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This monogram is so written that it is self contained for independent study as well and hope it very much useful for cognition of intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy set, generalized intuitionistic fuzzy sets, generalized interval-valued intuitionistic fuzzy sets, generalized intuitionistic fuzzy matrices, generalized interval-valued intuitionistic fuzzy matrices and neutrosophic intuitionistic fuzzy sets. The arrangement and presentation is simple. The chapters are arranged in logical order. The theorems and propositions have been stated carefully and whenever necessary complete proofs of the theorems and propositions have been given. Also numerical examples are given for concretization of the theorems and propositions. It is hope that the readers will benefit immensely from this monogram.