الفهرس 
Acknowledgements
PrefaceOnly 14 pages are availabe for public view
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Abstract
This introductorychapterisconsideredasabackgroundfor
the materialincludedinthethesis.Also,someconceptsrelated
fuzzy softtopologicalspaceshaveinvestigated.
1.1 Latticetheoreticalfoundation
The aimofthissectionistocollecttherelevantdefinitionsand
results fromlatticeaboutastrictlytwo-sidedcommutativequan-
tale andanorderreversinginvolution.Also,somepropertiesof
lattice arepresented.
In thisthesis,weusenotations,whichisstandardforthe
”fuzzy mathematics”usuallywithoutexplanation.Apartialorder
on aset L is abinaryrelation ” ” whichisreflexive,transitive
and antisymmetric.Aposet L = (L;) is asetequippedwith
a partialorder[13]. Wesayasubset D of L is directedprovided
it isnon-emptyandeveryfinitesubsetof D has anupperbound
in D. Wesayasubset C of L is totallyorderedorachainifit
1
Introduction
is non-emptyandallelementsof C are comparableunder ” ”
(that is,either x y or y x for allelements x; y 2 L). Clearly,
eachtotallyorderedisdirected.
Definition 1.1.1. [17, 23, 53] Let L = (L;) be aposet.
(1) L is calledalattice,if x _ y 2 L; x ^ y 2 L for all x; y 2 L;
(2) L is calledacompletelattice,if WS 2 L; VS 2 L for all S
L; In particular, WL = 1L and VL = 0L; where 1L and 0L
are theleastelementandthegreatestelement,respectively;
(3) L is calleddistributive,if x _ (y ^ z) =(x _ y) ^ (x _ z) and
x ^ (y _ z) =(x ^ y) _ (x ^ z) for all x; y;z 2 L;
(4) L is calledacompletedistributivelattice(resp.distributive
lattice), if L is acomplete(resp.alattice)anddistributive
lattice.
L0L = L