New Trends in Fusion Processes Based on Aggregation and Pre-aggregation Functions: Theory and Applications

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Logic".

Deadline for manuscript submissions: closed (10 January 2023) | Viewed by 7969

Special Issue Editors


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Guest Editor
Centro de Ciências Computacionais, Universidade Federal do Rio Grande, Rio Grande 96203-900, Brazil
Interests: mathematical computing; fuzzy logic; fuzzy set theory; fuzzy systems

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Guest Editor
Departamento de Informática e Matemática Aplicada, Universidade Federal do Rio Grande do Norte, Natal 59078-900, Brazil
Interests: fuzzy logic; interval mathematics; formal languages; classification and clustering data
Special Issues, Collections and Topics in MDPI journals

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Guest Editor
College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China
Interests: mathematical computing; fuzzy logic; fuzzy set theory; fuzzy systems

Special Issue Information

Dear Colleagues,

We have the intention of launching a Special Issue of Axioms. The central topic in the Special Issue will be “Aggregation and Pre-Aggregation Functions”, but not only in the fuzzy environment since we are also interested in the new trend of fusion processes beyond the unit interval.

The search for new information on fusion techniques is currently a hot topic in almost every research field, from image processing and decision making to deep learning and neurosciences. This interest has led to a new analysis of the notion of aggregation function, as well as to the introduction of new concepts that go beyond usual aggregation functions, either by considering more general definitions (e.g., considering weaker forms of monotonicity, as directional monotonicity and ordered directional monotonicity), or by extending them to other frameworks different from that of the unit interval (e.g., intervals, lattices, any closed real interval).   The study of such generalizations has led to more flexibility in applications, from the control of the uncertainty to novel forms of fusion data.

Among the topics that this Special Issue will address, we may consider the following non-exhaustive list:  aggregation functions;  pre-aggregation functions;  directional monotonicity; ordered directional monotonicity; new generalizations of monotonicity;  aggregation and pre-aggregation  functions on bounded posets and/or lattices; aggregation and pre-aggregation  functions on arbitrary closed intervals; interval-valued aggregation and pre-aggregation  functions;  fuzzy integrals and their generalizations; restricted dissimilarity/equivalence functions;  generalized forms of t-norms/t-conorms, overlap/grouping functions, uninorms, fuzzy implications functions; applications in any field of artificial intelligence and computer science, including, but not limited to, image processing, classification, recurrent neural networks, deep learning, transformers, big data, approximate reasoning, computational brain or decision-making.

We point out that the Special Issue is open to receiving further ideas, apart from the aforementioned topics.

In the hopes that this initiative is of interest, we encourage you to submit your current research to be included in the Special Issue.

Dr. Graçaliz Pereira Dimuro
Dr. Benjamin Bedregal
Dr. Junsheng Qiao
Guest Editors

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Published Papers (5 papers)

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Research

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16 pages, 315 KiB  
Article
Least Squares in a Data Fusion Scenario via Aggregation Operators
by Gildson Queiroz de Jesus and Eduardo Silva Palmeira
Axioms 2022, 11(12), 678; https://doi.org/10.3390/axioms11120678 - 28 Nov 2022
Viewed by 917
Abstract
In this paper, appropriate least-squares methods were developed to operate in data fusion scenarios. These methods generate optimal estimates by combining measurements from a finite collection of samples. The aggregation operators of the average type, namely, ordered weighted averaging (OWA), Choquet integral, and [...] Read more.
In this paper, appropriate least-squares methods were developed to operate in data fusion scenarios. These methods generate optimal estimates by combining measurements from a finite collection of samples. The aggregation operators of the average type, namely, ordered weighted averaging (OWA), Choquet integral, and mixture operators, were applied to formulate the optimization problem. Numerical examples about fitting curves to a given set of points are provided to show the effectiveness of the proposed algorithms. Full article
22 pages, 445 KiB  
Article
Development of the Generalized Multi-Dimensional Extended Partitioned Bonferroni Mean Operator and Its Application in Hierarchical MCDM
by Debasmita Banerjee, Debashree Guha, Radko Mesiar and Juliet Karmakar Mondol
Axioms 2022, 11(11), 600; https://doi.org/10.3390/axioms11110600 - 28 Oct 2022
Cited by 1 | Viewed by 1042
Abstract
In this article, we propose the generalized version of the extended, partitioned Bonferroni mean (EPBM) operator with a systematic investigation of its behavior and properties. It can aggregate data of various dimensions in one formulation by modeling mandatory conditions along with [...] Read more.
In this article, we propose the generalized version of the extended, partitioned Bonferroni mean (EPBM) operator with a systematic investigation of its behavior and properties. It can aggregate data of various dimensions in one formulation by modeling mandatory conditions along with partitioned structure interrelationships amongst the criterion set. In addition, we generate the condition for weight vectors satisfied by the weighting triangle associated with the proposed extended aggregation operator. We employed the proposed operator to aggregate a dataset following a hierarchical structure. We found that by implementing the proposed operator one can even rank the alternatives more intuitively with respect to any intermediate perspective of the hierarchical system. Finally, we present an application of the proposed extended aggregation operator in a case-based example of a child’s home environment quality evaluation with detailed analysis. Full article
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16 pages, 525 KiB  
Article
CT-Integral on Interval-Valued Sugeno Probability Measure and Its Application in Multi-Criteria Decision-Making Problems
by Hong Yang, Liyan Shang and Zengtai Gong
Axioms 2022, 11(7), 317; https://doi.org/10.3390/axioms11070317 - 29 Jun 2022
Cited by 1 | Viewed by 1042
Abstract
It is well known that the complexity of the decision-making environment frequently coexists with the diversity of linguistic information in the decision-making process. In order to solve this kind of uncertain multi-criteria decision-making problem, reasonable measures and integrals should be established. In this [...] Read more.
It is well known that the complexity of the decision-making environment frequently coexists with the diversity of linguistic information in the decision-making process. In order to solve this kind of uncertain multi-criteria decision-making problem, reasonable measures and integrals should be established. In this paper, the discrete expression of the CT-integral on the interval-valued Sugeno probability measure is proposed. The CT-integral is the Choquet integral when the t-norm is T(x,y)=xy in the CT-integral and is a pre-aggregation function. Then, the CT-integral on interval-valued Sugeno probability measure is applied to solve end-of-life (EOL) strategy in order to determine multi-criteria decision-making problems. Compared with the general Choquet integral, the method proposed in this paper significantly improves the calculation process, that is, the calculation is simpler and the amount of calculation is smaller. A case study was performed in order to validate the effectiveness of this conclusion. Full article
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13 pages, 514 KiB  
Article
Recursive Aggregation and Its Fusion Process for Intuitionistic Fuzzy Numbers Based on Non-Additive Measure
by Yongfu Shi and Zengtai Gong
Axioms 2022, 11(6), 257; https://doi.org/10.3390/axioms11060257 - 28 May 2022
Viewed by 1199
Abstract
In this paper, the recursive aggregation of OWA operators for intuitionistic fuzzy numbers (IFN) based on a non-additive measure (NAM) with σλ rules is constructed and investigated in light of the σλ rules of a non-additive measure (NAM). Additionally, [...] Read more.
In this paper, the recursive aggregation of OWA operators for intuitionistic fuzzy numbers (IFN) based on a non-additive measure (NAM) with σλ rules is constructed and investigated in light of the σλ rules of a non-additive measure (NAM). Additionally, an integrator is designed by drawing on the genetic algorithm and the process of calculation is elaborated by an example. Full article
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Other

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22 pages, 849 KiB  
Systematic Review
Systematic Review of Aggregation Functions Applied to Image Edge Detection
by Miqueias Amorim, Gracaliz Dimuro, Eduardo Borges, Bruno L. Dalmazo, Cedric Marco-Detchart, Giancarlo Lucca and Humberto Bustince
Axioms 2023, 12(4), 330; https://doi.org/10.3390/axioms12040330 - 28 Mar 2023
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Abstract
Edge detection is a crucial process in numerous stages of computer vision. This field of study has recently gained momentum due to its importance in various applications. The uncertainty, among other characteristics of images, makes it difficult to accurately determine the edge of [...] Read more.
Edge detection is a crucial process in numerous stages of computer vision. This field of study has recently gained momentum due to its importance in various applications. The uncertainty, among other characteristics of images, makes it difficult to accurately determine the edge of objects. Furthermore, even the definition of an edge is vague as an edge can be considered as the maximum boundary between two regions with different properties. Given the advancement of research in image discontinuity detection, especially using aggregation and pre-aggregation functions, and the lack of systematic literature reviews on this topic, this paper aims to gather and synthesize the current state of the art of this topic. To achieve this, this paper presents a systematic review of the literature, which selected 24 papers filtered from 428 articles found in computer databases in the last seven years. It was possible to synthesize important related information, which was grouped into three approaches: (i) based on both multiple descriptor extraction and data aggregation, (ii) based on both the aggregation of distance functions and fuzzy C-means, and (iii) based on fuzzy theory, namely type-2 fuzzy and neutrosophic sets. As a conclusion, this review provides interesting gaps that can be explored in future work. Full article
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