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In this article, firstly, we establish a novel definition of weighted interval-valued fractional integrals of a function <inline-formula><math display="inline"><semantics><mover accent="true"><mi mathvariant="sans-serif">Υ</mi><mo>˘</mo></mover></semantics></math></inline-formula> using an another function <inline-formula><math display="inline"><semantics><mrow><mi>ϑ</mi><mo>(</mo><mover accent="true"><mi>ζ</mi><mo>˙</mo></mover><mo>)</mo></mrow></semantics></math></inline-formula>. As an additional observation, it is noted that the new class of weighted interval-valued fractional integrals of a function <inline-formula><math display="inline"><semantics><mover accent="true"><mi mathvariant="sans-serif">Υ</mi><mo>˘</mo></mover></semantics></math></inline-formula> by employing an additional function <inline-formula><math display="inline"><semantics><mrow><mi>ϑ</mi><mo>(</mo><mover accent="true"><mi>ζ</mi><mo>˙</mo></mover><mo>)</mo></mrow></semantics></math></inline-formula> characterizes a variety of new classes as special cases, which is a generalization of the previous class. Secondly, we prove a new version of the Hermite-Hadamard-Fejér type inequality for <i>h</i>-convex interval-valued functions using weighted interval-valued fractional integrals of a function <inline-formula><math display="inline"><semantics><mover accent="true"><mi mathvariant="sans-serif">Υ</mi><mo>˘</mo></mover></semantics></math></inline-formula> according to another function <inline-formula><math display="inline"><semantics><mrow><mi>ϑ</mi><mo>(</mo><mover accent="true"><mi>ζ</mi><mo>˙</mo></mover><mo>)</mo><mo>.</mo></mrow></semantics></math></inline-formula> Finally, by using weighted interval-valued fractional integrals of a function <inline-formula><math display="inline"><semantics><mover accent="true"><mi mathvariant="sans-serif">Υ</mi><mo>˘</mo></mover></semantics></math></inline-formula> according to another function <inline-formula><math display="inline"><semantics><mrow><mi>ϑ</mi><mo>(</mo><mover accent="true"><mi>ζ</mi><mo>˙</mo></mover><mo>)</mo></mrow></semantics></math></inline-formula>, we are establishing a new Hermite-Hadamard-Fejér type inequality for harmonically <i>h</i>-convex interval-valued functions that is not previously known. Moreover, some examples are provided to demonstrate our results.