Some New Classes of Preinvex Fuzzy-Interval-Valued Functions and Inequalities

Khan, Muhammad Bilal; Noor, Muhammad Aslam; Abdullah, Lazim; Chu, Yu‐Ming

doi:10.2991/ijcis.d.210409.001

Cited by 64 publications

(21 citation statements)

References 49 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…They demonstrated the validity of characterizations with help of examples, and improved the previous results provided by Li and Noor [27]. We refer to the readers for further analysis of literature on the applications and properties of variational-like inequalities and generalized convex fuzzy mappings, see [2,9,16,[30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47] and the references therein.…”

Section: Introductionsupporting

confidence: 67%

“…The inequality of the type ( 43) is called HOS-fuzzy variational-like inequality. It is very important to note that the optimality condition of preinvex fuzzy mappings can't be obtained with the help of (43). So this idea inspires us to introduce a more general form of fuzzy variationallike inequality of which ( 43) is a special case.…”

Section: Higher-order Strongly Fuzzy Mixed Variational-like Inequalitiesmentioning

confidence: 99%

See 1 more Smart Citation

Higher-Order Strongly Preinvex Fuzzy Mappings and Fuzzy Mixed Variational-Like Inequalities

Khan¹,

Noor²,

Noor³

et al. 2021

IJCIS

Self Cite

View full text Add to dashboard Cite

A family of fuzzy mappings is called higher-order strongly preinvex fuzzy mappings (HOS-preinvex fuzzy mappings), which take the place of generalization of the notion of nonconvexity is introduced through the "fuzzy-max" order among fuzzy numbers. This family properly includes the family of preinvex fuzzy mappings and is included in the family of quasi preinvex fuzzy mappings. With the support of examples, we have discussed some special cases. Some properties are derived and relations among the HOS-preinvex fuzzy mappings, HOS-invex fuzzy mappings, and fuzzy HOS-monotonicity are obtained under some mild conditions. Then, we have shown that optimality conditions of generalized differentiable HOS-preinvex fuzzy mappings and for the sum of generalized differentiable (briefly, G-differentiable) preinvex fuzzy mappings and nongeneralized differentiable HOSpreinvex fuzzy mappings can be distinguished by HOS-fuzzy variational-like inequalities and HOS-fuzzy mixed variational-like inequalities, respectively which can be viewed as novel applications. These inequalities are very interesting outcome of our main results and appear to be new ones. Several exceptional cases are debated. Presented results in this paper can be considered and development of previously established results.

show abstract

Section: Introductionsupporting

confidence: 67%

Section: Higher-order Strongly Fuzzy Mixed Variational-like Inequalitiesmentioning

confidence: 99%

Higher-Order Strongly Preinvex Fuzzy Mappings and Fuzzy Mixed Variational-Like Inequalities

Khan¹,

Noor²,

Noor³

et al. 2021

IJCIS

Self Cite

View full text Add to dashboard Cite

show abstract

“…Remark 3. [41] If one attempt to take χ 2 (s) ≡ 1, then from (χ 1 , χ 2 )-pre-invex F-IV-F one achieves χ-pre-invex F-IV-F, that is…”

Section: 𝜉 ≼ 𝜛 If and Only If [𝜉] ≤ [𝜛]mentioning

confidence: 99%

“…Theorem 2. [41] Let χ : [0, 1] ⊆ [t, υ] → R be a non-negative real-valued function such that χ0 and let U : [t, υ] → F 0 be a F-IV-F, whose ς-cuts define the family of IV-Fs…”

Section: 𝜉 ≼ 𝜛 If and Only If [𝜉] ≤ [𝜛]mentioning

confidence: 99%

Some New Versions of Hermite–Hadamard Integral Inequalities in Fuzzy Fractional Calculus for Generalized Pre-Invex Functions via Fuzzy-Interval-Valued Settings

et al. 2022

Self Cite

View full text Add to dashboard Cite

The purpose of this study is to prove the existence of fractional integral inclusions that are connected to the Hermite–Hadamard and Hermite–Hadamard–Fejér type inequalities for χ-pre-invex fuzzy-interval-valued functions. Some of the related fractional integral inequalities are also proved via Riemann–Liouville fractional integral operator, where integrands are fuzzy-interval-valued functions. To prove the validity of our main results, some of the nontrivial examples are also provided. As specific situations, our findings can provide a variety of new and well-known outcomes which can be viewed as applications of our main results. The results in this paper can be seen as refinements and improvements to previously published findings.

show abstract

“…wherẽis a convex fuzzy-IVF. We urge the readers to [32][33][34][35][36][37][38][39][40][41][42] and the citations therein for further review of related literature on the implementations and characterization of fuzzy-interval, inequalities and generalized convex fuzzy mappings.…”

Section: Introductionmentioning

confidence: 99%

Harmonically Convex Fuzzy-Interval-Valued Functions and Fuzzy-Interval Riemann–Liouville Fractional Integral Inequalities

Sana¹,

Khan²,

Noor³

et al. 2021

IJCIS

Self Cite

View full text Add to dashboard Cite

It is well known that the concept of convexity establishes strong relationship with integral inequality for single-valued and interval-valued function. The single-valued function and interval-valued function both are special cases of fuzzy interval-valued function. The aim of this paper is to introduce a new class of convex fuzzy interval-valued functions, which is called harmonically convex fuzzy interval-valued functions (harmonically convex fuzzy-IVFs) by means of fuzzy order relation and to investigate this new class via fuzzy-interval Riemann-Liouville fractional operator. With the help of fuzzy order relation and fuzzyinterval Riemann-Liouville fractional, we derive some integrals inequalities of Hermite-Hadamard (H-H) type and Hermite-Hadamard-Fejér (H-H Fejér) type as well as some product inequities for harmonically convex fuzzy-IVFs. Our results represent a significant improvement and refinement of the known results. We hope that these interesting outcomes may open a new direction for fuzzy optimization, modeling and interval-valued function.

show abstract

Some New Classes of Preinvex Fuzzy-Interval-Valued Functions and Inequalities

Cited by 64 publications

References 49 publications

Higher-Order Strongly Preinvex Fuzzy Mappings and Fuzzy Mixed Variational-Like Inequalities

Higher-Order Strongly Preinvex Fuzzy Mappings and Fuzzy Mixed Variational-Like Inequalities

Some New Versions of Hermite–Hadamard Integral Inequalities in Fuzzy Fractional Calculus for Generalized Pre-Invex Functions via Fuzzy-Interval-Valued Settings

Harmonically Convex Fuzzy-Interval-Valued Functions and Fuzzy-Interval Riemann–Liouville Fractional Integral Inequalities

Contact Info

Product

Resources

About