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

Intertemporal Choice of Fuzzy Soft Sets

This paper first merges two noteworthy aspects of choice. On the one hand, soft sets and fuzzy soft sets are popular models that have been largely applied to decision making problems, such as real estate valuation, medical diagnosis (glaucoma, prostate cancer, etc.), data mining, or international trade. They provide crisp or fuzzy parameterized descriptions of the universe of alternatives. On the other hand, in many decisions, costs and benefits occur at different points in time. This brings about intertemporal choices, which may involve an indefinitely large number of periods. However, the literature does not provide a model, let alone a solution, to the intertemporal problem when the alternatives are described by (fuzzy) parameterizations. In this paper, we propose a novel soft set inspired model that applies to the intertemporal framework, hence it fills an important gap in the development of fuzzy soft set theory. An algorithm allows the selection of the optimal option in intertemporal choice problems with an infinite time horizon. We illustrate its application with a numerical example involving alternative portfolios of projects that a public administration may undertake. This allows us to establish a pioneering intertemporal model of choice in the framework of extended fuzzy set theorie

Convex and Concave Soft Sets and Some Properties

In this study, after given the definition of soft sets and their basic operations we define convex soft sets which is an important concept for operation research, optimization and related problems. Then, we define concave soft sets and give some properties for the concave sets. For these, we will use definition and properties of convex-concave fuzzy sets in literature. We also give different some properties for the convex and concave soft sets