George Klir: Uncertainty

“Probability theory is an ideal tool for formalizing uncertainty in situations where class frequencies are known or where evidence is based on outcomes of a sufficiently long series of independent random experiments. Possibility theory, on the other hand, is ideal for formalizing incomplete information expressed in terms of fuzzy propositions.”

George Klir

Source: Fuzzy sets and fuzzy logic (1995), p. 205 cited in: Flavio Comim, et al. (2008) The Capability Approach: Concepts, Measures and Applications. p. 298.

“The need for a fundamentally different approach to the study of physical processes at the molecular level motivated the development of relevant statistical methods, which turned out to be applicable not only to the study of molecular processes (statistical mechanics), but to a host of other areas such as the actuarial profession, design of large telephone exchanges, and the like. In statistical methods, specific manifestations of microscopic entities (molecules, individual telephone sites, etc.) are replaced with their statistical averages, which are connected with appropriate macroscopic variables. The role played in Newtonian mechanics by the calculus, which involves no uncertainty, is replaced in statistical mechanics by probability theory, a theory whose very purpose is to capture uncertainty of a certain type.”

George Klir

Source: Fuzzy sets and fuzzy logic (1995), p. 1-2.

Motivation , Study

“Among the various paradigmatic changes in science and mathematics in this century, one such change concerns the concept of uncertainty. In science, this change has been manifested by a gradual transition from the traditional view, which insists that uncertainty is undesirable in science and should be avoided by all possible means, to an alternative view, which is tolerant of uncertainty and insists that science cannot avoid it. According to the traditional view, science should strive for certainty in all its manifestations (precision, specificity, sharpness, consistency, etc.); hence, uncertainty (imprecision, nonspecificity, vagueness, inconsistency, etc.) is regarded as unscientific. According to the alternative (or modem) view, uncertainty is considered essential to science; it is not only an unavoidable plague, but it has, in fact, a great utility.”

George Klir

Source: Fuzzy sets and fuzzy logic (1995), p. 1.

Mathematics , Science , Change

“The first stage of the transition from the traditional view to the modem view of uncertainty began in the late 19th century, when physics became concerned with processes at the molecular level.”

George Klir

Source: Fuzzy sets and fuzzy logic (1995), p. 1.

“Among the various paradigmatic changes in science and mathematics in this century, one such change concerns the concept of uncertainty.”

George Klir

In science, this change has been manifested by a gradual transition from the traditional view, which insists that uncertainty is undesirable in science and should be avoided by all possible means, to an alternative view, which is tolerant of uncertainty and insists that science cannot avoid it. According to the traditional view, science should strive for certainty in all its manifestations (precision, specificity, sharpness, consistency, etc.); hence, uncertainty (imprecision, nonspecificity, vagueness, inconsistency,etc.) is regarded as unscientific. According to the alternative (or modem) view, uncertainty is considered essential to science; it is not only an unavoidable plague, but it has, in fact, a great utility.
Source: Fuzzy sets and fuzzy logic (1995), p. 1.

Science , Mathematics , Change