Related papers: The structure of multigranular rough sets

Multimodal normal incestual systems are investigated in terms of multiple categories. The different sorted composition of operators are exhibited as 2-cells in multiple categories built up from 2-categories giving rise to different axioms.…

We can define the adjacency algebra of an association scheme over arbitrary field. It is not always semisimple over a field of positive characteristic. The structures of adjacency algebras over a field of positive characteristic have not…

We describe various structures of algebraic nature on the space of continuous valuations on convex sets, their properties (like versions of Poincar\'e duality and hard Lefschetz theorem), and their relations and applications to integral…

Rational approximations are introduced and studied in granular graded rough sets and generalizations thereof by the first author in recent research papers. The concept of rationality is determined by related ontologies and coherence between…

This is a survey of characterizations and relationships between some properties of lattices, particularly the modular, Arguesian, linear, and distributive properties, but also some other related properties. The survey emphasizes finite and…

We consider problems with multiple linear objectives and linear constraints and use Adjustable Robust Optimization and Polynomial Optimization as tools to approximate the Pareto set with polynomials of arbitrarily large degree. The main…

We describe the mathematical properties of pairwise comparisons matrices with coefficients in an arbitrary group. We provide a vocabulary adapted for the description of main algebraic properties of inconsistency maps, describe an example…

We equip the whole space of fields of the triplectic formalism of Lagrangian quantization with an even supersymplectic structure and clarify its geometric meaning. We also discuss its relation to a closed two-form arising naturally in the…

The topological charge density and topological susceptibility are determined by multi-probing approximation using overlap fermions in quenched SU(3) gauge theory. Then we investigate the topological structure of the quenched QCD vacuum, and…

Rough sets are approximations of concrete sets. The theory of rough sets has been used widely for data-mining. While it is well-known that adjunctions are underlying in rough approximations, such adjunctions are not enough for…

Covering model provides a general framework for granular computing in that overlapping among granules are almost indispensable. For any given covering, both intersection and union of covering blocks containing an element are exploited as…

We investigate the caustic structure of a lens composed by a discrete number of point-masses, having mutual distances smaller than the Einstein radius of the total mass of the system. Along with the main critical curve, it is known that the…

We consider the enumeration of tropical curves in M\"obius strips for two different lattice structures and relate them to the enumeration of curves in two rational ruled surfaces over a complex elliptic curve. Using this correspondence, we…

We characterize the order of principal congruences of a bounded lattice as a bounded ordered set. We also state a number of open problems in this new field.

We consider a geometrization, i.e., we identify geometrical structures, for the space of density states of a quantum system. We also provide few comments on a possible application of this geometrization for composite systems.

This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…

Theories of rough sets and soft sets are powerful mathematical tools for modelling various types of vagueness. Hybrid model combining a rough set with a soft set which is called soft rough set proposed by Feng et al. [3] in 2010. In this…

We calculate the probability that random polynomial matrices over a finite field with certain structures are right prime or left prime, respectively. In particular, we give an asymptotic formula for the probability that finitely many…

We show that, for an arrangement of subspaces in a complex vector space with geometric intersection lattice, the complement of the arrangement is formal. We prove that the Morgan rational model for such an arrangement complement is formal…

We consider partially ordered sets of combinatorial structures under consecutive orders, meaning that two structures are related when one embeds in the other such that `consecutive' elements remain consecutive in the image. Given such a…