TY - JOUR ID - 120762 TI - A study on fundamentals of refined intuitionistic fuzzy set with some properties JO - Journal of Fuzzy Extension and Applications JA - JFEA LA - en SN - 2783-1442 AU - Rahman, Atiqe Ur AU - Ahmad, Muhammad Rayees AU - Saeed, Muhammad AU - Ahsan, Muhammad AU - Arshad, Muhammad AU - Ihsan, Muhammad AD - Department of Mathematics, University of Management and Technology, Lahore, Pakistan. Y1 - 2020 PY - 2020 VL - 1 IS - 4 SP - 279 EP - 292 KW - Fuzzy set KW - Intuitionistic fuzzy set KW - Refined Intuitionistic Fuzzy Set DO - 10.22105/jfea.2020.261946.1067 N2 - Zadeh conceptualized the theory of fuzzy set to provide a tool for the basis of the theory of possibility. Atanassov extended this theory with the introduction of intuitionistic fuzzy set. Smarandache introduced the concept of refined intuitionistic fuzzy set by further subdivision of membership and non-membership value. The meagerness regarding the allocation of a single membership and non-membership value to any object under consideration is addressed with this novel refinement. In this study, this novel idea is utilized to characterize the essential elements e.g. subset, equal set, null set, and complement set, for refined intuitionistic fuzzy set. Moreover, their basic set theoretic operations like union, intersection, extended intersection, restricted union, restricted intersection, and restricted difference, are conceptualized. Furthermore, some basic laws are also discussed with the help of an illustrative example in each case for vivid understanding. UR - https://www.journal-fea.com/article_120762.html L1 - https://www.journal-fea.com/article_120762_fbb95382675187e2d4cae7c799ea5348.pdf ER -