22 research outputs found
Related families-based attribute reduction of dynamic covering information systems with variations of object sets
In practice, there are many dynamic covering decision information systems,
and knowledge reduction of dynamic covering decision information systems is a
significant challenge of covering-based rough sets. In this paper, we first
study mechanisms of constructing attribute reducts for consistent covering
decision information systems when adding objects using related families. We
also employ examples to illustrate how to construct attribute reducts of
consistent covering decision information systems when adding objects. Then we
investigate mechanisms of constructing attribute reducts for consistent
covering decision information systems when deleting objects using related
families. We also employ examples to illustrate how to construct attribute
reducts of consistent covering decision information systems when deleting
objects. Finally, the experimental results illustrates that the related
family-based methods are effective to perform attribute reduction of dynamic
covering decision information systems when object sets are varying with time.Comment: arXiv admin note: substantial text overlap with arXiv:1711.0732
Conflict Analysis for Pythagorean Fuzzy Information Systems with Group Decision Making
Pythagorean fuzzy sets provide stronger ability than intuitionistic fuzzy
sets to model uncertainty information and knowledge, but little effort has been
paid to conflict analysis of Pythagorean fuzzy information systems. In this
paper, we present three types of positive, central, and negative alliances with
different thresholds, and employ examples to illustrate how to construct the
positive, central, and negative alliances. Then we study conflict analysis of
Pythagorean fuzzy information systems based on Bayesian minimum risk theory.
Finally, we investigate group conflict analysis of Pythagorean fuzzy
information systems based on Bayesian minimum risk theory
Comments on "Characteristic matrix of covering and its application to Boolean matrix decomposition[Information Sciences 263(1), 186-197, 2014]"
In this note, we show some improvements for Theorem 7 and Example 8 in
Shiping Wang[Information Sciences 263(1), 186-197, 2014]. Concretely, we study
further the sixth lower and upper approximations of sets for covering
approximation spaces. Furthermore, we present the sixth dual lower and upper
approximations of sets for covering approximation spaces. We also construct the
sixth dual lower and upper approximations of sets from the view of matrix.
Throughout, we use the same notations as Shiping Wang[Information Sciences
263(1), 186-197, 2014]
Incremental approaches to knowledge reduction of covering decision information systems with variations of coverings
In practical situations, calculating approximations of concepts is the
central step for knowledge reduction of dynamic covering decision information
system, which has received growing interests of researchers in recent years. In
this paper, the second and sixth lower and upper approximations of sets in
dynamic covering information systems with variations of coverings are computed
from the perspective of matrix using incremental approaches. Especially,
effective algorithms are designed for calculating the second and sixth lower
and upper approximations of sets in dynamic covering information systems with
the immigration of coverings. Experimental results demonstrate that the
designed algorithms provide an efficient and effective method for constructing
the second and sixth lower and upper approximations of sets in dynamic covering
information systems. Two examples are explored to illustrate the process of
knowledge reduction of dynamic covering decision information systems with the
covering immigration
Related family-based attribute reduction of covering information systems when varying attribute sets
In practical situations, there are many dynamic covering information systems
with variations of attributes, but there are few studies on related
family-based attribute reduction of dynamic covering information systems. In
this paper, we first investigate updated mechanisms of constructing attribute
reducts for consistent and inconsistent covering information systems when
varying attribute sets by using related families. Then we employ examples to
illustrate how to compute attribute reducts of dynamic covering information
systems with variations of attribute sets. Finally, the experimental results
illustrates that the related family-based methods are effective to perform
attribute reduction of dynamic covering information systems when attribute sets
are varying with time
Decision-theoretic rough sets-based three-way approximations of interval-valued fuzzy sets
In practical situations, interval-valued fuzzy sets are frequently
encountered. In this paper, firstly, we present shadowed sets for interpreting
and understanding interval fuzzy sets. We also provide an analytic solution to
computing the pair of thresholds by searching for a balance of uncertainty in
the framework of shadowed sets. Secondly, we construct errors-based three-way
approximations of interval-valued fuzzy sets. We also provide an alternative
decision-theoretic formulation for calculating the pair of thresholds by
transforming interval-valued loss functions into single-valued loss functions,
in which the required thresholds are computed by minimizing decision costs.
Thirdly, we compute errors-based three-way approximations of interval-valued
fuzzy sets by using interval-valued loss functions. Finally, we employ several
examples to illustrate that how to take an action for an object with
interval-valued membership grade by using interval-valued loss functions
Decision-theoretic rough sets based on time-dependent loss function
A fundamental notion of decision-theoretic rough sets is the concept of loss
functions, which provides a powerful tool of calculating a pair of thresholds
for making a decision with a minimum cost. In this paper, time-dependent loss
functions which are variations of the time are of interest because such
functions are frequently encountered in practical situations, we present the
relationship between the pair of thresholds and loss functions satisfying
time-dependent uniform distributions and normal processes in light of bayesian
decision procedure. Subsequently, with the aid of bayesian decision procedure,
we provide the relationship between the pair of thresholds and loss functions
which are time-dependent interval sets and fuzzy numbers. Finally, we employ
several examples to illustrate that how to calculate the thresholds for making
a decision by using time-dependent loss functions-based decision-theoretic
rough sets
Construction of symplectic (partitioned) Runge-Kutta methods with continuous stage
Hamiltonian systems are one of the most important class of dynamical systems
with a geometric structure called symplecticity and the numerical algorithms
which can preserve such geometric structure are of interest. In this article we
study the construction of symplectic (partitioned) Runge-Kutta methods with
continuous stage, which provides a new and simple way to construct symplectic
(partitioned) Runge-Kutta methods in classical sense. This line of construction
of symplectic methods relies heavily on the expansion of orthogonal polynomials
and the simplifying assumptions for (partitioned) Runge-Kutta type methods.Comment: 13 page
Generalized fuzzy rough sets based on fuzzy coverings
This paper further studies the fuzzy rough sets based on fuzzy coverings. We
first present the notions of the lower and upper approximation operators based
on fuzzy coverings and derive their basic properties. To facilitate the
computation of fuzzy coverings for fuzzy covering rough sets, the concepts of
fuzzy subcoverings, the reducible and intersectional elements, the union and
intersection operations are provided and their properties are discussed in
detail. Afterwards, we introduce the concepts of consistent functions and fuzzy
covering mappings and provide a basic theoretical foundation for the
communication between fuzzy covering information systems. In addition, the
notion of homomorphisms is proposed to reveal the relationship between fuzzy
covering information systems. We show how large-scale fuzzy covering
information systems and dynamic fuzzy covering information systems can be
converted into small-scale ones by means of homomorphisms. Finally, an
illustrative example is employed to show that the attribute reduction can be
simplified significantly by our proposed approach
Three-Way Decisions-Based Conflict Analysis Models
Three-way decision theory, which trisects the universe with less risks or
costs, is considered as a powerful mathematical tool for handling uncertainty
in incomplete and imprecise information tables, and provides an effective tool
for conflict analysis decision making in real-time situations. In this paper,
we propose the concepts of the agreement, disagreement and neutral subsets of a
strategy with two evaluation functions, which establish the three-way
decisions-based conflict analysis models(TWDCAMs) for trisecting the universe
of agents, and employ a pair of two-way decisions models to interpret the
mechanism of the three-way decision rules for an agent. Subsequently, we
develop the concepts of the agreement, disagreement and neutral strategies of
an agent group with two evaluation functions, which build the TWDCAMs for
trisecting the universe of issues, and take a couple of two-way decisions
models to explain the mechanism of the three-way decision rules for an issue.
Finally, we reconstruct Fan, Qi and Wei's conflict analysis models(FQWCAMs) and
Sun, Ma and Zhao's conflict analysis models(SMZCAMs) with two evaluation
functions, and interpret FQWCAMs and SMZCAMs with a pair of two-day decisions
models, which illustrates that FQWCAMs and SMZCAMs are special cases of
TWDCAMs