A STUDY OF FUZZY METRIC SPACES AND INTUTIONISTIC FUZZY METRIC SPACES . Author :

Mathematical deduction is not useful to the physicist if interpreted rigorously. It is necessary to know that its validity is unaltered when the premise and conclusion are only ”approximately true”. But the indeterminacy thus introduced, it is necessary to add in criticism, well invalidate the deduction unless the permissible limits of variation are specified. The same need was expressed by L.A. Zadeh in 1962, There is fairly wide gap between what might be regarded as ’’animate system theorists at the present time, and it is not at all certain that this gap will be narrowed, much km closed, in the near future, there are some who feel this gap reflects the fundamental in a adequacy of the conventional mathematics the mathematics of precisely defined points, functions, sets, probability measures, etc. for coping with the analysis of biological systems and that to deal effectively with such systems, which are generally orders of magnitude more complex than man-made systems, we need a radically different kind of mathematics. The mathematics of fuzzy or cloudy quantities which are not describable in terms of probability distributions. Indeed the need for such mathematics is becoming increasingly apartment even in the realm of inanimate systems, for in most practical cases the priori data as well as the criteria by which the performance of a man-made system is judged are far from being precisely specified or having accurately known probability distributions.