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On the characterization of fuzzy processes: Some observations

One of the most pervasive myths of the present day, entertained alike by many engineers, scientists, social scientists, and system scientists, is that the uncertainty, vagueness, ambiguity and fuzziness arising in the modelling and analysis of complex processes can be handled using the mathematical tools deeply rooted in the classical statistics. Most of us are aware of the ferment and controversies on the nature of statistical decision making. The birth of statistics through the efforts of Karl Pearson and R.A. Fisher, and the development of estimation theory and the Neyman-Pearson theory are well known to us. We are also aware of the rejection of most of this now classical picture of statistical inference by a group known as Bayesians, who have rejected the notion of frequency probability and consider that the whole process of forming conclusions and making decisions is a matter of combining a prior distribution with a probability of the data to obtain a posterior distribution. In this whole process, all probabilities, the prior ones and probabilities of data are belief probabilities, representing the subjectivity of the decision maker which depends upon his experience and judgment of the particular situation. In the conventional statistics, the basic difficulty is that the probability model for the data, in terms of some parameters, is not ever known. So whatever inferences are drawn are strongly subjective, i.e. conditional on the model assumption.