Decision making under incompleteness based on soft set theory

[EN]Decision making with complete and accurate information is ideal but infrequent. Unfortunately, in most cases the available infor- mation is vague, imprecise, uncertain or unknown. The theory of soft sets provides an appropriate framework for decision making that may be used to deal with uncertain decisions. The aim of this paper is to propose and analyze an effective algorithm for multiple attribute decision-making based on soft set theory in an incomplete information environment, when the distribution of incomplete data is unknown. This procedure provides an accurate solution through a combinatorial study of possible cases in the unknown data. Our theoretical development is complemented by practical examples that show the feasibility and implementability of this algorithm. Moreover, we review recent research on decision making from the standpoint of the theory of soft sets under incomplete information

Mathematical utility theory and the representability of demand by continuous homogeneous functions

The resort to utility-theoretical issues will permit us to propose a constructive procedure for deriving a homogeneous of degree one continuous function that gives raise to a primitive demand function under suitably mild conditions. This constitutes the first self-contained and elementary proof of a necessary and sufficient condition for an integrability problem to have a solution by continuous (subjective utility) functions.info:eu-repo/semantics/publishedVersio

On the structure of acyclic binary relations

We investigate the structure of acyclic binary relations from different points of view. On the one hand, given a nonempty set we study real-valued bivariate maps that satisfy suitable functional equations, in a way that their associated binary relation is acyclic. On the other hand, we consider acyclic directed graphs as well as their representation by means of incidence matrices. Acyclic binary relations can be extended to the asymmetric part of a linear order, so that, in particular, any directed acyclic graph has a topological sorting.This work has been partially supported by the research projects MTM2012-37894-C02-02, TIN2013-47605-P, ECO2015-65031-R, MTM2015-63608-P (MINECO/FEDER), TIN2016-77356-P and the Research Services of the Public University of Navarre (Spain)

Consistency properties for fuzzy choice functions: An analysis with the Lukasiewicz t-norm

International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU (17 th, 2018, Cádiz, Spain