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Advances in Fuzzy Intelligence and Non-Classical Logical Computing
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Advances in Fuzzy Intelligence and Non-Classical Logical Computing

A Special Issue of Mathematics (ISSN 2227-7390) belonging to the section "E: Applied Mathematics".

Deadline for manuscript submissions: 30 September 2026 | Viewed by 4871

Editors

Prof. Yu-Bin Zhong

E-Mail Website
Guest Editor
School of Mathematics and Information Science, Guangzhou University, Guangzhou, China
Interests: information systems and operational optimization; mathematical theory of super-algebraic structure; knowledge representation
Dr. Yi Xiang

E-Mail Website
Guest Editor
School of Software, South China University of Technology, Guangzhou 510641, China
Interests: computational intelligence; machine learning; multi-objective optimization
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue, hosted by the journal Mathematics and jointly supported by the Operations Research Society of China (Fuzzy Information and Engineering Branch), the Artificial Intelligence Foundation Committee of the Chinese Association for Artificial Intelligence, and the Non-Classical Logic and Computation Committee of the Chinese Association of Logic, aims to promote the latest theoretical and methodological advances at the intersection of fuzzy systems, non-classical logics, and artificial intelligence foundations.

We welcome original research articles, reviews, and application reports that advance the theoretical foundation, algorithm design, and interdisciplinary application of fuzzy intelligence and logical reasoning in uncertain and complex systems.

Topics of interest include (but are not limited to) the following:

A. Fuzzy Information and Engineering

A1. Theoretical Models of Fuzzy Information;

A1.1: Fuzzy Sets, Measures, and Inference Theory;

A1.2: Fuzzy Granulation, Similarity Measures, and Relational Models;

A1.3: Linguistic Variables and Semantic Interpretation;

A1.4: Uncertainty Modeling and Information Fusion in Fuzzy Systems;

A1.5: Statistical and Data-Driven Modeling for Fuzzy Information;

A2. Fuzzy Decision Making and Optimization;

A2.1: Multi-Attribute Decision-Making under Fuzziness;

A2.2: Fuzzy Multi-Objective Optimization and Evolutionary Algorithms;

A2.3: Fuzzy AHP, Fuzzy TOPSIS, and Aggregation Models;

A2.4: Group Decision-Making with Linguistic Preferences;

A2.5: Fuzzy Constrained Optimization and Game-Theoretic Models;

A3. Engineering Applications of Fuzzy Information;

A3.1: Fuzzy Technologies in Smart Manufacturing and Industry 4.0;

A3.2: Fuzzy Control Systems in Automation and Robotics;

A3.3: Fuzzy Data Mining in Healthcare, Finance, and Transportation;

A3.4: Fuzzy Models in Energy Management and Environmental Engineering;

A3.5: Integrated Fuzzy Modeling for Complex Engineering Systems.

B. Foundations of Artificial Intelligence

B1. Logical Foundations and Computability;

B1.1: Axiomatic Models of Artificial Intelligence;

B1.2: Formal Systems and Proof Theory in AI;

B1.3: Turing Computability, Decidability, and Complexity Theory;

B2. Knowledge Representation and Ontologies;

B2.1: Description Logics and Semantic Web Technologies;

B2.2: Ontology Construction and Concept Hierarchies;

B2.3: Symbolic vs. Sub-symbolic Representation Frameworks;

B3. Reasoning Mechanisms and Formal Inference;

B3.1: Deductive and Inductive Reasoning;

B3.2: Logic Programming and Answer Set Programming;

B3.3: Inference Engines and Explanation-Based Reasoning;

B4. Learning Theory and Generalization;

B4.1: Computational Learning Theory (PAC, VC-dimension, etc.);

B4.2: Inductive Logic Learning and Statistical Relational Learning;

B4.3: Theoretical Aspects of Deep and Symbolic Learning;

B5. Intelligent Agents and Cognitive Modeling;

B5.1: Agent Logics: Belief, Desire, Intention (BDI) Models;

B5.2: Cognitive Architectures (e.g., SOAR, ACT-R);

B5.3: Formal Modeling of Perception, Memory, and Decision.

C. Non-Classical Logic and Computational Methods

C1. Non-Classical Logical Systems;

C1.1: Modal Logic and Temporal Logic in Dynamic Systems;

C1.2: Intuitionistic, Many-Valued, and Paraconsistent Logics;

C1.3: Hybrid Logics and Fuzzy-Modal Extensions;

C2. Non-Monotonic and Argumentative Reasoning;

C2.1: Default Logic and Autoepistemic Reasoning;

C2.2: Belief Revision and Defeasible Reasoning;

C2.3: Structured Argumentation and Logic-Based Debating Systems;

C3. Causal and Counterfactual Models;

C3.1: Formal Models of Causality (e.g., Pearl’s Framework);

C3.2: Counterfactual Reasoning in AI Planning and Diagnosis;

C3.3: Causal Logic Programming and Explanatory Reasoning;

C4. Logic Programming and Computational Semantics;

C4.1: Non-Classical Constraint Satisfaction Problems;

C4.2: Semantic Models for Inconsistent or Incomplete Data;

C4.3: Applications in Robotics, Planning, and XAI Systems.

Prof. Yu-Bin Zhong
Dr. Yi Xiang
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-anonymized peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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

  • fuzzy logic and reasoning
  • causal models
  • computability
  • non-classical logics
  • artificial intelligence foundations
  • factor neural networks
  • knowledge representation
  • uncertainty modeling

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (6 papers)

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Research

16 pages, 668 KB  
Article
A Two-Stage Bayesian Ordinal Model with Rank-Based Fuzzy Evidence for Cross-Country Ride-Hailing Service Improvement
by Shun Peng, Gaoyi Xu, Hongwei Peng, Ran Chen, Guiying Wang and Xinxin Wang
Mathematics 2026, 14(17), 3212; https://doi.org/10.3390/math14173212 - 5 Sep 2026
Viewed by 202
Abstract
Multilingual online reviews combine ordinal ratings, asymmetric positive and negative evidence, sparse attribute occurrence, and substantial cross-country imbalance. This study presents an integrated inferential framework. Signed topic scores are converted to within-country rank intensities, and country-specific cumulative-logit models distinguish positive and negative occurrence [...] Read more.
Multilingual online reviews combine ordinal ratings, asymmetric positive and negative evidence, sparse attribute occurrence, and substantial cross-country imbalance. This study presents an integrated inferential framework. Signed topic scores are converted to within-country rank intensities, and country-specific cumulative-logit models distinguish positive and negative occurrence baselines from their corresponding intensity contrasts. The two intensity contrasts are then synthesized jointly through a bivariate Bayesian normal-normal random-effects model that retains their within-country covariance. The primary analysis uses all 30,042 reviews observed in the common 2019–2024 window; the complete 85,373-review corpus and repeated country-capped samples are sensitivity analyses. Separating the two occurrence baselines improves summed AIC from 32,347.7 to 32,167.8, while a transformation-by-function comparison shows that natural splines improve AIC and quadratic-weighted agreement. The linear-rank model is retained to provide comparable scalar intensity contrasts. Targeted partial proportional-odds fits substantially improve in-sample AIC in China and Japan but leave repeated-validation performance and all nine average effect directions essentially unchanged. A secondary semantic mapping audit agrees with 30 of 31 topic assignments. Simulation results show generally adequate interval coverage but reduced Kano-state accuracy under small K, sparse occurrence, and proportional-odds violations. The findings therefore support tiered, uncertainty-aware prioritization rather than a deterministic global ranking. Full article
(This article belongs to the Special Issue Advances in Fuzzy Intelligence and Non-Classical Logical Computing)
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16 pages, 1305 KB  
Article
GA-Optimized Feature Weighting for Fuzzy C-Means Classification
by Zhiwen Li, Xinghua Wang, Yongtao Li and Yubin Zhong
Mathematics 2026, 14(14), 2609; https://doi.org/10.3390/math14142609 - 18 Jul 2026
Viewed by 383
Abstract
The problem of insufficient classification accuracy in fuzzy clustering algorithms for multidimensional data is addressed in this paper. To tackle this issue, an improved genetic algorithm (GA)-based fuzzy controller is proposed, which combines the advantages of an improved genetic algorithm and a fuzzy [...] Read more.
The problem of insufficient classification accuracy in fuzzy clustering algorithms for multidimensional data is addressed in this paper. To tackle this issue, an improved genetic algorithm (GA)-based fuzzy controller is proposed, which combines the advantages of an improved genetic algorithm and a fuzzy C-means (FCM) clustering algorithm. The population initialization is performed using the Tent chaotic map, while the best individual retention strategy and last elimination selection operator are employed to adjust the population structure. Furthermore, an elitist crossover operator, an adaptive trial mutation operator, and a nonlinear convergence factor are introduced to mitigate the risk of falling into local optima. The controller algorithm integrates the intermediate parameters of FCM clustering into the fitness function of the genetic algorithm, and effectively improves the classification accuracy by screening the optimal feature subset and then fuzzy clustering. The experimental results on the Pistachio, WDBC, and Wine datasets show that the proposed method achieves competitive classification accuracy compared with other FCM-based feature-weighting optimization methods. Full article
(This article belongs to the Special Issue Advances in Fuzzy Intelligence and Non-Classical Logical Computing)
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34 pages, 1168 KB  
Article
A Product Lifecycle Management-Oriented Fuzzy MCDM Model for Prioritizing Virtual Reality and Augmented Reality Applications in Industrial Design and Manufacturing: Design Optimization and Robustness Analysis
by Linzi Ouyang, Yuling Lai, Raman Kumar and Yao Chen
Mathematics 2026, 14(10), 1646; https://doi.org/10.3390/math14101646 - 12 May 2026
Viewed by 586
Abstract
This study addresses the challenge of prioritizing Virtual Reality (VR) and Augmented Reality (AR) applications in Product Lifecycle Management (PLM) under multiple conflicting criteria. A comprehensive fuzzy Multi-Criteria Decision-Making (FMCDM) framework is proposed to support robust and unbiased decision-making. The methodology integrates multiple [...] Read more.
This study addresses the challenge of prioritizing Virtual Reality (VR) and Augmented Reality (AR) applications in Product Lifecycle Management (PLM) under multiple conflicting criteria. A comprehensive fuzzy Multi-Criteria Decision-Making (FMCDM) framework is proposed to support robust and unbiased decision-making. The methodology integrates multiple objective weighting techniques, including Entropy, Criteria Importance Through Intercriteria Correlation (CRITIC), Method based on the Removal Effects of Criteria (MEREC), and Standard Deviation, which are aggregated using the Bonferroni operator to obtain balanced criterion weights. The Fuzzy Measurement of Alternatives and Ranking according to Compromise Solution (MARCOS) method is employed as the primary ranking approach, supported by comparative methods such as Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), VIšekriterijumsko KOmpromisno Rangiranje (VIKOR), Evaluation based on Distance from Average Solution (EDAS), Weighted Aggregated Sum Product Assessment (WASPAS), and Multi-Objective Optimization on the basis of Ratio Analysis (MOORA) for validation. The results indicate that Virtual Reality Digital Prototyping and Design Review (A3) is the most preferred alternative, achieving the highest utility value (0.95267), followed by Augmented Reality-Assisted Assembly and Inspection Guidance (A1) and Augmented Reality-Supported Maintenance and Operator Training (A4). A high Stability Index of 0.9133 confirms robustness, and sensitivity analysis shows stable rankings. The framework provides a reliable and scalable decision-support system for smart manufacturing. Full article
(This article belongs to the Special Issue Advances in Fuzzy Intelligence and Non-Classical Logical Computing)
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19 pages, 910 KB  
Article
Analysis on Inclusion and Preference of Intuitionistic Fuzzy Sets Using Hesitation Degree and Its Application to Presidential Election in US and Korea
by Sanghyuk Lee and Eunmi Lee
Mathematics 2026, 14(7), 1123; https://doi.org/10.3390/math14071123 - 27 Mar 2026
Viewed by 601
Abstract
Inclusion and preference relations are fundamental comparison tools in intuitionistic fuzzy set (IFS) theory and play an important role in decision analysis under uncertainty. In IFS representations, the hesitation degree reflects information that is not captured by membership and non-membership values alone. This [...] Read more.
Inclusion and preference relations are fundamental comparison tools in intuitionistic fuzzy set (IFS) theory and play an important role in decision analysis under uncertainty. In IFS representations, the hesitation degree reflects information that is not captured by membership and non-membership values alone. This study investigates the structural relationship between hesitation and the inclusion and preference relations of IFSs. A proposed interpretation of membership and non-membership degrees is employed to provide a geometric perspective on hesitation. Within this framework, analytical relations between hesitation inequalities and preference conditions are derived. In particular, it is shown that the hesitation inequality constitutes a necessary condition for preference, whereas inclusion relations remain compatible with a wider range of hesitation configurations. The theoretical observations are illustrated using electoral datasets from the 2002 South Korean presidential election and the 2000 United States presidential election in Florida. Regional vote shares are transformed into intuitionistic fuzzy representations to analyze the distribution of hesitation across regions. The examples demonstrate how hesitation may influence the stability of preference relations while inclusion relations remain structurally preserved. Full article
(This article belongs to the Special Issue Advances in Fuzzy Intelligence and Non-Classical Logical Computing)
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25 pages, 410 KB  
Article
Logic and Probabilistic Operations on a Decision Matrix in a Fuzzy Multi-Criteria Decision-Making Problem
by Lydia Castronovo, Giuseppe Filippone, Gianmarco La Rosa, Giuseppe Sanfilippo and Marco Elio Tabacchi
Mathematics 2026, 14(5), 778; https://doi.org/10.3390/math14050778 - 25 Feb 2026
Cited by 1 | Viewed by 843
Abstract
In the framework of (fuzzy) Multi-Criteria Decision-Making, we propose a method that allows decision-makers to subjectively approach problems by suitably modifying a decision matrix. We consider a decision problem related to a random quantity X with a set of values [...] Read more.
In the framework of (fuzzy) Multi-Criteria Decision-Making, we propose a method that allows decision-makers to subjectively approach problems by suitably modifying a decision matrix. We consider a decision problem related to a random quantity X with a set of values {x1,x2,…,xn} and a set of properties {C1,C2,…,Cm} of X. In this setting, the properties Cj are the criteria of the decision problem, the alternatives represent the events Ai=(X=xi), for i=1,…,n, and the criteria’s weights wj, for j=1,…,m, are seen as the probabilities for the event that “Cj is relevant with respect to the decision problem”. For each i=1,…,n and j=1,…,m, we interpret the scores aij as membership functions representing “how much alternative Ai satisfies criterion Cj”. By adopting an interpretation of membership functions as suitable conditional probabilities together with the theory of logical operations between conditional events, we allow logical operations between criteria and consistently apply this interpretation to the corresponding scores. In particular, when considering the complement, conjunction, and disjunction of criteria, the resulting scores are the (coherent) previsions of the respective compound conditionals within the framework of conditional random quantities. To illustrate our approach, we present an example concerning career choices. Full article
(This article belongs to the Special Issue Advances in Fuzzy Intelligence and Non-Classical Logical Computing)
18 pages, 430 KB  
Article
Semi-Supervised Fuzzy Clustering Based on Prior Membership
by Yinghan Hong, Guoxiang Zhong, Jiahao Lian, Guizhen Mai, Honghong Zhou, Pinghua Chen, Junliu Zhong and Hui Cao
Mathematics 2025, 13(16), 2559; https://doi.org/10.3390/math13162559 - 10 Aug 2025
Cited by 2 | Viewed by 1282
Abstract
Traditional fuzzy clustering algorithms construct sample partition criteria solely based on similarity measures but lack an effective representation of prior membership information, which limits further improvements in clustering accuracy. To address this issue, this paper proposes a semi-supervised fuzzy clustering algorithm based on [...] Read more.
Traditional fuzzy clustering algorithms construct sample partition criteria solely based on similarity measures but lack an effective representation of prior membership information, which limits further improvements in clustering accuracy. To address this issue, this paper proposes a semi-supervised fuzzy clustering algorithm based on prior membership (SFCM-PM). The proposed algorithm introduces prior information entropy as a metric to quantify the divergence between partition membership and prior membership and incorporates this as an auxiliary partition criterion into the objective function. By jointly optimizing data similarity and consistency with prior knowledge during the clustering process, the algorithm achieves more accurate and reliable clustering results. The experimental results demonstrate that the SFCM-PM algorithm achieves significant performance improvements by incorporating a small number of prior membership samples across several standard and real-world datasets. It also performs outstandingly on datasets with unbalanced sample distributions. Full article
(This article belongs to the Special Issue Advances in Fuzzy Intelligence and Non-Classical Logical Computing)
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