Fuzzy Sets, Fuzzy Numbers, Fuzzy Modeling, and Their Applications in Management and Engineering, 2nd Edition

1. Introduction

As time progresses, companies as systems are becoming more complex, dynamic, and driven by uncertainty. As conditions change, decision-makers are often required to act based on subjective judgment or linguistic assessments relying on limited information. Classical crisp mathematical models are very robust, but their underlying assumptions often limit their ability to embrace uncertainty in practice. Due to this reason, fuzzy set theory [1], along with its extensions, has become an appropriate tool for modeling uncertainty and providing support for rational decision-making within uncertain internal and external conditions.

Using fuzzy sets and fuzzy decision-making frameworks enables the formal representation of imprecision and vagueness through partial membership, the use of linguistic variables, and flexible aggregation methods. All these properties make a fuzzy approach very useful for application in the field of management and engineering. Over time, the field has evolved from a theoretical base to becoming a complex collection of hybrid empirical and theoretical models that combine fuzzy logic with optimization, Multi-Criteria Decision Making (MCDM), system analysis, and data-driven methods.

This second edition of the Special Issue “Fuzzy Sets, Fuzzy Numbers, Fuzzy Modeling, and Their Applications in Management and Engineering” builds on earlier work by emphasizing methodological and applicable advancements. This Special Issue is intended to provide a platform for presenting novel fuzzy models, decision-making frameworks, and analytical tools, as well as their application to real problems in engineering and management.

2. Contributions

The contributions included in this Special Issue address a broad range of topics, dealing with theoretical developments, hybrid modeling approaches, and real-world applications.

This editorial begins with its opening article (Article 1), which introduces a flexible approach based on multiple factors to help choose workers for Taiwan’s electronics production sector. Instead of traditional methods, the authors used the Fuzzy Delphi Method, Interpretive Structural Modeling, and the Fuzzy Analytic Network Process to identify and structure key recruitment criteria. They highlight that adaptability, professional competence, and work attitude were critical criteria in developing recruitment policies in complex industrial settings.

In the second article, the authors focus on reverse logistics processes within emerging economies. The authors use the fuzzy DEMATEL method to investigate the interdependence between the economic, organizational, and regulatory barriers to implementing reverse logistics systems. They identified causal relationships among the barriers to building reverse logistics processes and provided heuristics for policymakers and managers to promote more sustainable logistics practices in uncertain environments.

Operational performance evaluation is addressed in a study (Article 3) that develops a fuzzy evaluation model for air-cleaning equipment. The authors utilized confidence intervals and cumulative fuzzy evaluation values in the development of an operational performance evaluation framework to support decision-making in manufacturing and environmental settings.

The fourth article examines urban development and infrastructure performance through a hybrid fuzzy evaluation model for city construction projects. The model itself is based on the integration of Buckley’s fuzzy approach with fuzzy axiomatic design. Model testing is conducted on the evaluation of construction performance across several criteria, resulting in practical recommendations for enhancing urban project planning.

In the fifth article, the VIKOR approach is extended by utilizing probabilistic uncertain linguistic term sets to investigate educational decision-making under uncertainty. The proposed model is applied to the evaluation of teaching reform plans in digital economy education. The results indicate model effectiveness in handling qualitative assessments and uncertain expert opinions.

The sixth article presents a methodology for building through the development of a total least squares regression approach for symmetric triangular fuzzy numbers. This work enhances regression analysis in fuzzy environments by introducing appropriate distance measures and solution procedures. The research is supported by an illustrative numerical example.

In addition to application-oriented studies, this Special Issue includes one review article (Article 7). A systematic literature review is reported on the integration of Failure Mode and Effects Analysis with multi-attribute decision-making methods under uncertainty. The review offers a valuable reference for researchers seeking to advance reliability and risk analysis by using fuzzy and hybrid methods through the classification of existing approaches, identifying prevailing trends, and highlighting research gaps.

Finally, the operational efficiency of passenger and freight air transport is analyzed using a fuzzy multi-criteria decision-making methodology in the eighth article. The study presents the application of the fuzzy MEREC method for criteria weighting and the fuzzy MARCOS method for ranking alternatives. The model itself provides a robust assessment of efficiency trends and demonstrates the applicability of fuzzy sets in transportation systems analysis.

One of the most notable aspects of this Special Issue is how fuzzy sets work well in situations where there is uncertainty, which is a common challenge in management and engineering today. Instead of exact numbers, these methods work with approximations, making them practical in real-world cases. Some papers show better ways to study systems using fuzzy logic, where clarity is limited. Others highlight decisions that gain clarity through structured vagueness.

A promising direction for future research lies in the systematic integration of fuzzy modeling with machine learning and artificial intelligence techniques, particularly in settings where data-driven models must coexist with expert judgment. It may be assumed that hybrid frameworks will become crucial in overcoming new issues in engineering and management systems.

As Guest Editor, I would like to acknowledge all the authors, since their effort made this Special Issue possible. I also extend my appreciation to the reviewers since their work improved the contributions to this Special Issue, and to the editorial staff of the journal for their continued support. I hope this Special Issue will serve as a valuable reference and a source of inspiration for researchers and practitioners working in the field of fuzzy modeling and decision-making.