Certain studies on intuitionistic fuzzy continuous and intuitionistic fuzzy open mappings

Abstract

The research reported in this thesis deals with the new class of newlineintuitionistic fuzzy open mappings and intuitionistic fuzzy continuous newlinemappings in intuitionistic fuzzy topological spaces Their characterizations newlinevarious properties and their inter relations have been discussed Intuitionistic newlinefuzzy totally continuous and intuitionistic fuzzy totally semi continuous newlinemappings have been introduced and their properties were studied The newlinerelationship between these mappings with existing intuitionistic fuzzy newlinecontinuous mapping are discussed The relationship between intuitionistic newlinefuzzy totally semicontinuous mapping and intuitionistic fuzzy semicontinuous newlinemapping has been discussed newlineIntuitionistic fuzzy semitotally continuous mapping is defined and newlinethe equivalent conditions for a mapping to be intuitionistic fuzzy semitotally newlinecontinuous mapping are obtained The relationship between intuitionistic newlinefuzzy semitotally continuous mapping and intuitionistic fuzzy totally semicontinuous newlinemapping are discussed Counter examples are given to prove that newlinethe reverse implications are not possible in some cases The equivalent newlineconditions for a mapping to be an intuitionistic fuzzy semitotally continuous newlinemapping are derived with the help of fuzzy points An intuitionistic fuzzy newlinespace is defined and the equivalent conditions of intuitionistic fuzzy newlinesemitotally continuous mappings are produced with the help of intuitionistic newlinefuzzy space and intuitionistic fuzzy points The composition of an newlineintuitionistic fuzzy totally semi continuous mapping with other intuitionistic newlinefuzzy continuous mapping are obtained newlineIntuitionistic fuzzy semitotally open mapping is defined and its newlineproperties are discussed The equivalent conditions for a mapping to be an newlineintuitionistic fuzzy semitotally continuous mapping are also derived newlineIntuitionistic fuzzy almost open mappings and intuitionistic fuzzy newlineweakly open mappings are defined and their interrelations are discussed newlineCounter examples are given to prove that the reverse implications are not newlinepossible in some cases newline