List manipulation: conditional result based on variable-length sublists

Suppose I have the following lists:

eqexp={a,b,c,d}
eqval={e,f,g,h}
signval={{},{1},{-1},{1,-1}}

I want to create a new list of inequalities, where the signval list signals whether to use greater than or less than. I need it to handle empty sublists, and multi-component sublists. My desired output is:

{{},{b>f},{ch,d

All lists have the same number of top-level elements. eqexp and eqval are one-dimensional. signval is two-dimensional, but the length of the sub-lists is variable. The only numerical values allowed in signval are 1 and -1.

How do I do this?

Answer

MapThread[#3 /. {1 -> #1 > #2, -1 -> #1 < #2} &, {eqexp, eqval, signval}]
(*    {{}, {b > f}, {c < g}, {d > h, d < h}}    *)

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