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Mathematics
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Probability-Based Fuzzy Sets: Extensions and Applications
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Probability-Based Fuzzy Sets: Extensions and Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Fuzzy Sets, Systems and Decision Making".

Deadline for manuscript submissions: closed (15 April 2023) | Viewed by 6454

Special Issue Editors

Prof. Dr. Zaoli Yang

E-Mail Website
Guest Editor
College of Economics and Management, Beijing University of Technology, Beijing 100124, China
Interests: fuzzy set theory; expert systems and decision support; energy and environmental assessment; multi-source heterogeneous data mining and fusion
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Shaomin Wu

E-Mail Website
Guest Editor
Kent Business School, University of Kent, Canterbury, Kent CT2 7FS, UK
Interests: recurrent event data analysis; machine learning; risk analysis; security analysis
Prof. Dr. Yi Su

E-Mail Website
Guest Editor
School of Economics and Management, Harbin Engineering University, Harbin 150001, China
Interests: innovation management; digital economy; digital transformation
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Since the concept of fuzzy sets was proposed by Zadeh in 1965, it has become possible to describe uncertainty and fuzziness information in practice quantitatively. Meanwhile, to reduce the loss of processed information, the probability theory is introduced into fuzzy sets to develop probabilistic fuzzy sets, hesitant probabilistic fuzzy sets, probabilistic intuitionistic fuzzy sets, etc. Their applications include probabilistic fuzzy clustering, probabilistic fuzzy image fusion, probabilistic fuzzy neural network control, and probabilistic fuzzy decision making. With the rapid development of artificial intelligence technology and tools, our understanding of the real world has been further deepened. Accordingly, researchers have successively defined various fuzzy set extensions to depict phenomena that are more complex in reality, such as the picture fuzzy sets, q‐rung orthopair fuzzy sets, T-spherical fuzzy sets, etc. Therefore, meaningfully introducing probability theory into these new extensions to enhance the accuracy of information expression becomes an intriguing and important issue. Especially research areas such as the definitions of novel forms of probability-based fuzzy sets, probability-based fuzzy system optimization, corresponding operational rules, distance measurement, information aggregation, and their applications in various fields need further investigation.

This Special Issue welcomes papers combining probability theory with recent, new concepts in fuzzy sets to address the uncertainty and complexity that people are encountering.

Prof. Dr. Zaoli Yang
Prof. Dr. Shaomin Wu
Prof. Dr. Yi Su
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 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. 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

  • probability theory
  • fuzzy sets theory
  • extensions of probability-based fuzzy sets
  • operational rules between new probabilistic-based fuzzy sets
  • distance measurement between new probabilistic-based fuzzy sets
  • new probabilistic-based fuzzy information aggregation
  • probabilistic fuzzy clustering
  • probability-based fuzzy system optimization
  • probabilistic fuzzy decision making
  • application of novel probabilistic fuzzy sets in various fields

Published Papers (3 papers)

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Research

13 pages, 1700 KiB  
Article
Knowledge Graph Completion Algorithm Based on Probabilistic Fuzzy Information Aggregation and Natural Language Processing Technology
by Canlin Zhang and Kai Lu
Mathematics 2022, 10(23), 4578; https://0-doi-org.brum.beds.ac.uk/10.3390/math10234578 - 02 Dec 2022
Cited by 2 | Viewed by 1179
Abstract
The knowledge graph was first used in the information search of the Internet as a way to improve the quality of the search because it contains a huge amount of structured knowledge data. In this paper, the knowledge map algorithm is studied through [...] Read more.
The knowledge graph was first used in the information search of the Internet as a way to improve the quality of the search because it contains a huge amount of structured knowledge data. In this paper, the knowledge map algorithm is studied through natural language processing technology and probabilistic fuzzy information aggregation, and the knowledge map completion algorithm is cognitive-fitted. NLP is natural language processing. Based on the experiments in this paper, it can be seen that, after combining the algorithm, the behavior data set of 1000 Amazon users was analyzed, and it can be found that the accuracy of the algorithm improves as the proportion of data in the experiment increases. Among them, the 10% dataset has a correct rate of 0.66; the 30% dataset has a final accuracy rate of 0.68; and the 50% dataset has a final accuracy rate of 0.70. The experimental results of this paper show that using probabilistic fuzzy information aggregation and natural language processing technology as a way to complete the knowledge graph can improve the accuracy of the operation. It plays an important role in the development of intelligent cognition and search engines. Full article
(This article belongs to the Special Issue Probability-Based Fuzzy Sets: Extensions and Applications)
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13 pages, 339 KiB  
Article
Estimation of Linear Regression with the Dimensional Analysis Method
by Luis Pérez-Domínguez, Harish Garg, David Luviano-Cruz and Jorge Luis García Alcaraz
Mathematics 2022, 10(10), 1645; https://0-doi-org.brum.beds.ac.uk/10.3390/math10101645 - 12 May 2022
Cited by 6 | Viewed by 1952
Abstract
Dimensional Analysis (DA) is a mathematical method that manipulates the data to be analyzed in a homogenized manner. Likewise, linear regression is a potent method for analyzing data in diverse fields. At the same time, data visualization has gained attention in tendency study. [...] Read more.
Dimensional Analysis (DA) is a mathematical method that manipulates the data to be analyzed in a homogenized manner. Likewise, linear regression is a potent method for analyzing data in diverse fields. At the same time, data visualization has gained attention in tendency study. In addition, linear regression is an important topic to address predictive models and patterns in data study. However, it is still pending to attack the manipulation of uncertainty related to the data transformation. In this sense, this work presents a new contribution with linear regression, combining the Dimensional Analysis (DA) to address instability and error issues. In addition, our method provides a second contribution related to including the decision maker’s attitude involved in the study. Therefore, the experimentation shows that DA manipulates the regression problem under a complex situation that the outcome may have in the investigation. A real-life case study is used to demonstrate our proposal. Full article
(This article belongs to the Special Issue Probability-Based Fuzzy Sets: Extensions and Applications)
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13 pages, 660 KiB  
Article
A Grey Incidence Based Group Decision-Making Approach and Its Application
by Huanhuan Zhao, Yunbo Yu, Sunping Qu and Yong Liu
Mathematics 2022, 10(7), 1034; https://0-doi-org.brum.beds.ac.uk/10.3390/math10071034 - 24 Mar 2022
Viewed by 1562
Abstract
We define the group measure matrix of the alternative scheme and the ideal scheme based on the relevant factor sequence and the system characteristic behavior sequence. Furthermore, the information distances of decision makers and decision criteria are defined, respectively. According to the information [...] Read more.
We define the group measure matrix of the alternative scheme and the ideal scheme based on the relevant factor sequence and the system characteristic behavior sequence. Furthermore, the information distances of decision makers and decision criteria are defined, respectively. According to the information distance, we obtain each scheme’s grey matrix incidence degree for the scheme ranking. Finally, we use an example to verify the rationality of the model and compare it with other classic methods, such as TOPSIS, VIKOR, MULTI-MOORA. Compared with previous grey incidence analysis model, the proposed model can make full use of information of the decision-maker dimension and the criteria dimension. The proposed model can avoid high-dimensional information loss. The results show that the proposed method has superiority in measuring decision-maker information and decision-making standard information. Full article
(This article belongs to the Special Issue Probability-Based Fuzzy Sets: Extensions and Applications)
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