The Lattice of Intuitionistic Fuzzy Topologies Generated by Intuitionistic Fuzzy Relations

We generalize the notion of fuzzy topology generated by fuzzy relation given by Mishra and Srivastava to the setting of intuitionistic fuzzy sets. Some fundamental properties and necessary examples are given. More specifically, we provide the lattice structure to a family of intuitionistic fuzzy topologies generated by intuitionistic fuzzy relations. To that end, we study necessary structural characteristics such as distributivity, modularity and complementary of this lattice

Function Spaces, Hyperspaces, and Asymmetric and Fuzzy Structures

Romaguera Bonilla, S.; Beer, G.; Sanchis, M. (2013). Function Spaces, Hyperspaces, and Asymmetric and Fuzzy Structures. Journal of Function Spaces and Applications. doi:10.1155/2013/619707

Linear logic for constructive mathematics

We show that numerous distinctive concepts of constructive mathematics arise automatically from an interpretation of "linear higher-order logic" into intuitionistic higher-order logic via a Chu construction. This includes apartness relations, complemented subsets, anti-subgroups and anti-ideals, strict and non-strict order pairs, cut-valued metrics, and apartness spaces. We also explain the constructive bifurcation of classical concepts using the choice between multiplicative and additive linear connectives. Linear logic thus systematically "constructivizes" classical definitions and deals automatically with the resulting bookkeeping, and could potentially be used directly as a basis for constructive mathematics in place of intuitionistic logic.Comment: 39 page

A fixed point theorem for preordered complete fuzzy quasi-metric spaces and an application

We obtain a fixed point theorem for a type of generalized contractions on preordered complete fuzzy quasi-metric spaces which is applied to deduce, among other results, a procedure to show in a direct and easy fashion the existence of solution for the recurrence equations that are typically associated to Quicksort and Divide and Conquer algorithms, respectively.The second and third named authors thank the supports of the Universitat Politecnica de Valencia, grant PAID-06-12-SP20120471, and the Ministry of Economy and Competitiveness of Spain, grant MTM2012-37894-C02-01.Castro Company, F.; Romaguera Bonilla, S.; Tirado Peláez, P. (2014). A fixed point theorem for preordered complete fuzzy quasi-metric spaces and an application. Journal of Inequalities and Applications. 2014(122):1-11. doi:10.1186/1029-242X-2014-122S111201412

Rough picture fuzzy set and picture fuzzy topologies

Approximation of a picture fuzzy set on a crisp approximation space gives a rough picture fuzzy set. In this paper, the concept of a rough picture set is introduced, besides, we also investigate some topological structures of a rough picture fuzzy set are investigated, such are lower and upper rough picture fuzzy approximation operators

Aggregation of L-probabilistic quasi-uniformities

[EN] The problem of aggregating fuzzy structures, mainly fuzzy binary relations, has deserved a lot of attention in the last years due to its application in several fields. Here, we face the problem of studying which properties must satisfy a function in order to merge an arbitrary family of (bases of) L-probabilistic quasi-uniformities into a single one. These fuzzy structures are special filters of fuzzy binary relations. Hence we first make a complete study of functions between partially-ordered sets that preserve some special sets, such as filters. Afterwards, a complete characterization of those functions aggregating bases of L-probabilistic quasi-uniformities is obtained. In particular, attention is paid to the case L={0,1}, which allows one to obtain results for functions which aggregate crisp quasi-uniformities. Moreover, we provide some examples of our results including one showing that Lowen's functor iota which transforms a probabilistic quasi-uniformity into a crisp quasi-uniformity can be constructed using this aggregation procedure.J. Rodriguez-Lopez acknowledges financial support from FEDER/Ministerio de Ciencia, Innovacion y Universidades-Agencia Estatal de Investigacion Proyecto PGC2018-095709-B-C21.Pedraza Aguilera, T.; Rodríguez López, J. (2020). Aggregation of L-probabilistic quasi-uniformities. Mathematics. 8(11):1-21. https://doi.org/10.3390/math8111980S12181