Title of the paper title of the paper title of the paper title of the paper title of the paper title of the paper Title of the paper title of the paper (18 points font size, Aptos Display is the font name)

Author’s Name^{1 *}, Author’s Name², Author’s Name³, Author’s Name⁴, Author’s Name⁵             

^1*Department of Mathematics, University of aaaaa, Wellington, Oxford – 650 254, UK. (firstauthoremail@gmail.com)

²Department of Civil Engineering, University of bbbbb, Wellington, Oxford – 650 254, India. (secondauthoremail@gmail.com)

³Department of Computer Science Engineering, University of cccc, Wellington– 650 254, Serbia. (thirdauthoremail@gmail.com)

⁴Department of Automobile Engineering, University of ddddd, Chennai, Oxford – 650 254, India. (fourthauthoremail@gmail.com)

⁵Department of Mathematics, University of eeeee, Wellington, Oxford – 650 254, UK. (fifthauthoremail@gmail.com)

Corresponding Author e-mail: firstauthoremail@gmail.com

To cite this article:

Author’s Name. Paper Title. Journal Title. Vol. x, No. x, 2023, pp. x-x. doi: 10.11648/j.xxx.xxxxxxxx.xx.

Received: 05^th March 2024; Revised: 25^th October 2024; Accepted: 30^th October 2024; Published: 07^th November 2024.

Abstract (11 points): The International Journal of Advanced Fuzzy Sets and Systems (IJAFSS) is one of the official journals of the Gerizim Academy of Research and Development (GARD) and it is a bi-monthly peer-reviewed journal that aims to provide a platform for disseminating cutting-edge research in fuzzy sets and systems, soft computing, and related disciplines. The language of publishing is English only. The journal’s scope has been expanded to include a broader range of topics, including Fuzzy decision-making and optimization, Artificial intelligence and fuzzy systems, Fuzzy control and automation, Fuzzy image processing and computer vision, Fuzzy data mining and knowledge discovery, Fuzzy expert systems, and decision support.

Keywords: Keyword1, Keyword2 … Keyword6

1. Introduction (14points, Font name: Aptos Display)

The International Journal of Advanced Fuzzy Sets and Systems (IJAFSS) is one of the official journals of the Gerizim Academy of Research and Development (GARD) and it is a bi-monthly peer-reviewed journal that aims to provide a platform for disseminating cutting-edge research in fuzzy sets and systems, soft computing, and related disciplines. The language of publishing is English only. The journal’s scope has been expanded to include a broader range of topics, including Fuzzy decision-making and optimization, Artificial intelligence and fuzzy systems, Fuzzy control and automation, Fuzzy image processing and computer vision, Fuzzy data mining and knowledge discovery, Fuzzy expert systems and decision support

Fuzzy neural networks and machine learning, Fuzzy optimization and scheduling, Fuzzy robotics and mechatronics, Fuzzy signal processing and communications, Fuzzy systems and bioinformatics, Fuzzy human-computer interaction, Fuzzy database systems and information retrieval, Fuzzy geographic information system, Fuzzy multi-agent systems and robotics, Fuzzy natural language processing, Fuzzy time series analysis and forecasting, Fuzzy logic and its applications, Soft computing, and intelligent systems, Uncertainty modeling and analysis, Fuzzy logic, fuzzy sets, and fuzzy controls, Fuzzy set theory, Fuzzy algebraic structures, Fuzzy metric spaces, Fuzzy topological spaces, Fuzzy relational calculus and applications, Fuzzy geometry, Fuzzy projective spaces, Fuzzy measure and integral, possibility theory and imprecise probability, Fuzzy clustering and fuzzy models, Fuzzy mathematical programming, Fuzzy modeling and fuzzy control of biotechnological processes, Fuzzy neural systems, Neuro-fuzzy systems, Fuzzy systems modeling and identification. The equations are as follows:

                                                                                                                                                                            (1.1)

                                                                                                                                                          (1.2)

Fuzzy pattern recognition, Fuzzy process control, Fuzzy reasoning system, Fuzzy rule-based system, Hybrid fuzzy systems, Fuzzy sets in bioinformatics, Fuzzy system applications in human-machine interface, Fuzzy logic with engineering applications, Fuzzy dynamical systems, Adaptive fuzzy control, Fuzzy supervisory control, Perspectives on fuzzy control, Fuzzy cognitive process and applications, Fuzzy performance evaluation, Application of fuzzy logic in economics, Application of fuzzy logic in commerce, e-commerce, Application of fuzzy logic in business, Application of fuzzy logic in the stock market, Industrial applications of fuzzy sets and systems, Intuitionistic fuzzy sets and systems, Neutrosophic sets and systems in engineering applications, Hyper sets and hypersoft sets, Plithogenic sets and systems, Fuzzy logic applications in medical, health, sustainability, Fuzzy logic applications in solving social causes.

2. Review of Literature (14 points, Font name: Aptos Display)

Uncertainty modeling and analysis, Fuzzy logic, fuzzy sets, and fuzzy controls [1], Fuzzy set theory, Fuzzy algebraic structures, Fuzzy metric spaces, Fuzzy topological spaces, Fuzzy relational calculus and applications, Fuzzy geometry, Fuzzy projective spaces [2], Fuzzy measure and integral [3], possibility theory and imprecise probability is discussed by Anand [4], Fuzzy clustering and fuzzy models is proposed by Tan [5], Fuzzy mathematical programming, Fuzzy modeling and fuzzy control of biotechnological processes, Fuzzy neural systems.

• Subtitle or subsection

The International Journal of Advanced Fuzzy Sets and Systems (IJAFSS) is one of the official journals of the Gerizim Academy of Research and Development (GARD) and it is a bi-monthly peer-reviewed journal that aims to provide a platform for disseminating cutting-edge research in fuzzy sets and systems, soft computing, and related disciplines.

• Subtitle or subsection

The International Journal of Advanced Fuzzy Sets and Systems (IJAFSS) is one of the official journals of the Gerizim Academy of Research and Development (GARD) and it is a bi-monthly peer-reviewed journal that aims to provide a platform for research in fuzzy sets and systems, soft computing, and related disciplines. All equations must be typed in the equation editor through Microsoft Word, the format of the equations is discussed in the following section 2.3.                    

• Equations

The International Journal of Advanced Fuzzy Sets and Systems (IJAFSS) is one of the official journals of the Gerizim Academy of Research and Development (GARD) and it is a bi-monthly peer-reviewed journal that aims to provide a platform for disseminating cutting-edge the following equation (2.1) says that, research in fuzzy sets and systems, soft computing, and related disciplines. The equations are as follows:

                                                                                                                                                                                                                                               (2.1)

The above equation (2.1) is one of the trigonometric formulas, which is discussed in section 2.3 and deals with the subsection and is discussed by Clement et., [3]. The International Journal of Advanced Fuzzy Sets and Systems (IJAFSS) is one of the official journals of the Gerizim Academy of Research and Development (GARD).

3. Basis Definitions and Theorems (14 points, Font name: Aptos Display)

Uncertainty modeling and analysis, Fuzzy logic, fuzzy sets, and fuzzy controls, Fuzzy set theory, Fuzzy algebraic structures, Fuzzy metric spaces, Fuzzy topological spaces, Fuzzy relational calculus and applications, Fuzzy geometry, Fuzzy projective spaces, Fuzzy measure and integral, possibility theory and imprecise probability, Fuzzy clustering and fuzzy models, Fuzzy mathematical programming, Fuzzy modeling and fuzzy control of biotechnological processes, Fuzzy neural systems.

Definition 3.1 [Fuzzy Sets]

A fuzzy set is a set whose elements have degrees of membership. Fuzzy sets are an extension of the classical notion of set (known as a Crisp Set). More mathematically, a fuzzy set is a pair where  is a set and . For all , is called the grade of membership of .

Definition 3.2 [Intuitionistic Fuzzy Sets]

A fuzzy set is a set whose elements have degrees of membership. Fuzzy sets are an extension of the classical notion of set (known as a Crisp Set). More mathematically, a fuzzy set is a pair where  is a set and . For all , is called the grade of membership of .

Definition 3.3 [Neutrosophic Fuzzy Sets]

A fuzzy set is a set whose elements have degrees of membership. Fuzzy sets are an extension of the classical notion of set (known as a Crisp Set). More mathematically, a fuzzy set is a pair where  is a set and . For all , is called the grade of membership of .

Theorem 3.1 [Fuzzy homomorphism theorems]

Statement: Gerizim Academy of Research and Development (GARD) is a bi-monthly peer-reviewed journal that aims to provide a platform for disseminating cutting-edge research in fuzzy sets and systems, soft computing, and related disciplines

Proof: Gerizim Academy of Research and Development (GARD) is a bi-monthly peer-reviewed journal that aims to provide a platform for disseminating cutting-edge research in fuzzy sets and systems, soft computing, and related disciplines. Hence the proof.

Theorem 3.3 [Fuzzy fundamental theorem of homomorphism]

Statement: Gerizim Academy of Research and Development (GARD) is a bi-monthly peer-reviewed journal that aims to provide a platform for disseminating cutting-edge research in fuzzy sets and systems, soft computing, and related disciplines

Proof: Gerizim Academy of Research and Development (GARD) is a bi-monthly peer-reviewed journal that aims to provide a platform for disseminating cutting-edge research in fuzzy sets and systems, soft computing, and related disciplines. Hence the proof.

• Subtitle or subsection

Definition 3.1 deals with the fuzzy sets and theorem 3.1 talks about the fuzzy homomorphism theorem is discussed and theorem 3.2 discusses the fuzzy fundamental theorem of homomorphism in the International Journal of Advanced Fuzzy Sets and Systems (IJAFSS) is one of the official journals of the Gerizim Academy of Research and Development (GARD) and it is a bi-monthly peer-reviewed journal that aims to provide a platform for disseminating cutting-edge research in fuzzy sets and systems, soft computing, and related disciplines.

• Subtitle or subsection

The International Journal of Advanced Fuzzy Sets and Systems (IJAFSS) is one of the official journals of the Gerizim Academy of Research and Development (GARD) and it is a bi-monthly peer-reviewed journal that aims to provide a platform for research in fuzzy sets and systems, soft computing, and related disciplines. All equations must be typed in the equation editor through Microsoft Word, the format of the equations is discussed in the following section 3.3.                    

• Equations

The International Journal of Advanced Fuzzy Sets and Systems (IJAFSS) is one of the official journals of the Gerizim Academy of Research and Development (GARD) and it is a bi-monthly peer-reviewed journal that aims to provide a platform for disseminating cutting-edge the following equation (2.1) says that, research in fuzzy sets and systems, soft computing, and related disciplines. The equations are as follows:

                                                                                                                                                    (3.1)

                                                                                                                                                               (3.2)

The above equation (3.2) is one of the trigonometric formulas, which is discussed in section 3.3 and deals with the subsection and is discussed by Clement et., [3]. The International Journal of Advanced Fuzzy Sets and Systems (IJAFSS) is one of the official journals of the Gerizim Academy of Research and Development (GARD).

4. Proposed Methods (14 points, Font name: Aptos Display)

Uncertainty modeling and analysis, Fuzzy logic, fuzzy sets, and fuzzy controls, Fuzzy set theory, Fuzzy algebraic structures, Fuzzy metric spaces, Fuzzy topological spaces, Fuzzy relational calculus and applications, Fuzzy geometry, Fuzzy projective spaces, Fuzzy measure and integral, possibility theory and imprecise probability, Fuzzy clustering and fuzzy models, Fuzzy mathematical programming, Fuzzy modeling and fuzzy control of biotechnological processes, Fuzzy neural systems.

Definition 4.1 [Type -1 Fuzzy Sets]

A fuzzy set is a set whose elements have degrees of membership. Fuzzy sets are an extension of the classical notion of set (known as a Crisp Set). More mathematically, a fuzzy set is a pair where  is a set and . For all , is called the grade of membership of .

Definition 4.2 [Type -2 Fuzzy Sets]

A fuzzy set is a set whose elements have degrees of membership. Fuzzy sets are an extension of the classical notion of set (known as a Crisp Set). More mathematically, a fuzzy set is a pair where  is a set and . For all , is called the grade of membership of .

Definition 4.3 [Type -1 Intuitionistic Fuzzy Sets]

A fuzzy set is a set whose elements have degrees of membership. Fuzzy sets are an extension of the classical notion of set (known as a Crisp Set). More mathematically, a fuzzy set is a pair where  is a set and . For all , is called the grade of membership of .

5. Materials and Methods (14 points, Font name: Aptos Display)

Uncertainty modeling and analysis, Fuzzy logic, fuzzy sets, and fuzzy controls, Fuzzy set theory, Fuzzy algebraic structures, Fuzzy metric spaces, Fuzzy topological spaces, Fuzzy relational calculus and applications, Fuzzy geometry, Fuzzy projective spaces, Fuzzy measure and integral, possibility theory and imprecise probability, Fuzzy clustering and fuzzy models, Fuzzy mathematical programming, Fuzzy modeling and fuzzy control of biotechnological processes, Fuzzy neural systems.

Algorithm 5.1 [Fuzzy Optimization Algorithm]

A fuzzy set is a set whose elements have degrees of membership. Fuzzy sets are an extension of the classical notion of set (known as a Crisp Set). More mathematically, a fuzzy set is a pair where  is a set and . For all , is called the grade of membership of .

6. Results and Discussions (14 points, Font name: Aptos Display)

Uncertainty modeling and analysis, the algorithm 5.1 discusses fuzzy optimization, Fuzzy logic, fuzzy sets, and fuzzy controls, Fuzzy set theory, Fuzzy algebraic structures, Fuzzy metric spaces, Fuzzy topological spaces, Fuzzy relational calculus and applications, Fuzzy geometry, Fuzzy projective spaces, Fuzzy measure and integral, possibility theory and imprecise probability, Fuzzy clustering and fuzzy models, Fuzzy mathematical programming, Fuzzy modeling and fuzzy control of biotechnological processes, Fuzzy neural systems.

Figure 1: The caption of the figure

Uncertainty modeling in Figure 1 is the sample of the figure and analysis, Fuzzy logic, fuzzy sets, and fuzzy controls, Fuzzy set theory, Fuzzy algebraic structures, Fuzzy metric spaces, Fuzzy topological spaces, Fuzzy relational calculus and applications, Fuzzy geometry, Fuzzy projective spaces, Fuzzy measure and integral, possibility theory and imprecise probability, Fuzzy clustering, and fuzzy models. The following Table 1 discusses the reinforcement learning of the raw data, which will help us to understand the effectiveness of the proposed model.

Table 1: Reinforcement learning of the raw data

The International Journal of Advanced Fuzzy Sets and Systems (IJAFSS) is one of the official journals of the Gerizim Academy of Research and Development (GARD) and it is a bi-monthly peer-reviewed journal that aims to provide a platform for disseminating cutting-edge research in fuzzy sets and systems, soft computing, and related disciplines.

7. Conclusion (14 points, Font name: Aptos Display)

The International Journal of Advanced Fuzzy Sets and Systems (IJAFSS) is one of the official journals of the Gerizim Academy of Research and Development (GARD) and it is a bi-monthly peer-reviewed journal that aims to provide a platform for disseminating cutting-edge research in fuzzy sets and systems, soft computing, and related disciplines. The International Journal of Advanced Fuzzy Sets and Systems (IJAFSS) is one of the official journals of the Gerizim Academy of Research and Development (GARD) and it is a bi-monthly peer-reviewed journal that aims to provide a platform for disseminating cutting-edge research in fuzzy sets and systems, soft computing, and related disciplines. The International Journal of Advanced Fuzzy Sets and Systems (IJAFSS) is one of the official journals of the Gerizim Academy of Research and Development (GARD) and it is a bi-monthly peer-reviewed journal that aims to provide a platform for disseminating cutting-edge research in fuzzy sets and systems, soft computing, and related disciplines.

• Suggestions

The International Journal of Advanced Fuzzy Sets and Systems (IJAFSS) is one of the official journals of the Gerizim Academy of Research and Development (GARD) and it is a bi-monthly peer-reviewed journal that aims to provide a platform for disseminating cutting-edge research in fuzzy sets and systems, soft computing, and related disciplines. The International Journal of Advanced Fuzzy Sets and Systems (IJAFSS) is one of the official journals of the Gerizim Academy of Research and Development (GARD) and it is a bi-monthly peer-reviewed journal that aims to provide a platform for disseminating cutting-edge research in fuzzy sets and systems, soft computing, and related disciplines.

List of Abbreviations:

FN                               – Fuzzy Number

TrFN               – Triangular Fuzzy Number

TpFN              – Trapezoidal Fuzzy Number

MCDM                        – Multi-Criteria Decision-Making Problem

____________________________________________________________________________________________

Acknowledgments: (Sample) The first author (Xinming Shi): Conceptualization, methodology, formal analysis, software, writing – original draft preparation; The second author (Peide Liu): Conceptualization, methodology, investigation, validation, writing – review and editing, supervision, funding acquisition. The third author (Yifan Wu): Conceptualization, investigation, validation, Soft, writing – review and editing, supervision. The fourth author (Xiaoming Wu): investigation, validation, Soft, Data, writing – review and editing, fund. This article does not contain any studies with human participants or animals performed by any of the authors.

Disclosure statement: (Sample) No potential conflict of interest was reported by the author(s).

Data availability statement: The data used in this manuscript are artificial and can be used without permission from the authors if the present article is appropriately cited.

Funding Agency: (Sample)This paper is supported by the National Natural Science Foundation of China (62473xxx9, 72101134, 720001154), Shandong Provincial Key Research and Development Program (Major Scientific and Technological Innovation Project) (No. 2021SFGC0102), Major bidding projects of National Social Science Fund of China (No. 19ZD88880), Taishan Scholars Project of Shandong Province, Jinan Scientific Research Leader Studio (202388068).

Appendixes: (Sample) The International Journal of Advanced Fuzzy Sets and Systems (IJAFSS) is one of the official journals of the Gerizim Academy of Research and Development (GARD). It is a bi-monthly peer-reviewed journal that aims to provide a platform for disseminating cutting-edge research in fuzzy sets and systems, soft computing, and related disciplines.

______________________________________________________________________________________________________________

References

• Ballard, T., (2017); The dynamics of avoidance goal regulation. Motivation and Emotion, 25(3), pp.1-10. https://doi.org/10.1007/s11031-017-9640-8
• Brown, C. G., & Xung. A. M., (2023); The potential of dogs to improve the acceptability of trauma‐focused therapies for children.Australian Journal of Engineering, 70(5), pp. 208-216. https://doi.org/10.1111/aje.12199
• Brown, C. G., Lee, T., & Chung, K., (2024); The potential of dogs to improve the acceptability of trauma‐focused therapies for children.Australian Journal of Engineering, 70(5), pp. 208-216. https://doi.org/10.1111/aje.12199
• Brown, C. G., et. al., (2021); The potential of dogs to improve the acceptability of trauma‐focused therapies for children.International Journal of Fuzzy Systems, 70(5), pp. 208-216. https://doi.org/10.1111/aje.12199
• Kushilevitz, E., & Malkin, T. (Eds.), (2016); Lecture notes in computer science: Vol. 9562. Theory of cryptography. Springer. https://doi.org/10.1007/978-3-662-49096-9
• Duckworth, A. L., Kelly, D. R., & Matthews, M. D., (2019); Cognitive and noncognitive predictors of success. Proceedings of the National Academy of Sciences, USA, 116(47), 23499–23504. https://doi.org/10.1073/pnas.1910510116
• Bedenel, A. L., Jourdan, L., & Biernacki, C., (2019); Probability estimation by an adapted genetic algorithm in web insurance. In R. Battiti, M. Brunato, I. Kotsireas, & P. Pardalos (Eds.), Lecture notes in computer science: Vol. 11353. Learning and intelligent optimization, pp. 225–240, Springer. https://doi.org/10.1007/978-3-030-05348-2_21
• Aron, L., Botella, M., & Lubart, T., (2019); Talent and their development. In Subotnik, R. F., Olszewski-Kubilius, P & Worrell, F. C. (Eds.), The psychology of high performance: Developing human potential into domain-specific talent, Vol. 56897, pp. 345–359. American Psychological Association. https://doi.org/10.1037/0000120-016
• Smith, J., (2024, November 25). The impact of climate change. Retrieved from https://www.worldometers.info/coronavirus/