The main purpose of this paper is to study initial and final Hutton type of linear fuzzifying uniformities. The detailed characterizations of initial and final linear fuzzifying uniformities are obtained. In addition, the boundedness, complete boundedness and T2 separation axiom of initial linear fuzzifying uniform spaces are investigated. Some examples with respect to initial and final linear fuzzifying uniformities are also provided.
BayoumiF., On initial and final fuzzy uniform structures, Fuzzy Sets and Systems133 (2003), 299–319.
2.
BayoumiF., On initial and final fuzzy uniform structures, Part II, Fuzzy Sets and Systems157 (2006), 1970–1982.
3.
BurtonM.H., de Prada VicenteM.A. and
Gutiérrez GarcíaJ., Generalized uniform spaces, J Fuzzy Math4 (1996), 363–380.
4.
GählerW., BayoumiF., KandilA., NouhA., The theory of global fuzzy neighborhood structures, Part I, The general case, Fuzzy Sets and Systems98 (1998), 175–199.
5.
Gutiérrez GarcíaJ. and
de Prada VicenteM.A., Hutton[0, 1]-quasi-uniformities induced by fuzzy (quasi-)metric spaces, Fuzzy Sets and Systems157 (2006), 755–766.
6.
Gutiérrez GarcíaJ.,
Rodríguez-LópezJ. and RomagueraS., On fuzzy uniformities induced by a fuzzy metric space, Fuzzy Sets and Systems330 (2018), 52–78.
7.
Gutiérrez GarcíaJ.,
de Prada VicenteM.A.
and
ŠostakA.P., A unified approach to the concept of a fuzzyL-uniform space, in [23], pp. 81–114.
8.
HöleU., Probabilistic uniformization of fuzzy topologies, Fuzzy Sets and Systems1 (1978), 311–332.
9.
HöleU., Probabilistic metrization of fuzzy uniformities, Fuzzy Sets and Systems8 (1982), 63–69.
YueY., FangJ., Uniformities in fuzzy metric spaces, Iranian Journal of Fuzzy Systems12(1) (2015), 43–57.
21.
QiuD., Fuzzifying topological linear spaces, Fuzzy Sets and Systems147 (2004), 249–272.
22.
RodabaughS.E., Point-set lattice-theoretic topology, Fuzzy Sets and Systems40 (1991), 297–345.
23.
RodabaughS.E. and KlementE.P., (Eds.), Topological and Algebraic Structures in Fuzzy Sets: A Handbook of Recent Developments in the Mathematics of Fuzzy Sets, Trends in Logic, Vol. 20, Kluwer Academic Publishers, Dordrecht, 2003.