## Topic Editors Prof. Dr. Changyou Wang
College of Applied Mathematics, Chengdu University of Information Technology, Chengdu 610225, China College of Science, Chongqing University of Posts and Telecommunications, Chongqing 400065, China School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001, China

# Fuzzy Number, Fuzzy Difference, Fuzzy Differential: Theory and Applications

20 October 2023
20 December 2023
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3619

## Topic Information

Dear Colleagues,

With the rapid development of new technologies such as artificial intelligence and big date, as the mathematical basis of artificial intelligence, fuzzy set theory has always been concerned by scholars. And fuzzy analysis theory is an important part of it. As the basic concept of fuzzy analysis, fuzzy number, fuzzy difference, fuzzy differential, etc. involve many related important theories, such as: fuzzy difference equation, fuzzy differential equation, fuzzy optimization, fuzzy game, fuzzy decision-making, fuzzy control, etc. Therefore, it is necessary to study the fuzzy number, fuzzy difference, fuzzy differential and related theories and applications.

This Topic, “Fuzzy Number, Fuzzy Difference, Fuzzy Differential：Theory and  Applications”, invites papers on theoretical and applied issues, including, but not limited to, the following:

• Theories and applications of fuzzy Number.
• Theories and applications of fuzzy difference equation.
• Theories and applications of fuzzy differential equation.
• Techniques and algorithms of fuzzy optimization.
• Strategy of fuzzy game.
• Methods and analysis fuzzy decision-making.
• Techniques and methods of fuzzy control.
• This Topic will present the results of research describing recent advances in fuzzy number, fuzzy difference, and fuzzy differential.

Prof. Dr. Changyou Wang
Prof. Dr. Dong Qiu
Dr. Yonghong Shen
Topic Editors

## Keywords

•  fuzzy number
•  fuzzy difference equation
•  fuzzy differential equation
•  fuzzy optimization
•  fuzzy decision-making
•  fuzzy game
•  fuzzy control

## Participating Journals

Journal Name Impact Factor CiteScore Launched Year First Decision (median) APC Algorithms
algorithms
2.3 3.7 2008 19.1 Days CHF 1600 Axioms
axioms
2.0 2.2 2012 20 Days CHF 2400 Information
information
3.1 5.8 2010 22.6 Days CHF 1600 Mathematics
mathematics
2.4 3.5 2013 17.7 Days CHF 2600 Symmetry
symmetry
2.7 4.9 2009 14.7 Days CHF 2400 Preprints is a platform dedicated to making early versions of research outputs permanently available and citable. MDPI journals allow posting on preprint servers such as Preprints.org prior to publication. For more details about reprints, please visit https://www.preprints.org.

## Published Papers (4 papers)

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Article
Interval-Valued Topology on Soft Sets
Axioms 2023, 12(7), 692; https://doi.org/10.3390/axioms12070692 - 16 Jul 2023
Viewed by 402
Abstract
In this paper, we study the concept of interval-valued fuzzy set on the family $\mathsf{SS}\left(X,E\right)$ of all soft sets over X with the set of parameters E and examine its basic properties. Later, we define the concept of interval-valued fuzzy [...] Read more.
In this paper, we study the concept of interval-valued fuzzy set on the family $\mathsf{SS}\left(X,E\right)$ of all soft sets over X with the set of parameters E and examine its basic properties. Later, we define the concept of interval-valued fuzzy topology (cotopology) $\tau$ on $\mathsf{SS}\left(X,E\right)$. We obtain that each interval-valued fuzzy topology is a descending family of soft topologies. In addition, we study some topological structures such as interval-valued fuzzy neighborhood system of a soft point, base and subbase of $\tau$ and investigate some relationships among them. Finally, we give some concepts such as direct sum, open mapping and continuous mapping and consider connections between them. A few examples support the presented results. Full article
Article
Multiple-Attribute Decision Making Based on the Probabilistic Dominance Relationship with Fuzzy Algebras
Symmetry 2023, 15(6), 1188; https://doi.org/10.3390/sym15061188 - 02 Jun 2023
Cited by 1 | Viewed by 471
Abstract
In multiple-attribute decision-making (MADM) problems, ranking the alternatives is an important step for making the best decision. Intuitionistic fuzzy numbers (IFNs) are a powerful tool for expressing uncertainty and vagueness in MADM problems. However, existing ranking methods for IFNs do not consider the [...] Read more.
In multiple-attribute decision-making (MADM) problems, ranking the alternatives is an important step for making the best decision. Intuitionistic fuzzy numbers (IFNs) are a powerful tool for expressing uncertainty and vagueness in MADM problems. However, existing ranking methods for IFNs do not consider the probabilistic dominance relationship between alternatives, which can lead to inconsistent and inaccurate rankings. In this paper, we propose a new ranking method for IFNs based on the probabilistic dominance relationship and fuzzy algebras. The proposed method is able to handle incomplete and uncertain information and can generate consistent and accurate rankings. Full article
Article
New Arithmetic Operations of Non-Normal Fuzzy Sets Using Compatibility
Axioms 2023, 12(3), 277; https://doi.org/10.3390/axioms12030277 - 07 Mar 2023
Cited by 1 | Viewed by 758
Abstract
The new arithmetic operations of non-normal fuzzy sets are studied in this paper by using the extension principle and considering the general aggregation function. Usually, the aggregation functions are taken to be the minimum function or t-norms. In this paper, we considered a [...] Read more.
The new arithmetic operations of non-normal fuzzy sets are studied in this paper by using the extension principle and considering the general aggregation function. Usually, the aggregation functions are taken to be the minimum function or t-norms. In this paper, we considered a general aggregation function to set up the arithmetic operations of non-normal fuzzy sets. In applications, the arithmetic operations of fuzzy sets are always transferred to the arithmetic operations of their corresponding $\alpha$-level sets. When the aggregation function is taken to be the minimum function, this transformation is clearly realized. Since the general aggregation function was adopted in this paper, the concept of compatibility with $\alpha$-level sets is needed and is proposed, which can cover the conventional case using minimum functions as the special case. Full article
Article
Best Approximation Results for Fuzzy-Number-Valued Continuous Functions
Axioms 2023, 12(2), 192; https://doi.org/10.3390/axioms12020192 - 11 Feb 2023
Viewed by 622
Abstract
In this paper, we study the best approximation of a fixed fuzzy-number-valued continuous function to a subset of fuzzy-number-valued continuous functions. We also introduce a method to measure the distance between a fuzzy-number-valued continuous function and a real-valued one. Then, we prove the [...] Read more.
In this paper, we study the best approximation of a fixed fuzzy-number-valued continuous function to a subset of fuzzy-number-valued continuous functions. We also introduce a method to measure the distance between a fuzzy-number-valued continuous function and a real-valued one. Then, we prove the existence of the best approximation of a fuzzy-number-valued continuous function to the space of real-valued continuous functions by using the well-known Michael selection theorem. Full article