An abstract approach to convex and concave sets under refined neutrosophic set environment

Authors

  • Muhammad Arshad Department of Mathematics, University of Management and Technology Lahore, Pakistan
  • Atiqe Ur Rahman Department of Mathematics, University of Management and Technology Lahore, Pakistan
  • Muhammad Saeed 2Department of Mathematics, University of Management and Technology Lahore, Pakistan

Keywords:

Sub-belonging grade; Sub non-belonging grade; Sub-indeterminacy grade; Infimum projection; Supremum projection; Ortho-convexity; Ortho-concavity

Abstract

A refined neutrosophic set (RNS) is an extension of a neutrosophic set in which all the uncertain
belonging-based entities like belonging-grade, non-belonging-grade, and indeterminate-grade are further categorized into their respective sub-belonging grades, sub-non-belonging-grades, and sub-indeterminate-grades,
respectively. In other words, the RNS provides multi sub-grades for each uncertain component of theneutrosophic set. This study is aimed to integrate the classical concepts of convexity and concavity with RNS to make
the RNS applicable to various optimization problems.Thus, convex RNS and concave RNS are developed. Some
of their important aggregation operations and results are investigated and then modified.

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Published

2023-01-01

Issue

Vol. 53 (2023): Neutrosophic Sets and Systems

Section

Articles

License

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

 Creative Commons Attribution (CC BY) license.

How to Cite

Muhammad Arshad, Atiqe Ur Rahman, & Muhammad Saeed. (2023). An abstract approach to convex and concave sets under refined neutrosophic set environment. Neutrosophic Sets and Systems, 53, 274-296. https://fs.unm.edu/nss8/index.php/111/article/view/3227