by means of a kind of new idea, we consider the $(in,ivq)$-fuzzy$h$-ideals of a hemiring. first, the concepts of $(in,ivq)$-fuzzyleft(right) $h$-ideals of a hemiring are provided and some relatedproperties are investigated. then, a kind of quotient hemiring ofa hemiring by an $(in,ivq)$-fuzzy $h$-ideal is presented andstudied. moreover, the notions of generalized $varphi$-compatible$(in,ivq...