The aim of this paper is to introduce and study the concepts of fuzzifying semipre-θ-neighborhood system of a point, fuzzifying semipre-θ-closure of a set, fuzzifying semipre-θ-interior of a set, fuzzifying semipre-θ-open sets and fuzzifying semipre-θ-closed sets in fuzzifying topological spaces, and investigate some of their basic properties. Also, we present two types of functions in a fuzzifying topological spaces called fuzzifying strong β -irresolute and fuzzifying weak β -irresolute functions. The interrelations of these functions with the parallel existing allied concepts are established. Further, several characterizations of these functions along with different conditions for their existence are obtained.
ParkJ.H. and LeeB.Y., Fuzzy i-preopen sets and fuzzy iprecontinuous mappings, Fuzzy Sets Syst67 (1994), 359–364.
9.
ZahranA.M., On fuzzy SP-continuity and β s(β*s)-closedness, J Fuzzy Math7(3) (1999), 707–721.
10.
YingM., A new approach for fuzzy topology (I), Fuzzy Sets Syst39(3) (1991), 302–321.
11.
El-HakeimA., ZeyadaF.M. and SayedO.R., β -continuity and D(c, β)-continuity in fuzzifying topology, J Fuzzy Math7(3) (1999), 547–558.
12.
SayedO.R. and Abd-AllahM.A., Fuzzy β -irresolute functions and fuzzy β -compact spaces in fuzzifying topology*, Iran J Sci & Tech, Trans A30 (2006), 297–314.
13.
SayedO.R., β -Separation axioms based on Łukasiewicz logic, Eng Sci Letters1(1) (2012), 1–24.
14.
SayedO.R., A Unified theory (I) for neighborhood systems and basic concepts on fuzzifying topological spaces, Applied Math3 (2012), 983–996.
15.
LiL. and LiQ., On enriched L-topologies: Base and subbase, J Intell Fuzzy Syst28(6) (2015), 2423–2432.
16.
ZhouL. and ZhangJ., Lukasiewicz antic MV-topology for MV-algebra and its application to Lukasiewicz propositional logic, J Intell Fuzzy Syst33(1) (2017), 377–387.
17.
YingM., A new approach for fuzzy topology (II), Fuzzy Sets Syst47(2) (1992), 221–232.
18.
YingM., A new approach for fuzzy topology (III), Fuzzy Sets Syst55(2) (1993), 193–207.
19.
YingM., Fuzzifying topology based on complete residuated lattice-valued logic (I), Fuzzy Sets Syst56 (1993), 337–373.
20.
El-DarderyM., RamadanA.A. and KimY.C., L-fuzzy topogenous orders and L-fuzzy topologies, J Intell Fuzzy Syst24(4) (2013), 685–691.
21.
RamadanA.A., El-DarderyM. and KimY.C., Relationships between Lfuzzy quasi-uniform structures and L-fuzzy topologies, J Intell Fuzzy Syst28(5) (2015), 2319–2327.
22.
ShiY. and ShiF.-G., Characterizations of L-topologies, J Intell Fuzzy Syst34(1) (2018), 613–623.
23.
PawlakZ., Rough sets, Inter J Comput Inform Sci11(5) (1982), 341–356.
24.
CaoH., ShiJ., LiS.G. and ChenJ., Application of point set topology in the description of topological relations, 77– 82. In Chinese, J Engin Math18 (2001).
25.
CaspardN. and MonjardetB., The lattices of closure systems, closure operators, and implicational systems on a finite set: A survey, Discrete Appl Math127(2) (2003), 241–269.
26.
DemetrovicsJ., LibkinL. and MuchnikI.B., Functional dependencies in relational databases: A lattice point of view, Discrete Appl Math40(2) (1992), 155–185.
27.
DiattaJ., On critical sets of a finite Moore family, Adv Data Anal Classif3(3) (2009), 291–304.
28.
DuquenneV., Latticial structures in data analysis, Theor Comput Sci217(2) (1999), 407–436.
