Applying granular computing in uncertain optimization problems

Abstract

Shortest path problem got a lot of attention from many researchers, in our case the distances between the nodes are represented by different types of uncertain numbers such as: interval numbers, fuzzy numbers, rough numbers and also some of them could be represented by classical real numbers. These heterogeneous types of numbers are forming a challenge in calculation the shortest path. In this work we propose a Unified Granular Number (UGN), that we call it G- Number to act as a general form for any uncertain granular number. G- Number represents higher level of abstract that hold only common properties of different types of uncertain granular numbers while ignoring some particular properties which are not necessary to be considered in such higher abstract level. The main benefit of using such a proposed G- number is the ability to represent all types of granular numbers using unified formality that greatly simplifies arithmetic operations.