The Gap Between Scientific Theory and Application: Black and Zadeh - Vagueness and Fuzzy Sets

In this paper we examine important research pertaining to vagueness and fuzziness carried out by 20th century thinkers, especially Max Black and Lotfi A. Zadeh. We discuss discrepancies between scientific theory and the real world. In the process, we consider the application of fuzzy set theory in science as well as in linguistics, and describe the role of natural language as the best representation system human beings have to express their often imprecise and complex thoughts, feelings, and observations. We note similarities in the approaches followed by Black, Zadeh, and their colleagues and show that their analysis of vagueness and fuzziness respectively were attempts to bridge the gap between theory and reality. Finally, we look at recent efforts to use more sophisticated type-2 fuzzy sets to deal with uncertainties