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Axioms
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Advances in Fuzzy Logic with Applications
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Advances in Fuzzy Logic with Applications

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

Deadline for manuscript submissions: 30 August 2026 | Viewed by 8216

Special Issue Editors

Dr. Diego García-Zamora

E-Mail Website
Guest Editor
Department of Mathematics, University of Jaen, 23071 Jaen, Spain
Interests: fuzzy logic; aggregation operators; fuzzy metric spaces; optimization
Prof. Dr. Juan Martínez-Moreno

E-Mail Website
Guest Editor
Department of Mathematics, University of Jaén Campus Las Lagunillas s/n, 23071 Jaen, Spain
Interests: fixed point theory; fuzzy theory; mathematical analysis
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

We are excited to announce the Special Issue titled "Advances in Fuzzy Logic with Applications", which is dedicated to the latest theoretical advancements and practical applications of fuzzy logic. This Special Issue aims to provide a comprehensive platform for researchers, scholars, and practitioners to present cutting-edge research bridging the gap between theory and practice in this dynamic field.

On the theoretical side, we welcome submissions exploring innovations in fuzzy logic theory, including advanced fuzzy inference systems, new developments in fuzzy set theory, and the integration of fuzzy logic with other computational intelligence techniques. Additionally, we seek contributions delving into the mathematical foundations of fuzzy logic, such as theoretical studies, novel mathematical models, and advances in fuzzy algebra and calculus. Research focused on developing and aggregation operators and methodologies for approximate reasoning is also encouraged. Moreover, fuzzy metrics, in their various forms and versions, along with related structures like Menger spaces, fuzzy normed spaces, and Hutton quasi-uniformities, serve as essential tools in the development of general topology.

For applied contributions, we are interested in practical implementations of uncertainty modeling, featuring case studies in various applications and comparative studies on uncertainty modeling techniques. Papers on real-world applications of fuzzy decision-making and comparative studies of fuzzy decision-making methods are particularly relevant. We invite submissions on the implementation of fuzzy systems in control engineering, robotics, automation, or telecommunications. Business and economics applications, such as financial modeling, risk assessment, decision support systems in management, and market analysis, are also sought. We also encourage papers on hybrid models that integrate fuzzy logic with neural networks, genetic algorithms, and other AI techniques, as well as innovative applications showcasing the practical utility of fuzzy systems. New and significant contributions to fixed-point theory in fuzzy metrics are highly valued. Additionally, we are interested in advanced applications in areas such as spanning optimization and decision-making, control systems, computer science, and algorithms, including fuzzy clustering and pattern recognition.

We invite high-quality original research papers, review articles, and case studies addressing both theoretical advancements and practical applications in fuzzy logic. Submissions should adhere to the journal's guidelines and formatting requirements and will undergo a rigorous peer-review process to ensure high-quality research.

Dr. Diego García-Zamora
Prof. Dr. Juan Martínez-Moreno
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • decision-making
  • fuzzy logic
  • aggregation operators
  • uncertainty modeling
  • approximate reasoning
  • fuzzy metric spaces

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Published Papers (7 papers)

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Research

18 pages, 289 KB  
Article
The New Bipolar Intuitionistic Fuzzy Metric Space (NBIFM-Space) with Applications
by Bratislav Iričanin, Tatjana Došenović, Nebojša M. Ralević and Biljana Carić
Axioms 2026, 15(3), 239; https://doi.org/10.3390/axioms15030239 - 23 Mar 2026
Viewed by 520
Abstract
This paper introduces the New Bipolar Intuitionistic Fuzzy Metric Space (NBIFM-space)—a mathematical framework that extends intuitionistic and previously proposed bipolar intuitionistic structures by providing a complete three-component formulation based on positive similarity, negative similarity, and indeterminacy. Unlike earlier bipolar intuitionistic models, [...] Read more.
This paper introduces the New Bipolar Intuitionistic Fuzzy Metric Space (NBIFM-space)—a mathematical framework that extends intuitionistic and previously proposed bipolar intuitionistic structures by providing a complete three-component formulation based on positive similarity, negative similarity, and indeterminacy. Unlike earlier bipolar intuitionistic models, the NBIFM-space employs normalized metric components and coordinated triangular norms denoted by t-norm/t-conorm interactions, yielding a fully consistent topological and analytic setting. We have developed the basic properties of this structure and have demonstrated its effectiveness in image processing, where the explicit separation of attraction, repulsion, and uncertainty leads to robust edge-preserving filtering. Furthermore, a Banach-type fixed point theorem is established in the full NBIFM framework. Full article
(This article belongs to the Special Issue Advances in Fuzzy Logic with Applications)
25 pages, 333 KB  
Article
Modus Tollens in the Setting of Discrete Uninorms
by Isabel Aguiló, Pilar Fuster-Parra and Juan Vicente Riera
Axioms 2026, 15(1), 77; https://doi.org/10.3390/axioms15010077 - 21 Jan 2026
Viewed by 390
Abstract
This study focuses on the Modus Tollens (MT) property induced by discrete uninorms. Specifically, we identify the set of necessary and sufficient criteria for a discrete implication function to comply with this logical property. This rule of inference is studied by using discrete [...] Read more.
This study focuses on the Modus Tollens (MT) property induced by discrete uninorms. Specifically, we identify the set of necessary and sufficient criteria for a discrete implication function to comply with this logical property. This rule of inference is studied by using discrete residual implication functions derived from uninorms of two of the most important families of these discrete operators (Umin, idempotents), exploring which properties these operators must satisfy, as well as providing some characterizations of the Modus Tollens in this domain of definition. Our findings contribute to a deeper understanding of reasoning mechanisms in fuzzy logic, particularly in discrete settings. Full article
(This article belongs to the Special Issue Advances in Fuzzy Logic with Applications)
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25 pages, 395 KB  
Article
Two-Stage Three-Dimensional Transportation Optimization Under Elliptic Intuitionistic Fuzzy Quadruples: An Index-Matrix Interpretation
by Velichka Traneva and Stoyan Tranev
Axioms 2025, 14(11), 849; https://doi.org/10.3390/axioms14110849 - 18 Nov 2025
Cited by 2 | Viewed by 617
Abstract
The transportation problem (TP) is a canonical linear programming model for minimizing the cost of distributing goods from multiple sources to multiple destinations. Classical TPs assume deterministic costs, supplies, and demands, whereas real supply chains are affected by volatility in fuel prices, inflation, [...] Read more.
The transportation problem (TP) is a canonical linear programming model for minimizing the cost of distributing goods from multiple sources to multiple destinations. Classical TPs assume deterministic costs, supplies, and demands, whereas real supply chains are affected by volatility in fuel prices, inflation, disruptions, and weather, making such parameters uncertain. Fuzzy sets (FSs) and intuitionistic fuzzy sets (IFSs) have been widely used to handle vagueness; however, while Atanassov’s IFSs incorporate hesitation in addition to membership and non-membership, they remain limited to isotropic representations of uncertainty. This paper introduces an index-matrix interpretation for a two-stage three-dimensional transportation problem (2-S 3-D TP) defined under Elliptic Intuitionistic Fuzzy Quadruples (E-IFQs). Within this framework, transportation costs, supplies, and demands are represented as E-IFQs, allowing the modeling of anisotropic and correlated uncertainty along the membership and non-membership axes. The two-stage formulation extends previous intuitionistic fuzzy approaches by adding a temporal dimension and incorporating practical constraints such as cost thresholds and feasibility checks. The objective is to determine optimal producer–hub–buyer allocations that minimize the total E-IFQ cost while preserving consistency across all stages and time periods. A detailed case study on EV battery module distribution demonstrates the effectiveness of the proposed model. Compared with conventional fuzzy and intuitionistic fuzzy formulations, the 2-S 3-D E-IFTP yields more robust and precise decisions under complex, multidimensional uncertainty, offering improved interpretability and policy integration over time. Full article
(This article belongs to the Special Issue Advances in Fuzzy Logic with Applications)
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14 pages, 275 KB  
Article
Paraconsistency in the Logic sqŁ*
by Lei Cai and Wenjuan Chen
Axioms 2025, 14(4), 241; https://doi.org/10.3390/axioms14040241 - 21 Mar 2025
Viewed by 668
Abstract
The logic sqŁ* is closely related to complex fuzzy sets. In this paper, we continue our study on sqŁ* by establishing a system that includes all formulas with values 0 in sqŁ*. This system has paraconsistent formulas within sqŁ [...] Read more.
The logic sqŁ* is closely related to complex fuzzy sets. In this paper, we continue our study on sqŁ* by establishing a system that includes all formulas with values 0 in sqŁ*. This system has paraconsistent formulas within sqŁ*. Moreover, we show that this logical system is both sound and weakly complete. Full article
(This article belongs to the Special Issue Advances in Fuzzy Logic with Applications)
18 pages, 282 KB  
Article
A New Double Fuzzy Integral Transform for Solving an Advection–Diffusion Equation
by Atanaska Georgieva, Slav I. Cholakov and Mira Spasova
Axioms 2025, 14(4), 240; https://doi.org/10.3390/axioms14040240 - 21 Mar 2025
Cited by 1 | Viewed by 691
Abstract
This article presents a new approach to solving fuzzy advection–diffusion equations using double fuzzy transforms, called the double fuzzy Yang–General transform. This unique double fuzzy transformation is a combination of single fuzzy Yang and General transforms. Some of the basic properties of this [...] Read more.
This article presents a new approach to solving fuzzy advection–diffusion equations using double fuzzy transforms, called the double fuzzy Yang–General transform. This unique double fuzzy transformation is a combination of single fuzzy Yang and General transforms. Some of the basic properties of this new transform include existence and linearity and how they relate to partial derivatives. A solution framework for the linear fuzzy advection–diffusion equation is developed to show the application of the double fuzzy Yang–General transform. To illustrate the proposed method for solving these equations, we have included a solution to a numerical problem. Full article
(This article belongs to the Special Issue Advances in Fuzzy Logic with Applications)
20 pages, 499 KB  
Article
Definition of Triangular Norms and Triangular Conorms on Subfamilies of Type-2 Fuzzy Sets
by Pablo Hernández-Varela, Francisco Javier Talavera, Susana Cubillo, Carmen Torres-Blanc and Jorge Elorza
Axioms 2025, 14(1), 27; https://doi.org/10.3390/axioms14010027 - 31 Dec 2024
Cited by 2 | Viewed by 2286
Abstract
In certain stages of the application of a type-2 fuzzy logic system, it is necessary to perform operations between input or output fuzzy variables in order to compute the union, intersection, aggregation, complement, and so forth. In this context, operators that satisfy the [...] Read more.
In certain stages of the application of a type-2 fuzzy logic system, it is necessary to perform operations between input or output fuzzy variables in order to compute the union, intersection, aggregation, complement, and so forth. In this context, operators that satisfy the axioms of t-norms and t-conorms are of particular significance, as they are applied to model intersection and union, respectively. Furthermore, the existence of a range of these operators allows for the selection of the t-norm or t-conorm that offers the optimal performance, in accordance with the specific context of the system. In this paper, we obtain new t-norms and t-conorms on some important subfamilies of the set of functions from [0,1] to [0,1]. The structure of these families provides a more solid algebraic foundation for the applications. In particular, we define these new operators on the subsets of the functions that are convex, normal, and normal and convex, as well as the functions taking only the values 0 or 1 and the subset of functions whose support is a finite union of closed intervals. These t-norms and t-conorms are generalized to the type-2 fuzzy set framework. Full article
(This article belongs to the Special Issue Advances in Fuzzy Logic with Applications)
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24 pages, 332 KB  
Article
Intuitionistic Hesitant Fuzzy Rough Aggregation Operator-Based EDAS Method and Its Application to Multi-Criteria Decision-Making Problems
by Muhammad Kamraz Khan, Muhammad Sajjad Ali Khan, Kamran and Ioan-Lucian Popa
Axioms 2025, 14(1), 21; https://doi.org/10.3390/axioms14010021 - 30 Dec 2024
Cited by 3 | Viewed by 1410
Abstract
The fundamental notions of the intuitionistic hesitant fuzzy set (IHFS) and rough set (RS) are general mathematical tools that may easily manage imprecise and uncertain information. The EDAS (Evaluation based on Distance from Average Solution) approach has an important role in decision-making (DM) [...] Read more.
The fundamental notions of the intuitionistic hesitant fuzzy set (IHFS) and rough set (RS) are general mathematical tools that may easily manage imprecise and uncertain information. The EDAS (Evaluation based on Distance from Average Solution) approach has an important role in decision-making (DM) problems, particularly in multi-attribute group decision-making (MAGDM) scenarios, where there are many conflicting criteria. This paper aims to introduce the IHFR-EDAS approach, which utilizes the IHF rough averaging aggregation operator. The aggregation operator is crucial for aggregating intuitionistic hesitant fuzzy numbers into a cohesive component. Additionally, we introduce the concepts of the IHF rough weighted averaging (IHFRWA) operator. For the proposed operator, a new accuracy function (AF) and score function (SF) are established. Subsequently, the suggested approach is used to show the IHFR-EDAS model for MAGDM and its stepwise procedure. In conclusion, a numerical example of the constructed model is demonstrated, and a general comparison between the investigated models and the current methods demonstrates that the investigated models are more feasible and efficient than the present methods. Full article
(This article belongs to the Special Issue Advances in Fuzzy Logic with Applications)
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