Iqrar Ali Pali 13MSM13 Supervisor Dr. Muhammad Afzal Soomro creator Department of Mathematics & Statistics text QUEST 2018 monographic 45 ABSTRACT In this dissertation we define an intuitionistic fuzzy soft r-semigroup. It is also an extension of intuitionistic fuzzy soft semigroup. Fuzzy subsets were initiated, and intuitionistic fuzzy soft semigroup was introduced as generalization of fuzzy soft set. On the other hand r-semigroup, and soft set were introduced. In 2011 Jiehua et al. [24] gave the notion of intuitionistic fuzzy soft semigroup. Muhammad Akram, et al.[l] in 2014 defined fuzzy soft r-semigroup. Our work is the extension of these last two structures. Moreover, the notion of intuitionistic fuzzy soft ideal over f -semigroup is also defined. We also investigate some related properties of the ideals. http://tinyurl.com/5h4strz4 http://tinyurl.com/5h4strz4