Imprecision to Insights: Theoretical Advances in Fuzzy Uncertainty Modeling and Their Applications in New Frontiers

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

Deadline for manuscript submissions: closed (30 April 2024) | Viewed by 7350

Special Issue Editors


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Guest Editor
School of Technology and Innovations, University of Vaasa, Wolffintie 34, FI-65200 Vaasa, Finland
Interests: computational intelligence; fuzzy sets; industry 4.0; transfer learning anomaly detection
Special Issues, Collections and Topics in MDPI journals

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Guest Editor
Department of Computer Science, South Asian University, New Delhi 110021, India
Interests: computational intelligence; real-time systems; fuzzy sets and systems

Special Issue Information

Dear Colleagues,

With the rapid advancement of technology, the amount of data being generated has increased dramatically, creating a need for more sophisticated methods of analysis. Traditional analysis methods are often insufficient to handle the complexity and diversity of data, particularly in the presence of noise. This problem has become of great concern, as the use of inaccurate or misleading results due to noise can have significant consequences in several research fields. Therefore, there is a need for novel approaches that can account for uncertainty in data, and fuzzy uncertainty modeling is an effective approach to address this challenge. For the uninitiated, Fuzzy Logic extends classical (or "crisp") logic by allowing degrees of truth to be represented as real numbers between 0 and 1, rather than just binary true/false values. This allows for a more nuanced representation of uncertainty and provides a framework for defining and manipulating fuzzy sets, relations, and rules.

By incorporating fuzzy uncertainty, researchers can make more informed decisions and extract valuable insights that might have been missed with traditional methods. Therefore, this Special Issue aims to provide a platform for researchers to present their latest developments in fuzzy uncertainty modeling (theoretical as well as practical), focusing on the challenges and opportunities in the field. We invite submissions of original research papers, reviews and case studies that address, but are not limited to, the following topics:

  • Theoretical foundations on Fuzzy Uncertainty Modeling;
  • Fuzzy sets and systems in uncertainty modeling;
  • Industrial Energy Optimization;
  • Energy Efficiency issues in Industry, Transportation and HVAC;
  • Fuzzy modeling in engineering and natural sciences;
  • Trustworthy and Explainable AI;
  • Image and Signal Processing;
  • Security, Defence and Bioinformatics;
  • Finance and Economics;
  • Transfer Learning;
  • Multi-objective optimization;
  • Recommendation systems;
  • Quantum Computing;
  • Digital Economy;
  • Fraud Detection;
  • Sentiment Analysis;
  • Hyperspectral Imaging;
  • Other Emerging Areas.

Dr. Amit K. Shukla
Prof. Dr. Pranab K. Muhuri
Guest Editors

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Published Papers (6 papers)

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Research

22 pages, 370 KiB  
Article
Developing Constrained Interval Operators for Fuzzy Logic with Interval Values
by Jocivania Pinheiro, Regivan H. N. Santiago, Benjamin Bedregal and Flaulles Bergamaschi
Axioms 2023, 12(12), 1115; https://doi.org/10.3390/axioms12121115 - 13 Dec 2023
Viewed by 833
Abstract
A well-known problem in the interval analysis literature is the overestimation and loss of information. In this article, we define new interval operators, called constrained interval operators, that preserve information and mitigate overestimation. These operators are investigated in terms of correction, algebraic [...] Read more.
A well-known problem in the interval analysis literature is the overestimation and loss of information. In this article, we define new interval operators, called constrained interval operators, that preserve information and mitigate overestimation. These operators are investigated in terms of correction, algebraic properties, and orders. It is shown that a large part of the properties studied is preserved by this operator, while others remain preserved with the condition of continuity, as is the case of the exchange principle. In addition, a comparative study is carried out between this operator g¨ and the best interval representation: g^. Although g¨g^ and g¨ do not preserve the Moore correction, we do not have a loss of relevant information since everything that is lost is irrelevant, mitigating the overestimation. Full article
12 pages, 303 KiB  
Article
n-K-Increasing Aggregation Functions
by Radko Mesiar, Anna Kolesárová, Adam Šeliga and Radomír Halaš
Axioms 2023, 12(12), 1065; https://doi.org/10.3390/axioms12121065 - 21 Nov 2023
Viewed by 784
Abstract
We introduce and discuss the concept of n-ary K-increasing fusion functions and n-ary K-increasing aggregation functions, K being a subset of the index set {1,,n} indicating in which variables a considered function is [...] Read more.
We introduce and discuss the concept of n-ary K-increasing fusion functions and n-ary K-increasing aggregation functions, K being a subset of the index set {1,,n} indicating in which variables a considered function is increasing. It is also assumed that this function is decreasing in all other variables. We show that each n-ary K-increasing aggregation function is generated by some aggregation function which enables us to introduce and study the properties of n-ary K-increasing aggregation functions related to the properties of their generating aggregation functions. In particular, we also discuss binary K-increasing aggregation functions, including fuzzy implication and complication functions, among others. Full article
21 pages, 5092 KiB  
Article
Interval Type-3 Fuzzy Aggregation for Hybrid-Hierarchical Neural Classification and Prediction Models in Decision-Making
by Martha Ramírez, Patricia Melin and Oscar Castillo
Axioms 2023, 12(10), 906; https://doi.org/10.3390/axioms12100906 - 24 Sep 2023
Cited by 1 | Viewed by 1459
Abstract
In all organizations, many decision analysts acquire their skills through the experience of facing challenges to structure complex problems. Therefore, every day, the use of tools to integrate indicators through multi-attribute ordering, component-based separation, and clustering to reduce the criteria required for decision-making [...] Read more.
In all organizations, many decision analysts acquire their skills through the experience of facing challenges to structure complex problems. Therefore, every day, the use of tools to integrate indicators through multi-attribute ordering, component-based separation, and clustering to reduce the criteria required for decision-making and the achievement of goals and objectives is more frequent. Thus, our proposal consists of a new hybrid-hierarchical model for the classification and prediction of country indicators such as inflation, unemployment, population growth, and labor force, among others, in a decision-making environment using unsupervised neural networks and type-3 fuzzy systems. The contribution is achieving a type-3 fuzzy aggregation method in which the hierarchy is first represented by neural networks and later a set of type-1, type-2, and type-3 systems to combine the results, which allows multiple indicators to be separated and then integrated in an appropriate fashion. We can point out as one of the advantages of utilizing the method that the user can evaluate a range of qualities in multiple variables through the classification and prediction of time series attributes and assess a range of qualities for decision-making with uncertainty, according to the results of the simulations carried out. Full article
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27 pages, 2148 KiB  
Article
Enhancing Dynamic Parameter Adaptation in the Bird Swarm Algorithm Using General Type-2 Fuzzy Analysis and Mathematical Functions
by Ivette Miramontes and Patricia Melin
Axioms 2023, 12(9), 834; https://doi.org/10.3390/axioms12090834 - 29 Aug 2023
Cited by 1 | Viewed by 1174
Abstract
The pursuit of continuous improvement across diverse processes presents a pressing challenge. Precision in manufacturing, efficient delivery route planning, and accurate diagnostics are imperative, prompting the exploration of innovative solutions. Nature-inspired algorithms offer a pathway for enhancing these processes. In this study, we [...] Read more.
The pursuit of continuous improvement across diverse processes presents a pressing challenge. Precision in manufacturing, efficient delivery route planning, and accurate diagnostics are imperative, prompting the exploration of innovative solutions. Nature-inspired algorithms offer a pathway for enhancing these processes. In this study, we address this challenge by dynamically adapting parameters in the Bird Swarm Algorithm using General Type-2 Fuzzy Systems, encompassing a range of rules and membership functions. Two complex case studies validate the effectiveness of our approach. The first evaluates Congress of Evolutionary Competition 2017 functions, while the second tackles the intricacies of Congress of Evolutionary Competition 2019 functions. Our methodology achieves an 97% improvement for Congress of Evolutionary Competition 2017 functions and a significant 70% enhancement for Congress of Evolutionary Competition 2019 functions. Notably, our results are benchmarked against the original method. Crucially, rigorous statistical analysis underscores the significant advancements facilitated by our proposed method. The comparison demonstrates clear and statistically significant improvements over the original approach. This study proves the marked impact of integrating General Type-2 Fuzzy Systems into the Bird Swarm Algorithm, presenting a promising avenue for addressing intricate optimization challenges in diverse domains. Full article
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20 pages, 342 KiB  
Article
On Orthogonal Fuzzy Interpolative Contractions with Applications to Volterra Type Integral Equations and Fractional Differential Equations
by Umar Ishtiaq, Fahad Jahangeer, Doha A. Kattan, Ioannis K. Argyros and Samundra Regmi
Axioms 2023, 12(8), 725; https://doi.org/10.3390/axioms12080725 - 26 Jul 2023
Cited by 1 | Viewed by 695
Abstract
In this paper, orthogonal fuzzy versions are reported for some celebrated iterative mappings. We provide various concrete conditions on the real valued functions J,S:(0,1](,) for the existence of [...] Read more.
In this paper, orthogonal fuzzy versions are reported for some celebrated iterative mappings. We provide various concrete conditions on the real valued functions J,S:(0,1](,) for the existence of fixed-points of (J,S)-fuzzy interpolative contractions. This way, many fixed point theorems are developed in orthogonal fuzzy metric spaces. We apply the (J,S)-fuzzy version of Banach fixed point theorem to demonstrate the existence and uniqueness of the solution. These results are supported with several non-trivial examples and applications to Volterra-type integral equations and fractional differential equations. Full article
13 pages, 1165 KiB  
Article
An Interpretation of the Surface Temperature Time Series through Fuzzy Measures
by Rashmi Rekha Devi and Surajit Chattopadhyay
Axioms 2023, 12(5), 475; https://doi.org/10.3390/axioms12050475 - 15 May 2023
Cited by 3 | Viewed by 1211
Abstract
This paper reports a study to interpret the surface temperature based on time series and fuzzy measures. We demonstrated a method to identify the uncertainty around the surface temperature data concerning the summer monsoon in India. The random variables were standardized, and the [...] Read more.
This paper reports a study to interpret the surface temperature based on time series and fuzzy measures. We demonstrated a method to identify the uncertainty around the surface temperature data concerning the summer monsoon in India. The random variables were standardized, and the Dempster-Shafer Theory was used to generate common goals. Two criteria, represented as fuzzy numbers, were used for this purpose. We constructed three polynomials to illustrate a functional connection between time series and the measure of joint belief. The analysis of the obtained results showed that the certainty increased over time. It confirmed that the degree of the evidence is a more predictable parameter at a more extended period. Full article
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