Non Deterministic Approaches

Technion - Israel Institute of Technology, Faculty of Mechanical Engineering

Prof. Yakov Ben-Haim - Yitzhak Moda'i Chair in Technology and Economics

Outline of Info-Gap Theory and Its Applications

Planning and design in engineering, biological conservation, medicine, management, homeland security, economics and other fields is based on models which are wrong in ways we sometimes cannot even imagine. In addition, our data may lack evidence about surprises - catastrophes as well as windfalls - which impact the success and survival of the system. These model- and data-deficiencies are information-gaps or epistemic limitations. Info-gap uncertainty is an incomplete understanding of the system being managed. This is a broader conception of uncertainty than is usually handled by probability. Info-gap theory provides decision-making tools for modelling and managing severe uncertainty.

Info-gap theory is a design methodology, based on two decision functions. The robustness function expresses the greatest level of uncertainty at which failure cannot occur. Robustness is a function of the decision variables, and one is inclined to prefer more robust designs over less robust designs. However, a basic theorem of info-gap theory establishes an irrevocable trade-off between robustness to uncertainty, and the quality of outcome: aspirations for quality entail loss of robustness. This trade-off is quantified by the robustness function.

The second design function is the opportuneness function which expresses the least uncertainty which entails the possibility of sweeping success. Uncertainty may be propitious, and the opportuness function evaluates a design's propensity to exploit favorable uncertainty and to lead to outcomes far better than anticipated. Once again a trade-off is involved: greater windfall is possible only at greater uncertainty.

Further information:

Info-gap robustness and opportuneness functions have been used in analysis and design of many technological systems. A thorough exposition of info-gap theory, with examples in many disciplines including engineering design, is found in:

• Yakov Ben-Haim, 2006, Info-Gap Decision Theory: Decisions Under Severe Uncertainty, 2nd edition, Academic Press, London, ISBN 0-12-373552-1.

Related material, with applications exclusively in mechanics, appears in:

• Yakov Ben-Haim, 1996, Robust Reliability in the Mechanical Sciences, Springer-Verlag, Berlin, ISBN 3-540-61058-8.

Additional sources:

• Article in Wikipedia on info-gap theory.
• Workshop on Info-Gap Applications in Engineering, University of Newcastle-upon-Tyne, 29-30 Sept. 2005
• My website contains many articles, by myself and others, on applications of info-gap theory.

Reference:
prof Yakov Ben-Haim
Yitzhak Moda'i Chair in Technology and Economics
Faculty of Mechanical Engineering
Technion - Israel Institute of Technology
Haifa 32000 Israel
yakov@technion.ac.il
Tel: 972-4-829-3262
Fax: 972-4-829-5711