Handbook of Management under Uncertainty

By Pompella, Maurizio | Journal of Risk and Insurance, December 2003 | Go to article overview

Handbook of Management under Uncertainty


Pompella, Maurizio, Journal of Risk and Insurance


Handbook of Management under Uncertainty, edited by Jaime Gil-Aluja, 2001, Kluwer Academic Publishers, New York, NY

Western science throughout centuries has been constructed taking as one of its unquestionable supports the excluded middle principle [...]. A single logical operator allows for the linking of proposals by means of two modes ("ponens" and "tollens"). At the present time and as a consequence of repeatedly stated reasons [...], it is not possible to base all research activity on the excluded middle principle. This is the starting point, as stated by the editor, on which this Handbook seems to be based. A brief introduction outlines the pattern that is followed in the volume-from the objectivity of reality to the algorithms needed to deal with uncertainty-as well as the principle that inspired the choice of contributors.

The leitmotif of the book featuring a collection of articles is to apply to management science tools used to deal with the uncertainty of economic phenomena, particularly when measurements and objective numerical assignments are not possible. The instruments used are mainly the theory of fuzzy sets and its variations, since they prove "perfectly adequate" to match the situations where objectivity is lacking and subjective estimates are needed in order to make the best use of available data and information. The theory of the fuzzy sets has been developed to try to solve problems in which the description of the activity and the observations are imprecise, vague, or uncertain. The term "fuzzy" refers to the situation in which well-defined limits for the total of activities or observations do not exist.

What is the common nexus that inspired this gathering of the authors? An unusual one, as is specified in the circumstance that "their life and work have been carried out and continue to be carried out on the shore of [...] the Mediterranean," and the "special way of understanding, explaining and facing reality" characterizing the people who live there, being the reason of their choice. Taken together, the chapters included in the Handbook, in fact, seem to be quite heterogenous, and not always easily readable, as they range from financial aspects of management under uncertainty, to mathematics (formal approach to uncertainty), cost management, accounting, marketing, to resources management, and even to environmental economics. By considering just a few contributions-in a sense-"marginal" to the general design of the work, however, the very comprehensive purpose of producing a review of management problems within a sphere of uncertainty, is nearly achieved.

In the first chapter (Management Problems in Uncertainty) the editor, Gil-Aluja, explains how the classical models for business decisions are based on a simplified reality, where quantitative information and data are just presented as certain or random, although in most cases they are uncertain. If the theory of probability is used to handle random data, a special category of models is needed to deal with uncertain data, since they cannot be measured, by definition. Thus, the concepts of subjectivity, fuzziness, vagueness, and also assignment and grouping techniques must be taken into account. Having illustrated-superbly-the relationship between imagination and freedom, the importance of perception and thought differences, and the uncertainty that all this produces in the outline of whatever future scenery, the author introduces the "principle of gradual simultaneity" as an evolution of the excluded middle principle, and specifies the difference between randomness and uncertainty. An introduction to the theory of fuzzy subsets and its potential benefit for management ends the chapter.

Crisp and Non-Crisp Hierarchical Systems in Management is the title of the second chapter (Tacu and Stefan). It consists of a formal analysis of the fundamentals of fuzzy sets: definitions, differences between classical (crisp) and fuzzy sets, membership fuzzy function, operations with the fuzzy sets, and it illustrates a series of propositions and theorems related to the fuzzy subsets. …

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