Metric spaces and textures

[EN] Textures are point-set setting for fuzzy sets, and they provide a framework for the complement-free mathematical concepts. Further dimetric on textures is a gener- alization of classical metric spaces. The aim of this paper is to give some properties of dimetric texture space by using categorical approach. We prove that the category of clas- sical metric spaces is isomorphic to a full subcategory of dimetric texture spaces, and give a natural transformation from metric topologies to dimetric ditopologies. Further, it is pre- sented a relation between dimetric texture spaces and quasi-pseudo metric spaces in the sense of J. F. Kelly. Guardar / Salir Siguiente >Dost, S. (2017). Metric spaces and textures. Applied General Topology. 18(1):203-217. doi:10.4995/agt.2017.6889.SWORD203217181Brown, L. M., & Diker, M. (1998). Ditopological texture spaces and intuitionistic sets. Fuzzy Sets and Systems, 98(2), 217-224. doi:10.1016/s0165-0114(97)00358-8Brown, L. M., & Ertürk, R. (2000). Fuzzy sets as texture spaces, I. Representation theorems. Fuzzy Sets and Systems, 110(2), 227-235. doi:10.1016/s0165-0114(98)00157-2Brown, L. M., & Ertürk, R. (2000). Fuzzy sets as texture spaces, II. Subtextures and quotient textures. Fuzzy Sets and Systems, 110(2), 237-245. doi:10.1016/s0165-0114(98)00158-4Brown, L. M., Ertürk, R., & Dost, Ş. (2004). Ditopological texture spaces and fuzzy topology, I. Basic concepts. Fuzzy Sets and Systems, 147(2), 171-199. doi:10.1016/j.fss.2004.02.009Brown, L. M., Ertürk, R., & Dost, Ş. (2004). Ditopological texture spaces and fuzzy topology, II. Topological considerations. Fuzzy Sets and Systems, 147(2), 201-231. doi:10.1016/j.fss.2004.02.010Brown, L. M., Ertürk, R., & Dost, Ş. (2006). Ditopological texture spaces and fuzzy topology—III: Separation axioms. Fuzzy Sets and Systems, 157(14), 1886-1912. doi:10.1016/j.fss.2006.02.001Diker, M., & Altay Uğur, A. (2012). Textures and covering based rough sets. Information Sciences, 184(1), 44-63. doi:10.1016/j.ins.2011.08.012Dost, Ş. (2017). Semi-compactness in ditopological texture spaces and soft fuzzy topological spaces. Journal of Intelligent & Fuzzy Systems, 32(1), 925-936. doi:10.3233/jifs-1614

GENERALIZATION SOME FUZZY SEPARATION AXIOMS TO DITOPOLOGICAL TEXTURE SPACES

The authors characterize the notion of quasi coincident in texture spaces and study the generalization of fuzzy quasi separation axioms defined by [12] to the ditopological texture spaces

Generalized closed sets in ditopological texture spaces with application in rough set theory

In this paper, the counterparts of generalized open (g-open) and generalized closed (g-closed) sets for ditopological texture spaces are introduced and some of their characterizations are obtained. Some characterizations are presented for generalized bicontinuous difunctions. Also, we introduce new notions of compactness and stability in ditopological texture spaces based on the notion of g-open and g-closed sets. Finally, as an application of g-open and g-closed sets, we generalize the subsystem based denition of rough set theory by using new subsystem, called generalized open sets to dene new types of lower and upper approximation operators, called g-lower and g-upper approximations. These decrease the upper approximation and increase the lower approximation and hence increase the accuracy. Properties of these approximations are studied. An example of multi-valued information systems are given

Some categorical aspects of the inverse limits in ditopological context

[EN] This paper considers some various categorical aspects of the inverse systems (projective spectrums) and inverse limits described in the category ifPDitop, whose objects are ditopological plain texture spaces and morphisms are bicontinuous point functions satisfying a compatibility condition between those spaces. In this context, the category InvifPDitop consisting of the inverse systems constructed by the objects and morphisms of ifPDitop, besides the inverse systems of mappings, described between inverse systems, is introduced, and the related ideas are studied in a categorical - functorial setting. In conclusion, an identity natural transformation is obtained in the context of inverse systems - limits constructed in ifPDitop and the ditopological infinite products are characterized by the finite products via inverse limits.Yildiz, F. (2018). Some categorical aspects of the inverse limits in ditopological context. Applied General Topology. 19(1):101-127. https://doi.org/10.4995/agt.2018.781210112719