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Applied Sciences
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Fuzzy Control Systems and Decision-Making
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Fuzzy Control Systems and Decision-Making

A special issue of Applied Sciences (ISSN 2076-3417). This special issue belongs to the section "Computing and Artificial Intelligence".

Deadline for manuscript submissions: 10 May 2025 | Viewed by 3881

Special Issue Editor

Dr. Baigang Du

E-Mail Website
Guest Editor
School of Mechanical and Electronic Engineering, Wuhan University of Technology, Wuhan 430070, China
Interests: intelligent decision-making; optimization algorithms; reliability engineering

Special Issue Information

Dear Colleagues,

In recent years, there have been significant advances in fuzzy control systems and decision-making; techniques that enable more flexible and robust decision-making in complex and uncertain industrial environments. We invite researchers to submit their contributions to this Special Issue, which aims to present original research and review papers that include the design and application of fuzzy control systems and decision-making. The topics include, but are not limited to:

  • Fuzzy systems theory and models;
  • Decision-making;
  • Intelligent optimization;
  • Decision support systems;
  • Computers in design and manufacturing;
  • Innovative manufacturing processes;
  • Reliability engineering;
  • Industrial engineering.

Dr. Baigang Du
Guest Editor

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 100 words) can be sent to the Editorial Office for announcement on this website.

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. Applied Sciences 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 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

  • fuzzy control systems
  • decision-making
  • optimization algorithms
  • artificial intelligence

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

Published Papers (4 papers)

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Research

27 pages, 15483 KiB  
Article
Online Three-Dimensional Fuzzy Multi-Output Support Vector Regression Learning Modeling for Complex Distributed Parameter Systems
by Gang Zhou, Xianxia Zhang, Hanyu Yuan and Bing Wang
Appl. Sci. 2025, 15(5), 2750; https://doi.org/10.3390/app15052750 - 4 Mar 2025
Viewed by 223
Abstract
Complex distributed parameter systems (DPSs) are prevalent in numerous industrial processes. However, the nonlinear spatiotemporal dynamics inherent in DPS present significant challenges for accurate modeling. In this paper, an innovative online three-dimensional (3D) fuzzy multi-output support vector regression learning method is proposed for [...] Read more.
Complex distributed parameter systems (DPSs) are prevalent in numerous industrial processes. However, the nonlinear spatiotemporal dynamics inherent in DPS present significant challenges for accurate modeling. In this paper, an innovative online three-dimensional (3D) fuzzy multi-output support vector regression learning method is proposed for DPS modeling. The proposed method employs spatial fuzzy basis functions from the 3D fuzzy model as kernel functions, enabling direct construction of a comprehensive fuzzy rule base. Parameters C and ε in the 3D fuzzy model adaptively adjust according to data sequence variations, effectively responding to system dynamics. Furthermore, a stochastic gradient descent algorithm has been implemented for real-time updating of learning parameters and bias terms. The proposed method was validated through two typical DPS and an actual rotary hearth furnace industrial system. The experimental results show the effectiveness of the proposed modeling method. Full article
(This article belongs to the Special Issue Fuzzy Control Systems and Decision-Making)
►▼ Show Figures

Figure 1

Figure 1
<p>The framework of 3D fuzzy modeling.</p> Full article ">Figure 2
<p>Framework of 3D-OMSVR-SGD.</p> Full article ">Figure 3
<p>Nonisothermal fixed-bed reactor.</p> Full article ">Figure 4
<p>Prediction results of 3D-OMSVR-SGD for nonisothermal catalytic packed-bed reactors.</p> Full article ">Figure 5
<p>Model prediction and system output at the <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>S</mi> </mrow> <mrow> <mn>3</mn> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>S</mi> </mrow> <mrow> <mn>7</mn> </mrow> </msub> </mrow> </semantics></math> sensors.</p> Full article ">Figure 6
<p>Prediction error for the nonisothermal packed-bed catalytic reactor model.</p> Full article ">Figure 7
<p>Relative error of the nonisothermal packed-bed catalytic reactor model.</p> Full article ">Figure 8
<p>TNAE comparison of the different methods in Case 1.</p> Full article ">Figure 9
<p>RLNE comparison of the different methods in Case 1.</p> Full article ">Figure 10
<p>System structure of RTCVD.</p> Full article ">Figure 11
<p>Measurement output and prediction output under external disturbances in RTCVD.</p> Full article ">Figure 12
<p>Model prediction results of sensors <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>S</mi> </mrow> <mrow> <mn>5</mn> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>S</mi> </mrow> <mrow> <mn>11</mn> </mrow> </msub> </mrow> </semantics></math> under external disturbances.</p> Full article ">Figure 13
<p>Prediction error of different models under external disturbances.</p> Full article ">Figure 14
<p>Relative error of different models under external disturbances.</p> Full article ">Figure 15
<p>TNAE comparison of different methods under external disturbance in Case 2.</p> Full article ">Figure 16
<p>RLNE comparison of different methods under external disturbance in Case 2.</p> Full article ">Figure 17
<p>Measurement output and prediction output under internal disturbances in RTCVD.</p> Full article ">Figure 18
<p>Model prediction results of sensors <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>S</mi> </mrow> <mrow> <mn>5</mn> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>S</mi> </mrow> <mrow> <mn>11</mn> </mrow> </msub> </mrow> </semantics></math> under internal disturbances.</p> Full article ">Figure 19
<p>Prediction error of different models under internal disturbance.</p> Full article ">Figure 20
<p>Relative error of different models under internal disturbance.</p> Full article ">Figure 21
<p>TNAE comparison of different methods under internal disturbance in Case 2.</p> Full article ">Figure 22
<p>RLNE comparison of different methods under internal disturbance in Case 2.</p> Full article ">Figure 23
<p>Rotary hearth furnace combustion system.</p> Full article ">Figure 24
<p>Prediction results of 3D-OMSVR-SGD for rotary hearth furnace (Reduction zone 1).</p> Full article ">Figure 25
<p>Predictions of the rotary hearth furnace model at sensors  <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>S</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>S</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> </semantics></math> (Reduction zone 1).</p> Full article ">Figure 26
<p>Prediction error for the rotary hearth furnace (Reduction zone 1).</p> Full article ">Figure 27
<p>Relative error of the rotary hearth furnace (Reduction zone 1).</p> Full article ">Figure 28
<p>TNAE comparison of the different methods in Case 3 (Reduction zone 1).</p> Full article ">Figure 29
<p>RLNE comparison of the different methods in Case 3 (Reduction zone 1).</p> Full article ">
16 pages, 448 KiB  
Article
Evaluating the Impact of Membership Functions and Defuzzification Methods in a Fuzzy System: Case of Air Quality Levels
by Juan Fernando Lima, Andrés Patiño-León, Marcos Orellana and Jorge Luis Zambrano-Martinez
Appl. Sci. 2025, 15(4), 1934; https://doi.org/10.3390/app15041934 - 13 Feb 2025
Viewed by 393
Abstract
Since the 1960s, fuzzy logic has contributed to developing control systems based on modeling nonlinear problems using linguistic terms and inference rules. In the air quality domain, fuzzy logic has allowed us to tackle inferential environmental systems that are tolerant of human uncertainty [...] Read more.
Since the 1960s, fuzzy logic has contributed to developing control systems based on modeling nonlinear problems using linguistic terms and inference rules. In the air quality domain, fuzzy logic has allowed us to tackle inferential environmental systems that are tolerant of human uncertainty and aimed at decision support. These systems are composed of three processes: a function to define a membership degree of the system’s value concerning a human linguistic term; an inference engine for decision making; and defuzzification methods focused on transforming the aggregated fuzzy set into a real-world value. Over the years, multiple mathematical formulas have been proposed to enrich membership functions or defuzzification methods; however, their use is sometimes limited to classical functions, limiting the importance of other proposals. This paper aims to evaluate the impact of the transformation functions in an air quality fuzzy system. The results of this work prove that the defuzzification method has a more significant effect than the others. It should be noted that by considering these results or their evaluation method, the quality of future fuzzy systems can be improved in both industrial and academic domains. Full article
(This article belongs to the Special Issue Fuzzy Control Systems and Decision-Making)
►▼ Show Figures

Figure 1

Figure 1
<p>The activities for evaluating core MFs and defuzzification method are shown in a logic sequence. SPEM2.0 notation incorporates activities, metrics, databases, and scripts.</p> Full article ">Figure 2
<p>Linguistic terminology may be inadequate when the UoD is established from the gathered data. The terms “unhealthy groups” and “unhealthy” exhibit significant inconsistencies, which must be rectified.</p> Full article ">Figure 3
<p><math display="inline"><semantics> <msub> <mi>PM</mi> <mrow> <mn>2.5</mn> </mrow> </msub> </semantics></math> data distribution: (<b>a</b>) box plot shows multiple outliers redefining the UoD, (<b>b</b>) histogram indicates low frequencies of these outliers. This behavior is typical for other variables.</p> Full article ">Figure 4
<p>A definition of MFs and their UoDs using Equation (<a href="#FD4-applsci-15-01934" class="html-disp-formula">4</a>), based on representative values of collected data.</p> Full article ">Figure 5
<p>The accuracy of systems in forecasting <math display="inline"><semantics> <msub> <mi>PM</mi> <mrow> <mn>2.5</mn> </mrow> </msub> </semantics></math> through a conditional rule (Rule 1). The lowest MAPE values showed better accuracy in their forecasting task.</p> Full article ">Figure 6
<p>The accuracy of systems in forecasting the <math display="inline"><semantics> <msub> <mi mathvariant="normal">O</mi> <mn>3</mn> </msub> </semantics></math> through conjunctive Algorithm 2 (Rules 2 and 3). The lowest MAPE values showed better accuracy in their forecasting task.</p> Full article ">
23 pages, 1357 KiB  
Article
Three-Dimensional Fuzzy Modeling for Nonlinear Distributed Parameter Systems Using Simultaneous Perturbation Stochastic Approximation
by Xianxia Zhang, Tangchen Wang, Chong Cheng and Shaopu Wang
Appl. Sci. 2024, 14(17), 7860; https://doi.org/10.3390/app14177860 - 4 Sep 2024
Cited by 1 | Viewed by 781
Abstract
Many systems in the manufacturing industry have spatial distribution characteristics, which correlate with both time and space. Such systems are known as distributed parameter systems (DPSs). Due to the spatiotemporal coupling characteristics, the modeling of such systems is quite complex. The paper presents [...] Read more.
Many systems in the manufacturing industry have spatial distribution characteristics, which correlate with both time and space. Such systems are known as distributed parameter systems (DPSs). Due to the spatiotemporal coupling characteristics, the modeling of such systems is quite complex. The paper presents a new approach for three-dimensional fuzzy modeling using Simultaneous Perturbation Stochastic Approximation (SPSA) for nonlinear DPSs. The Affinity Propagation clustering approach is utilized to determine the optimal number of fuzzy rules and construct a collection of preceding components for three-dimensional fuzzy models. Fourier space base functions are used in the resulting components of three-dimensional fuzzy models, and their parameters are learned by the SPSA algorithm. The proposed three-dimensional fuzzy modeling technique was utilized on a conventional DPS within the semiconductor manufacturing industry, with the simulation experiments confirming its efficacy. Full article
(This article belongs to the Special Issue Fuzzy Control Systems and Decision-Making)
►▼ Show Figures

Figure 1

Figure 1
<p>Framework of three-dimensional fuzzy model (three-dimensional abbreviated as 3D).</p> Full article ">Figure 2
<p>Scheme of SPSA learning-based three-dimensional fuzzy modeling.</p> Full article ">Figure 3
<p>Flowchart of SPSA learning-based three-dimensional fuzzy modeling (three-dimensional abbreviated as 3D).</p> Full article ">Figure 4
<p>Sketch for the RTCVD system.</p> Full article ">Figure 5
<p>Radiation flux distribution of Lamp banks 1, 2, and 3.</p> Full article ">Figure 6
<p>Seven space base functions learned by the SPSA algorithm.</p> Full article ">Figure 7
<p>The predicted process output of the AP-Fourier-SPSA-3D model in the training data.</p> Full article ">Figure 8
<p>The predicted errors of the AP-Fourier-SPSA-3D model in training data.</p> Full article ">Figure 9
<p>The predicted process output of the AP-Fourier-SPSA-3D model in test data.</p> Full article ">Figure 10
<p>The predicted errors of the AP-Fourier-SPSA-3D model in test data.</p> Full article ">Figure 11
<p>Prediction error of the KL-LS model on the training set.</p> Full article ">Figure 12
<p>Prediction error of the KL-LS model on the test set.</p> Full article ">Figure 13
<p>Prediction error of the NNC-SVR-3D model on the training set.</p> Full article ">Figure 14
<p>Prediction error of the NNC-SVR-3D model on the test set.</p> Full article ">Figure 15
<p>TNAE of the four models on the training data.</p> Full article ">Figure 16
<p>TNAE of the four models on the test data.</p> Full article ">Figure A1
<p>Affinity Propagation factor graph.</p> Full article ">Figure A2
<p>The direction of the passing message.</p> Full article ">Figure A3
<p>Flow chart of the AP clustering algorithm.</p> Full article ">
22 pages, 12215 KiB  
Article
An AI-Powered Product Identity Form Design Method Based on Shape Grammar and Kansei Engineering: Integrating Midjourney and Grey-AHP-QFD
by Chenlu Wang, Jie Zhang, Dashuai Liu, Yuchao Cai and Quan Gu
Appl. Sci. 2024, 14(17), 7444; https://doi.org/10.3390/app14177444 - 23 Aug 2024
Cited by 2 | Viewed by 1762
Abstract
Product Identity (PI) is a strategic instrument for enterprises to forge brand strength through New Product Development (NPD). Concurrently, facing increasingly fierce market competition, the NPD for consumer emotional requirements (CRs) has become a significant objective in enterprise research and development (R&D). The [...] Read more.
Product Identity (PI) is a strategic instrument for enterprises to forge brand strength through New Product Development (NPD). Concurrently, facing increasingly fierce market competition, the NPD for consumer emotional requirements (CRs) has become a significant objective in enterprise research and development (R&D). The design of new product forms must ensure the continuity of PI and concurrently address the emotional needs of users. It demands a high level of experience from designers and significant investment in R&D. To solve this problem, a generative and quantitative design method powered by AI, based on Shape Grammar (SG) and Kansei Engineering (KE), is proposed. The specific method is as follows: Firstly, representative products for Morphological Analysis (MA) are selected, SG is applied to establish initial shapes and transformation rules, and prompts are input into Midjourney. This process generates conceptual sketches and iteratively refines them, resulting in a set of conceptual sketches that preserve the PI. Secondly, a web crawler mines online reviews to extract Kansei words. Factor Analysis (FA) clusters them into Kansei factors, and the Grey Analytic Hierarchy Process (G-AHP) calculates their grey weights. Thirdly, after analyzing the PI conceptual sketches for feature extraction, the features are integrated with CRs into the Quality Function Deployment (QFD) matrix. Experts evaluate the relationships using interval grey numbers, calculating the optimal ranking of PI Engineering Characteristics (PIECs). Finally, professional designers refine the selected sketches into 3D models and detailed designs. Using a Chinese brand as a case study, we have designed a female electric moped (E-moped) to fit the PI and users’ emotional needs. Through a questionnaire survey on the design scheme, we argue that the proposed innovative method is efficient, applicable, and effective in balancing the product form design of PI and user emotions. Full article
(This article belongs to the Special Issue Fuzzy Control Systems and Decision-Making)
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Figure 1

Figure 1
<p>Components of the HoQ.</p> Full article ">Figure 2
<p>The research framework for product form design of PI and KE.</p> Full article ">Figure 3
<p>The process of inputting PIECs and FCRs into QFDs.</p> Full article ">Figure 4
<p>Six possible scenarios (<b>a</b>–<b>f</b>) of <math display="inline"><semantics> <mrow> <mo>⨂</mo> <msub> <mrow> <mi>G</mi> <mi>N</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mo>⨂</mo> <msub> <mrow> <mi>G</mi> <mi>N</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> </semantics></math>.</p> Full article ">Figure 5
<p>Areas of 8 vector spaces.</p> Full article ">Figure 6
<p>Three types of modifications for female E-mopeds.</p> Full article ">Figure 7
<p>The form design features of the E-moped.</p> Full article ">Figure 8
<p>Three main PI form elements.</p> Full article ">Figure 9
<p>Pre-training image of the side body cover.</p> Full article ">Figure 10
<p>The interface of Midjourney for sketch generation.</p> Full article ">Figure 11
<p>The side view of screened sketch alternatives.</p> Full article ">Figure 12
<p>Three selected products.</p> Full article ">Figure 13
<p>Three selected conceptual sketches.</p> Full article ">Figure 14
<p>Female E-moped design scheme.</p> Full article ">Figure 15
<p>Compliant degree of Kansei factors and PI consistency.</p> Full article ">
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