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International Journal of Fuzzy Logic and Intelligent Systems 2021; 21(3): 233-242

Published online September 25, 2021

https://doi.org/10.5391/IJFIS.2021.21.3.233

© The Korean Institute of Intelligent Systems

Convexity-Cum-Concavity on Fuzzy Soft Expert Set with Certain Properties

Muhammad Ihsan1, Atiqe Ur Rahman1, Muhammad Saeed1, and Hamiden Abd El-Wahed Khalifa2

1Department of Mathematics, University of Management and Technology, Lahore, Pakistan
2Department of Mathematics, College of Science and Arts, Qassim University, Al-Badaya, Saudi Arabia

Correspondence to :
Muhammad Ihsan (mihkhb@gmail.com)

Received: December 3, 2020; Revised: June 3, 2021; Accepted: July 26, 2021

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted noncommercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Molodtsov presented the idea of the soft set theory as a universal scientific apparatus for the provisioning of a parameterization tool. Alkhazaleh and Salleh (2011) characterized the idea of soft expert sets in which the client can understand the assessment of specialists in a single pattern and allow the use of this idea for dynamic issues. In this study, we summarize the idea of a soft expert set to fuzzy soft expert set, which will be progressively viable and helpful. The idea of convex and concave sets is crucial for optimization and related theories. In this investigation, convex and concave fuzzy soft expert sets are characterized first, and a portion of their significant properties are then discussed.

Keywords: Soft set, Fuzzy soft set, Soft expert set, Convex fuzzy soft expert set, Concave fuzzy soft expert set

No potential conflicts of interest relevant to this article are reported.

Muhammad Ihsan received his M.Sc. degrees from the Department of Mathematics, University of Sargodha, M.Phil. degree from the National College of Business Administration and Economics Lahore, Pakistan in the field of inequality. He is a PhD candidate at the Department of Mathematics, University of Management and Technology, Lahore, Pakistan. His research interests include fuzzy sets, soft sets, soft expert sets, and optimization.

E-mail: mihkhb@gmail.com


Atiqe Ur Rahman received his M.Sc. degrees from the Department of Mathematics, University of Sargodha, M.Phil. degree from the National College of Business Administration and Economics Lahore, Pakistan in the field of inequality. He is a PhD candidate at the Department of Mathematics, University of Management and Technology, Lahore, Pakistan. His areas of interest are fuzzy set, intuitionistic fuzzy set, neutrosophic set, soft set, hypersoft set with their hybrids and algebraic structures, complexity, and convexity in fuzzy and soft like environments, mathematical inequalities, and time scale calculus.

E-mail: aurkhb@gmail.com


Muhammad Saeed received a Ph.D. degree from Quid-e-Azam University, Islamabad, Pakistan. Recently attached to the Department of Mathematics, University of Management and Technology, Lahore, Pakistan, as an associate professor. He has published more than 100 publications in peer-reviewed journals with 496 citations. He has edited a book titled, Theory and Application of Hypersoft Set. He has supervised more than 15 million students and four Ph.D. students. His areas of interest are fuzzy set theory, rough sets, soft set theory, hypersoft set, neutrosophic sets, algebraic and hybrid structures of soft sets and hypersoft sets, multi-criteria decision making, optimizations, artificial intelligence, pattern recognition and optimization under convex environments, graph theory under fuzzy-like, soft-like and hypersoft-like environments, similarity, distance measures and their relevant operators in multipolar hybrid structures, and many other research areas in pure and applied mathematics.

E-mail: muhammad.saeed@umt.edu.pk


Hamiden Abd El-Wahed Khalifa received a Ph.D. degree from the Tanta University Faculty of Science, Tanta, Gharbia Governorate, Egypt. Recently attached to the Operations Research Department, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza, Egypt, as an associate professor. She is also attached to the Department of Mathematics, College of Science and Arts, Al-Badaya, Qassim University, Saudi Arabia, for research projects. She has published more than 50 publications in peer-reviewed journals. Her areas of interest are game theory, operation research, multi-objective linear programming, fuzzy mathematics, rough sets, decision making, and optimization.

E-mail: hamiden@cu.edu.eg; ha.ahmed@qu.edu.sa


Article

Original Article

International Journal of Fuzzy Logic and Intelligent Systems 2021; 21(3): 233-242

Published online September 25, 2021 https://doi.org/10.5391/IJFIS.2021.21.3.233

Copyright © The Korean Institute of Intelligent Systems.

Convexity-Cum-Concavity on Fuzzy Soft Expert Set with Certain Properties

Muhammad Ihsan1, Atiqe Ur Rahman1, Muhammad Saeed1, and Hamiden Abd El-Wahed Khalifa2

1Department of Mathematics, University of Management and Technology, Lahore, Pakistan
2Department of Mathematics, College of Science and Arts, Qassim University, Al-Badaya, Saudi Arabia

Correspondence to:Muhammad Ihsan (mihkhb@gmail.com)

Received: December 3, 2020; Revised: June 3, 2021; Accepted: July 26, 2021

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted noncommercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Molodtsov presented the idea of the soft set theory as a universal scientific apparatus for the provisioning of a parameterization tool. Alkhazaleh and Salleh (2011) characterized the idea of soft expert sets in which the client can understand the assessment of specialists in a single pattern and allow the use of this idea for dynamic issues. In this study, we summarize the idea of a soft expert set to fuzzy soft expert set, which will be progressively viable and helpful. The idea of convex and concave sets is crucial for optimization and related theories. In this investigation, convex and concave fuzzy soft expert sets are characterized first, and a portion of their significant properties are then discussed.

Keywords: Soft set, Fuzzy soft set, Soft expert set, Convex fuzzy soft expert set, Concave fuzzy soft expert set

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