New Approaches to Data Analysis and Data Analytics

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "D2: Operations Research and Fuzzy Decision Making".

Deadline for manuscript submissions: 1 October 2025 | Viewed by 754

Special Issue Editors


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Guest Editor
Centro de Investigación en Computación, Instituto Politecnico Nacional, Ciudad de México 07738, Mexico
Interests: artificial intelligence; computational intelligence; fuzzy systems; fuzzy relations; entropy of fuzzy sets; fuzzy logic operations; negation; involutive systems; correlation functions; similarity measures

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Guest Editor
Department of Computer Science, University of Texas at El Paso, 500 W University, El Paso, TX 79968, USA
Interests: interval computations; uncertainty processing; foundations of heuristic techniques

Special Issue Information

Dear Colleagues,

In recent years, the rapid growth of artificial intelligence and data science has increased the demand for the development of novel methods for representing, modeling, and analyzing different types of data, including uncertain and subjective information. The promising methods of research in this area are the generalization and synergy of methods of algebra, logic, theory of fuzzy sets and systems, probability theory and statistics, artificial intelligence, and machine learning. Examples include the theories of t-norms, aggregation functions, measures of possibility, and adaptive rule-based fuzzy inference systems, which have also significantly contributed to the development of data science.

For this Special Issue, we invite submissions of papers on novel and hybrid mathematical models and methods of data analysis and data analytics, including the following data types and models:

  • Subjective, linguistic, qualitative, categorical, fuzzy, probabilistic, interval, structured, and other data types;
  • Similarity, dissimilarity, association, correlation, preference, dependence, and causality relationship measures and functions;
  • Fuzzy similarity relations, ultrametrics, and partial ordering in clustering and data structure analysis;
  • Visualization, explanation, and interpretation of data structures and relationships;
  • Negation, involution, reflection operations, bipolarity, and data symmetry;
  • Data transformation and data aggregation;
  • Fuzzy distribution sets and subjective distributions of membership, probability, weight, and importance;
  • Negation, union, intersection and aggregation of subjective probability and weight distributions;
  • Divergence, entropy, and uncertainty measures;
  • Applications to business analytics.

Prof. Dr. Ildar Z. Batyrshin
Prof. Dr. Vladik Kreinovich
Guest Editors

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Keywords

  • subjective information
  • uncertainty modeling
  • fuzzy-probabilistic models
  • fuzzy relations
  • measures of relationships
  • similarity measures
  • correlation functions
  • involutivity
  • bipolarity

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Published Papers (1 paper)

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Research

23 pages, 1723 KiB  
Article
A Comprehensive Study on the Different Approaches of the Symmetric Difference in Nilpotent Fuzzy Systems
by Luca Sára Pusztaházi, György Eigner and Orsolya Csiszár
Mathematics 2025, 13(11), 1898; https://doi.org/10.3390/math13111898 - 5 Jun 2025
Viewed by 285
Abstract
This paper comprehensively examines symmetric difference operators within logical systems generated by nilpotent t-norms and t-conorms, specifically addressing their behavior and applicability in bounded and Łukasiewicz fuzzy logic systems. We identify two distinct symmetric difference operators and analyze their fundamental properties, revealing their [...] Read more.
This paper comprehensively examines symmetric difference operators within logical systems generated by nilpotent t-norms and t-conorms, specifically addressing their behavior and applicability in bounded and Łukasiewicz fuzzy logic systems. We identify two distinct symmetric difference operators and analyze their fundamental properties, revealing their inherent non-associativity. Recognizing the limitations posed by non-associative behavior in practical multi-step logical operations, we introduce a novel aggregated symmetric difference operator constructed through the arithmetic mean of the previously defined operators. The primary theoretical contribution of our research is establishing the associativity of this new aggregated operator, significantly enhancing its effectiveness for consistent multi-stage computations. Moreover, this operator retains critical properties including symmetry, neutrality, antitonicity, and invariance under negation, thus making it particularly valuable for various computational and applied domains such as image processing, pattern recognition, fuzzy neural networks, cryptographic schemes, and medical data analysis. The demonstrated theoretical robustness and practical versatility of our associative operator provide a clear improvement over existing methodologies, laying a solid foundation for future research in fuzzy logic and interdisciplinary applications. Our broader aim is to derive and study symmetric difference operators in both bounded and Łukasiewicz systems, as this represents a new direction of research. Full article
(This article belongs to the Special Issue New Approaches to Data Analysis and Data Analytics)
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