Granular based analytical hierarchical process

Analytical Hierarchical Process (AHP) is one of the famous methods of solving multi criteria decision making problems, in some cases the preference ratios can be represented by different types of uncertain numbers such as: interval numbers, fuzzy numbers and rough numbers. These heterogeneous types of numbers are forming a challenge in computing and choosing the best alternative. This work proposes a Unified Granular Number (UGN) that we call G-Number to act as a general form for any uncertain number. G-Number represents a higher level of abstract that hold only common properties of different types of uncertain numbers while ignoring 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 its ability to represent all types of granular numbers using unified formality that greatly simplifies arithmetic. G-Number based Analytical Hierarchical Process (GAHP) is introduced to overcome the limitations of handling different types of uncertainty representations in multi criteria decision making problems.