Bidirectional Absolute GRA/GIA Model for Uncertain Systems: Application in Project Management

Abstract

This paper extends the existing absolute grey relational analysis (Absolute GRA) model, also called the absolute degree grey incidence analysis (ADGIA) model. By working on the limitations of the existing Absolute GRA model, the proposed model, named Bidirectional Absolute GRA (BAGRA) model, is better equipped to handle uncertain systems being represented by uncertain data. It is suitable for simultaneous handling of both linear and nonlinear arrays of data with both consistent and inconsistent directions of motion. The model introduces a bidirectional grey relational degree that is a composite measure of both direction and strength of the relationship. The study also introduced two scales to test the appropriateness of collected data to measure the confidence level on the information extracted from that data. In the end, after the pilot testing, the model is being applied on an R&D project management case from a real world. The work is important both theoretically and practically, especially for the data analysts concerned with the uncertain relationships between different data arrays, in general, and for the grey systems analysts, in particular. INDEX TERMS Uncertain systems, uncertain data relations, bidirectional absolute, grey incidence analysis, integral proximity, grey relational analysis, project management. I. INTRODUCTION Projects and uncertainties have very close relationship. Project management literature is full of debates and discussions on uncertainty and risk. Even the presence of Project Risk Management in the ten knowledge areas of project management as identified by the PMBOK R is enough to justify their mutual relationship. One of the ''four major activities of the project office'' includes ''scheduling with risk and uncertainty'' [1, p. 132]. Tonchia [2, p. 15] stresses that ''projects are changing, becoming more and more.. . extreme/agile.. .. because of the stress caused by high uncertainty and frequent changes''. In PBMOK [3] one finds a very interesting passage linking complexity, projects, uncertainty and systems: ''Complexity within projects is a result of the organization's system behavior, human behavior, and the uncertainty at work in the organization or its environment.. .. Three dimensions of complexity are.. . : The associate editor coordinating the review of this manuscript and approving it for publication was Ding Zhai. • System behavior. The interdependencies of components and systems. • Human behavior. The interplay between diverse individuals and groups. • Ambiguity. Uncertainty of emerging issues and lack of understanding or confusion'' (pp.68). This passage is very easy to grasp for the Systems Thinkers and project managers alike. Not only it acknowledges the interdependencies of systems and components (or, subsystems), interactions between diverse individuals and groups (groups are also subsystems) but also the uncertainty at workplace or in the workplace environment (both of which are also systems/sub-systems). One can find similar echo in the work of Javed and Liu [4]; '...

Systems Evaluation through New Grey Relational Analysis Approach: An Application on Thermal Conductivity—Petrophysical Parameters’ Relationships

“…However, grey system theory, guided by its own distinct approaches, deals with uncertainty unlike other uncertainty theories [29,30]. GST categorizes all systems of the world into three classes; black, white and grey [31]. A black system implies a system for which no information is available and the white system is the system for which the entire information is available.…”

“…Grey data sequence [6,31] is an array of data values (x i ) available for grey data analysis. It is generally represented as…”

“…In other words, it defines the relationships among the parameters of a grey system. It can also be referred to as a proximity or closeness between the grey data sequences representing different variables/factors/parameters associated with a system [6,31].…”

“…Unlike Deng's GRG, absolute GRG is independent of the order of the sequences thus it is more likely to yield a measure of association (or correlation) [4,6]. If the absolute GRG can reveal both the degree of integral proximity and the direction of integral proximity, then it would be referred as bidirectional absolute GRG and would be estimated following the steps mentioned by Javed and Liu [31].…”

“…The direction of grey incidence [31] implies the nature of the relationship (positive/negative) between the data sequences. Grey incidence direction is represented by +/− sign in the bidirectional Processes 2019, 7, 348 9 of 19 absolute grey relational grade (ε ± ).…”