional asymmetry parameter that defines the “level of [...] Read more.

In this paper, we suggest an implementation of non-commutative logic and apply its operators for decision-making in a group of autonomous agents. The suggested operators extend the uninorm and absorbing norm aggregators and use an additional asymmetry parameter that defines the “level of non-commutativity”. The value of this parameter is specified using the perception bias of humans measured in the experiments. The suggested operators and decision-making method are illustrated by the simulated behavior of mobile robots in the group, which verified the possibility of processing systematic sensing errors, as well as of distinguishing and mimicking the biased decisions. Full article

(This article belongs to the Special Issue Multi-robot Systems: State of the Art and Future Progress)

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27 pages, 408 KiB

Open AccessArticle

Filters in Strong BI-Algebras and Residuated Pseudo-SBI-Algebras

by Xiaohong Zhang, Xiangyu Ma and Xuejiao Wang

Mathematics 2020, 8(9), 1513; https://doi.org/10.3390/math8091513 - 4 Sep 2020

Cited by 5 | Viewed by 2577

Abstract

The concept of basic implication algebra (BI-algebra) has been proposed to describe general non-classical implicative logics (such as associative or non-associative fuzzy logic, commutative or non-commutative fuzzy logic, quantum logic). However, this algebra structure does not have enough characteristics to describe residual implications [...] Read more.

The concept of basic implication algebra (BI-algebra) has been proposed to describe general non-classical implicative logics (such as associative or non-associative fuzzy logic, commutative or non-commutative fuzzy logic, quantum logic). However, this algebra structure does not have enough characteristics to describe residual implications in depth, so we propose a new concept of strong BI-algebra, which is exactly the algebraic abstraction of fuzzy implication with pseudo-exchange principle (PEP). Furthermore, in order to describe the characteristics of the algebraic structure corresponding to the non-commutative fuzzy logics, we extend strong BI-algebra to the non-commutative case, and propose the concept of pseudo-strong BI (SBI)-algebra, which is the common extension of quantum B-algebras, pseudo-BCK/BCI-algebras and other algebraic structures. We establish the filter theory and quotient structure of pseudo-SBI- algebras. Moreover, based on prequantales, semi-uninorms, t-norms and their residual implications, we introduce the concept of residual pseudo-SBI-algebra, which is a common extension of (non-commutative) residual lattices, non-associative residual lattices, and also a special kind of residual partially-ordered groupoids. Finally, we investigate the filters and quotient algebraic structures of residuated pseudo-SBI-algebras, and obtain a unity frame of filter theory for various algebraic systems. Full article

(This article belongs to the Special Issue General Algebraic Structures 2020)

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26 pages, 3094 KiB

Open AccessArticle

On Neutrosophic Offuninorms

by Erick González Caballero, Florentin Smarandache and Maikel Leyva Vázquez

Symmetry 2019, 11(9), 1136; https://doi.org/10.3390/sym11091136 - 6 Sep 2019

Cited by 28 | Viewed by 4366

Abstract

Uninorms comprise an important kind of operator in fuzzy theory. They are obtained from the generalization of the t-norm and t-conorm axiomatic. Uninorms are theoretically remarkable, and furthermore, they have a wide range of applications. For that reason, when fuzzy sets have been [...] Read more.

Uninorms comprise an important kind of operator in fuzzy theory. They are obtained from the generalization of the t-norm and t-conorm axiomatic. Uninorms are theoretically remarkable, and furthermore, they have a wide range of applications. For that reason, when fuzzy sets have been generalized to others—e.g., intuitionistic fuzzy sets, interval-valued fuzzy sets, interval-valued intuitionistic fuzzy sets, or neutrosophic sets—then uninorm generalizations have emerged in those novel frameworks. Neutrosophic sets contain the notion of indeterminacy—which is caused by unknown, contradictory, and paradoxical information—and thus, it includes, aside from the membership and non-membership functions, an indeterminate-membership function. Also, the relationship among them does not satisfy any restriction. Along this line of generalizations, this paper aims to extend uninorms to the framework of neutrosophic offsets, which are called neutrosophic offuninorms. Offsets are neutrosophic sets such that their domains exceed the scope of the interval [0,1]. In the present paper, the definition, properties, and application areas of this new concept are provided. It is necessary to emphasize that the neutrosophic offuninorms are feasible for application in several fields, as we illustrate in this paper. Full article

(This article belongs to the Special Issue New types of Neutrosophic Set/Logic/Probability, Neutrosophic Over-/Under-/Off-Set, Neutrosophic Refined Set, and their Extension to Plithogenic Set/Logic/Probability, with Applications)

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50 pages, 734 KiB

Open AccessArticle

A Proof of the Standard Completeness for the Involutive Uninorm Logic

by SanMin Wang

Symmetry 2019, 11(4), 445; https://doi.org/10.3390/sym11040445 - 27 Mar 2019

Cited by 5 | Viewed by 3296

Abstract

In this paper, we solve a long-standing open problem in the field of fuzzy logics, that is, the standard completeness for the involutive uninorm logic IUL. In fact, we present a uniform method of density elimination for several semilinear substructural logics. Especially, [...] Read more.

In this paper, we solve a long-standing open problem in the field of fuzzy logics, that is, the standard completeness for the involutive uninorm logic IUL. In fact, we present a uniform method of density elimination for several semilinear substructural logics. Especially, the density elimination for IUL is proved. Then the standard completeness for IUL follows as a lemma by virtue of previous work by Metcalfe and Montagna. Full article

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13 pages, 424 KiB

Open AccessArticle

The Logic of Pseudo-Uninorms and Their Residua

by SanMin Wang

Symmetry 2019, 11(3), 368; https://doi.org/10.3390/sym11030368 - 12 Mar 2019

Cited by 3 | Viewed by 2487

Abstract

Our method for density elimination is generalized to the non-commutative substructural logic

{GpsUL}^{*}

. Then, the standard completeness of

{HpsUL}^{*}

follows as a lemma by virtue of previous work by Metcalfe and Montagna. This result shows that

{HpsUL}^{*}

is the [...] Read more.

Our method for density elimination is generalized to the non-commutative substructural logic

{GpsUL}^{*}

. Then, the standard completeness of

{HpsUL}^{*}

follows as a lemma by virtue of previous work by Metcalfe and Montagna. This result shows that

{HpsUL}^{*}

is the logic of pseudo-uninorms and their residua and answered the question posed by Prof. Metcalfe, Olivetti, Gabbay and Tsinakis. Full article

(This article belongs to the Special Issue Mathematical Fuzzy Logic and Fuzzy Set Theory)

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15 pages, 297 KiB

Open AccessArticle

Fixpointed Idempotent Uninorm (Based) Logics

by Eunsuk Yang

Mathematics 2019, 7(1), 107; https://doi.org/10.3390/math7010107 - 20 Jan 2019

Cited by 6 | Viewed by 3137

Abstract

Idempotent uninorms are simply defined by fixpointed negations. These uninorms, called here fixpointed idempotent uninorms, have been extensively studied because of their simplicity, whereas logics characterizing such uninorms have not. Recently, fixpointed uninorm mingle logic (fUML) was introduced, and its standard [...] Read more.

Idempotent uninorms are simply defined by fixpointed negations. These uninorms, called here fixpointed idempotent uninorms, have been extensively studied because of their simplicity, whereas logics characterizing such uninorms have not. Recently, fixpointed uninorm mingle logic (fUML) was introduced, and its standard completeness, i.e., completeness on real unit interval

[0, 1]

, was proved by Baldi and Ciabattoni. However, their proof is not algebraic and does not shed any light on the algebraic feature by which an idempotent uninorm is characterized, using operations defined by a fixpointed negation. To shed a light on this feature, this paper algebraically investigates logics based on fixpointed idempotent uninorms. First, several such logics are introduced as axiomatic extensions of uninorm mingle logic (UML). The algebraic structures corresponding to the systems are then defined, and the results of the associated algebraic completeness are provided. Next, standard completeness is established for the systems using an Esteva–Godo-style approach for proving standard completeness. Full article

(This article belongs to the Special Issue Fuzziness and Mathematical Logic )

18 pages, 767 KiB

Open AccessArticle

On Extended Representable Uninorms and Their Extended Fuzzy Implications (Coimplications)

by Aifang Xie

Symmetry 2017, 9(8), 160; https://doi.org/10.3390/sym9080160 - 18 Aug 2017

Cited by 1 | Viewed by 3674

Abstract

In this work, by Zadeh’s extension principle, we extend representable uninorms and their fuzzy implications (coimplications) to type-2 fuzzy sets. Emphatically, we investigate in which algebras of fuzzy truth values the extended operations are type-2 uninorms and type-2 fuzzy implications (coimplications), respectively. Full article

(This article belongs to the Special Issue Fuzzy Sets Theory and Its Applications)

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