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

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

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	Submit
Axioms axioms	2.0	2.2	2012	20 Days	CHF 2400	Submit
Information information	3.1	5.8	2010	22.6 Days	CHF 1600	Submit
Mathematics mathematics	2.4	3.5	2013	17.7 Days	CHF 2600	Submit
Symmetry symmetry	2.7	4.9	2009	14.7 Days	CHF 2400	Submit

Published Papers (4 papers)

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Journals

All Algorithms Axioms Information Mathematics Symmetry

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Open AccessArticle

Interval-Valued Topology on Soft Sets

by

Sadi Bayramov

,

Çiğdem Gündüz Aras

and

Ljubiša D. R. Kočinac

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

(This article belongs to the Topic Fuzzy Number, Fuzzy Difference, Fuzzy Differential: Theory and Applications)

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Open AccessArticle

Multiple-Attribute Decision Making Based on the Probabilistic Dominance Relationship with Fuzzy Algebras

by

Amir Baklouti

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

(This article belongs to the Topic Fuzzy Number, Fuzzy Difference, Fuzzy Differential: Theory and Applications)

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Open AccessArticle

New Arithmetic Operations of Non-Normal Fuzzy Sets Using Compatibility

by

Hsien-Chung Wu

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

(This article belongs to the Topic Fuzzy Number, Fuzzy Difference, Fuzzy Differential: Theory and Applications)

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Open AccessArticle

Best Approximation Results for Fuzzy-Number-Valued Continuous Functions

by

Juan J. Font

and

Sergio Macario

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

(This article belongs to the Topic Fuzzy Number, Fuzzy Difference, Fuzzy Differential: Theory and Applications)

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