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Imposing a probability law on an interval in which a normal fuzzy number has been defined, and then trying to find consistency between randomness and fuzziness is not logical. If we need to establish a probability law followed by a random variable defined in a given interval, there are mathematical formalisms in the theory of statistical inferences to do so. Instead, defining a normal fuzzy number around a point, and then using a conversion factor to deduce a probability density function from the fuzzy membership function is against statistical norms. Probability densities are...

Two things we are aiming to discuss. First, it has been accepted that intersection of a fuzzy set and its complement is not the void set. Similarly it has also been accepted that the union of a fuzzy set and its complement is not the universal set.Accordingly, the fuzzy sets have been accepted not to form a field. However, can the intersection of anything, a fuzzy set or whatever else, and its complement be non-null? Secondly, when it was seen that the fuzzy sets do not allow the additivity postulate for a measure to hold, a new definition of fuzzy measure was formalized. Can it...

With a view to provide a comprehensive overview on few emerging issues of education in India, total seven (7) chapters have been included in this book. Each chapter gives a clear concept & picture over a specific topic. All the topics are considered as more relevant to the emergent trend of education. The contents laid down in each chapter, may be treated as new addition of knowledge in the field of education. Each chapter of this book, presents the overall concept and knowledge on the given topic in complete and concise manner. Effort is made to ensure that the readers can grasp the subject...

Making a paradigm shift in any branch of knowledge needs a lot of self-belief and courage. Lofty Zadeh did have self-belief as well as courage to propose the Mathematics of Fuzziness way back in 1965. By now, it has entered into the applied matters in nearly all branches of scientific knowledge. Such paradigm shifts have occurred not many times in the history of science.In the Zadehian theory of fuzzy sets there are two flaws.Instead of saying, that the theory of fuzzy sets has been incorrectly explained Hemanta K. Baruah has started the whole process anew naming by the theory of imprecise...