2021
DOI: 10.1186/s13662-021-03245-8
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New Hermite–Hadamard-type inequalities for "Equation missing"-convex fuzzy-interval-valued functions

Abstract: In this paper, we introduce the non-convex interval-valued functions for fuzzy-interval-valued functions, which are called "Equation missing"-convex fuzzy-interval-valued functions, by means of fuzzy order relation. This fuzzy order relation is defined level-wise through Kulisch–Miranker order relation given on the interval space. By using the "Equation missing"-convexity concept, we present fuzzy-interval Hermite–Hadamard inequalities for fuzzy-interval-valued functions. Several exceptional cases are debated,… Show more

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Cited by 75 publications
(21 citation statements)
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“…Due to the vast applications of convexity and fractional HH-inequality in mathematical analysis and optimization, many authors have discussed the applications, refinements, generalizations, and extensions, see [27][28][29][30][31][32][33][34][35][36][37][38] and the references therein.…”
Section: Introductionmentioning
confidence: 99%
“…Due to the vast applications of convexity and fractional HH-inequality in mathematical analysis and optimization, many authors have discussed the applications, refinements, generalizations, and extensions, see [27][28][29][30][31][32][33][34][35][36][37][38] and the references therein.…”
Section: Introductionmentioning
confidence: 99%
“…and , ς) and 1 = ς and χ(s) = s, then from (31) and (36) one achieves coming inequality given in [27]:…”
Section: 𝜉 ≼ 𝜛 If and Only If [𝜉] ≤ [𝜛]mentioning
confidence: 78%
“…Khan et al [24][25][26][27] extended the class of convex F•Ms and defined h-convex and (h 1 , h 2 )-convex F-IV-Fs using fuzzy partial order relation. Moreover, they introduced H.H, Hermite-Hadamard-Fejér (H.H Fejér), fractional H.H and H.H Fejér for h-convex and (h 1 , h 2 )-convex F•I•V•Fs via fuzzy Riemannian and fuzzy Riemann-Liouville fractional integrals.…”
Section: Introductionmentioning
confidence: 99%
“…Moreover, Khan et al [21] exploited fuzzy order relations to introduce a new class of convex fuzzy-interval-valued functions (convex F-I•V-Fs), known as (h 1 , h 2 )-convex F-I•V-Fs, as well as a novel version of the H-H type inequality for (h 1 , h 2 )-convex F-I•V-Fs that incorporates the fuzzy interval Riemann integral. Khan et al went a step further by providing new convex and extended convex I•V-F classes, as well as new fractional H-H type and H-H type inequalities for left and right (h 1 , h 2 )-preinvex I•V-F [22], left and right p-convex I•V-Fs [23], left and right log-h-convex I•V-Fs [24], and the references therein.…”
Section: Introductionmentioning
confidence: 99%