function members_format_notifications( $action, $item_id, $secondary_item_id, $total_items, $format = 'string' ) {

	switch ( $action ) {
		case 'accepted_invitation':

			// Set up the string and the filter.
			if ( (int) $total_items > 1 ) {
				$link   = bp_get_notifications_permalink();
				$amount = 'multiple';

				// This is the inviter whose invitation was accepted.
				if ( 0 !== (int) $secondary_item_id )  {
					/* translators: %d: the number of new users */
					$text = sprintf( __( '%d members accepted your membership invitations', 'buddypress' ), (int) $total_items );
				// This is someone who also invited that user to join.
				} else {
					/* translators: %d: the number of new users */
					$text = sprintf( __( '%d members are now members of the site', 'buddypress' ), (int) $total_items );
				}
			} else {
				$link   = add_query_arg( 'welcome', 1, bp_core_get_user_domain( $item_id ) );
				$amount = 'single';

				// This is the inviter whose invitation was accepted.
				if ( 0 !== (int) $secondary_item_id )  {
					/* translators: %s: new user name */
					$text = sprintf( __( '%s accepted your membership invitation', 'buddypress' ),  bp_core_get_user_displayname( $item_id ) );
					// This is someone who also invited that user to join.
				} else {
					/* translators: %s: new user name */
					$text = sprintf( __( '%s is now a member of the site', 'buddypress' ),  bp_core_get_user_displayname( $item_id ) );
				}
			}
			break;
	}

	// Return either an HTML link or an array, depending on the requested format.
	if ( 'string' == $format ) {

		/**
		 * Filters the format of members notifications based on type and amount * of notifications pending.
		 *
		 * This is a variable filter that has several versions.
		 * The possible versions are:
		 *   - bp_members_single_accepted_invitation_notification
		 *   - bp_members_multiple_accepted_invitation_notification
		 *
		 * @since 8.0.0
		 *
		 * @param string|array $value             Depending on format, an HTML link to new requests profile tab or array with link and text.
		 * @param int          $total_items       The total number of messaging-related notifications waiting for the user.
		 * @param int          $item_id           The primary item ID.
		 * @param int          $secondary_item_id The secondary item ID.
		 */
		$return = apply_filters( 'bp_members_' . $amount . '_'. $action . '_notification', '<a href="' . esc_url( $link ) . '">' . esc_html( $text ) . '</a>', (int) $total_items, $item_id, $secondary_item_id );
	} else {
		/** This filter is documented in bp-members/bp-members-notifications.php */
		$return = apply_filters( 'bp_members_' . $amount . '_'. $action . '_notification', array(
			'link' => $link,
			'text' => $text
		), (int) $total_items, $item_id, $secondary_item_id );
	}

	/**
	 * Fires at the end of the bp-members notification format callback.
	 *
	 * @since 8.0.0
	 *
	 * @param string       $action            The kind of notification being rendered.
	 * @param int          $item_id           The primary item ID.
	 * @param int          $secondary_item_id The secondary item ID.
	 * @param int          $total_items       The total number of members-related notifications
	 *                                        waiting for the user.
	 * @param array|string $return            Notification text string or array of link and text.
	 */
	do_action( 'members_format_notifications', $action, $item_id, $secondary_item_id, $total_items, $return );

	return $return;
}