Paper Info
Title
Fuzzy Mixed Variational-like and Integral Inequalities for Strongly Preinvex Fuzzy Mappings
Abstract
It is a familiar fact that convex and non-convex fuzzy mappings play a critical role in the study of fuzzy optimization. Due to the behavior of its definition, the idea of convexity plays a significant role in the subject of inequalities. The concepts of convexity and symmetry have a tight connection. We may use whatever we learn from one to the other, thanks to the significant correlation that has developed between both in recent years. Our aim is to consider a new class of fuzzy mappings (FMs) known as strongly preinvex fuzzy mappings (strongly preinvex-FMs) on the invex set. These FMs are more general than convex fuzzy mappings (convex-FMs) and preinvex fuzzy mappings (preinvex-FMs), and when generalized differentiable (briefly, G-differentiable), strongly preinvex-FMs are strongly invex fuzzy mappings (strongly invex-FMs). Some new relationships among various concepts of strongly preinvex-FMs are established and verified with the support of some useful examples. We have also shown that optimality conditions of G-differentiable strongly preinvex-FMs and the fuzzy functional, which is the sum of G-differentiable preinvex-FMs and non G-differentiable strongly preinvex-FMs, can be distinguished by strongly fuzzy variational-like inequalities and strongly fuzzy mixed variational-like inequalities, respectively. In the end, we have established and verified a strong relationship between the Hermite-Hadamard inequality and strongly preinvex-FM. Several exceptional cases are also discussed. These inequalities are a very interesting outcome of our main results and appear to be new ones. The results in this research can be seen as refinements and improvements to previously published findings.</p>
Year
DOI
Venue
2021
10.3390/sym13101816
SYMMETRY-BASEL
Keywords
DocType
Volume
preinvex fuzzy mappings, strongly preinvex fuzzy mappings, strongly invex fuzzy mappings, strongly fuzzy monotonicity, strongly fuzzy mixed variational-like inequalities
Journal
13
Issue
Citations 
PageRank 
10
0
0.34
References 
Authors
0
4
Name
Order
Citations
PageRank
Muhammad Bilal Khan173.26
Hari Mohan Srivastava204.73
Pshtiwan Othman Mohammed300.34
Juan Luis García Guirao421.80