notified under the preceding sections may appear before such board on
the day fixed for hearing such remonstrances with regard to awards and
assessments, and remonstrate against the same. All persons appearing
before said board having an interest in said proceedings shall be given
a hearing. After such remonstrances shall have been received and said
hearings had, said board shall thereupon either sustain or modify,
by increasing or decreasing the awards or assessments. Any person
thus remonstrating, who is aggrieved by the decision of the board,
may, within fifteen days thereafter, take an appeal to the circuit or
superior court in the county in which such city is located. Such appeal
shall only affect the amount of the assessment or award of the person
appealing.