106 Bishnupada Debnath International Journal of Computer & Mathematical Sciences IJCMS ISSN 2347 – 8527 Volume 6, Issue 9 September 2017 Pairwise Fuzzy Faintly Semi Paracompactness in Fuzzy Bitopological Space Bishnupada Debnath Research Scholar, Department of Mathematics, Tripura University,Suryamaninagar, Agartala, Tripura, India. ABSTRACT: In this paper the concept of fuzzy pairwise faintly semi paracompact spaces in fuzzy bitopological spaces by means of locally finite pairwise faintly semi-open refinement are introduced. Further some characterizations of fuzzy pairwise faintly semi paracompactness are also obtained. Moreover, the behavior of fuzzy pairwise faintly semi paracompact spaces under various types of maps are also investigated. AMS SUBJECT CLASSIFICATIN: 54 A 40 KEYWORDS: Fuzzy pairwise semi open sets, fuzzy pairwise faintly semi open(closed) sets, fuzzy pairwise semi paracompact spaces, fuzzy pairwise faintly semi paracompact spaces etc. 1. INTRODUCTION & PRELIMINERIES In 1963, J.C.Kelly introduced the concept of bitopological spaces using two topologies on a non-empty set whereas the notion of fuzzy bitopological spaces was first initiated by Kandil[4]. A non-empty set X equipped with two arbitrary fuzzy topologies 1 and 2 is called a fuzzy bitopological space which is denoted by(X,1,2). A fuzzy point [9] is a fuzzy set which is denoted by xt and defined by xt = t (0<t 1), for, y = x, = 0 , for, y  x . In 2009, Mukherjee & Choudhury [1], introduced fuzzy pairwise faintly semi-open set and fuzzy pairwise faintly semi-closed set in fbts in the following way: A fuzzy set αI X of a fuzzy bitopological space (X,1,2) is called (i) a ij-fuzzy faintly semi open ( briefly, ij- SfO) set of X if  a i and j such that   α j-Cl()i-Cl() and α is said to be pairwise fuzzy faintly semi open (briefly, PSfO) if it is both ij-fuzzy faintly semi open and ji-fuzzy faintly semi open. (ii) a ij-fuzzy faintly semi closed ( briefly, ij-SfC) of X if  a i-closed set  and j-closed set  such that j- Int()i-Int()  α  and α is said to be pairwise fuzzy faintly semi closed (briefly, PSfC) if it is both ij- fuzzy faintly semi closed and ji-fuzzy faintly semi closed. The collection of all fuzzy pairwise faintly semi-open sets & fuzzy pairwise faintly semi closed sets in X are respectably denoted by FPSfO(X) & FPSfC(X). In fuzzy bitopological space, S.S.Kumar [6] defined ij-fuzzy semi-open set and ij-fuzzy semi-closed set as follows: A fuzzy set I X of a fuzzy bitopological space (X,1,2) is called (i) a ij-fuzzy semi open (briefly, ij-FSO) if  a i such that j-Cl() and  is said to be pairwise fuzzy semi open if it is both ij-fuzzy semi open and ji- fuzzy semi open. (ii) a ij-fuzzy semi closed (briefly,ij-FSC) if  a i-fuzzy closed set  such that j- Int()  and  is said to be pairwise fuzzy semi closed if it is both ij-fuzzy semi closed and ji-fuzzy semi closed. A bitopological space (X,τ1,τ2) is said to be ij-fuzzy regular if for each point xt ∈ X and for each i-open set V of X containing xt there exists an i-open set U such that xt ∈ U ⊆ j-cl(U) ⊆V, and X is said to be pairwise fuzzy regular if it is both ij-fuzzy regular and ji-fuzzy regular.