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Class-based Rough Approximation with Dominance Principle  [PDF]
Junyi Chai,James N. K. Liu
Computer Science , 2011,
Abstract: Dominance-based Rough Set Approach (DRSA), as the extension of Pawlak's Rough Set theory, is effective and fundamentally important in Multiple Criteria Decision Analysis (MCDA). In previous DRSA models, the definitions of the upper and lower approximations are preserving the class unions rather than the singleton class. In this paper, we propose a new Class-based Rough Approximation with respect to a series of previous DRSA models, including Classical DRSA model, VC-DRSA model and VP-DRSA model. In addition, the new class-based reducts are investigated.
Intuitionistic Fuzzy Dominance–based Rough Set Approach: Model and Attribute Reductions  [cached]
Yanqin Zhang,Xibei Yang
Journal of Software , 2012, DOI: 10.4304/jsw.7.3.551-563
Abstract: The dominance--based rough set approach plays an important role in the development of the rough set theory. It can be used to express the inconsistencies coming from consideration of the preference--ordered domains of the attributes. The purpose of this paper is to further generalize the dominance--based rough set model to fuzzy environment. The constructive approach is used to define the intuitionistic fuzzy dominance--based lower and upper approximations respectively. Basic properties of the intuitionistic fuzzy dominance--based rough approximations are then examined. By introducing the concept of approximate distribution reducts into intuitionistic fuzzy dominance--based rough approximations, four different forms of reducts are defined. The judgment theorems and discernibility matrixes associated with these reducts are also obtained. Such results are all intuitionistic fuzzy generalizations of the classical dominance--based rough set approach. Some numerical examples are employed to substantiate the conceptual arguments.
The Computational Complexity of Dominance and Consistency in CP-Nets  [PDF]
Judy Goldsmith,Jerome Lang,Miroslaw Truszczyski,Nic Wilson
Computer Science , 2014, DOI: 10.1613/jair.2627
Abstract: We investigate the computational complexity of testing dominance and consistency in CP-nets. Previously, the complexity of dominance has been determined for restricted classes in which the dependency graph of the CP-net is acyclic. However, there are preferences of interest that define cyclic dependency graphs; these are modeled with general CP-nets. In our main results, we show here that both dominance and consistency for general CP-nets are PSPACE-complete. We then consider the concept of strong dominance, dominance equivalence and dominance incomparability, and several notions of optimality, and identify the complexity of the corresponding decision problems. The reductions used in the proofs are from STRIPS planning, and thus reinforce the earlier established connections between both areas.
Interactive multiobjective optimization using dominance-based rough set approach
Interactive multiobjective optimization using dominance based rough set approach

GRECO Salvatore,MATARAZZO Benedetto,SLOWINSKI Roman,
GRECO Salvatore

重庆邮电大学学报(自然科学版) , 2008,
Abstract: We present main ideas of a recently proposed method for interactive multiobjective optimization, which is based on application of a logical preference model built using the Dominance-based Rough Set Approach (DRSA).
Application of dominance rough set in seismology

ZHU Bing-bing,WU Shao-chun,WANG Wei,

计算机应用 , 2006,
Abstract: In seismology, rough set can be used in the reduction of attributes. But classical rough set are based on indisceroibility relation or similarity relation. The problems in Seismology deal with ordering objects instead of classifying objects. Now we presented an extension of the classical rough set called dominance-based rough set, and an attribute-reduction algorithm based on dominance matrix. The experiment indicates that the results will be more meaningful than those induced by the classical rough set theory.
Decision Analysis of RoboCup with Dominance-based Rough Sets

LI Yan,YANG Xi-bei,YANG Jing-yu,

计算机科学 , 2009,
Abstract: Interception is one of the most important technological movements in RoboCup(Robot World Cup).By combining analytical method and empirical method,an intercept strategy based on the rough set with dominance relation was proposed.In such strategy,the methods of knowledge reduction and rule extraction of dominance-based rough sets were investigated.Furthermore,the dichotomy was used to solve the interception point based on Robocup movement model.Finally,an illustrative example from RoboCup simulator game was a...
Dominance-Based Rough Set Approach in Selection of Portfolio of Sustainable Development Projects  [PDF]
Kazimierz Zaras, Jean-Charles Marin, Bryan Boudreau-Trude
American Journal of Operations Research (AJOR) , 2012, DOI: 10.4236/ajor.2012.24059
Abstract: In our study, the Dominance-based Rough Set Approach (DRSA) has been proposed to assist the Board of Directors of the Community Futures Development Corporations (CFDC), the sub-region of Abitibi-West (Quebec). The CFDC needs a tool for decision support to select the projects that are proposed by the contractors and partners of its territory. In decision making, a balanced set of 22 indicators is considered. These indicators derive from five perspectives: economic, social, demographic, health and wellness. The DRSA proposal is suitable for the data processing with multiple indicators providing on many examples to infer decision rules related to the preference model. In this paper we show that decision rules developed with the use of rough set theory allow us to simplify the process of selecting a portfolio for sustainable development by reducing a number of redundant indicators and identifying the critical values of selected indicators.
Fuzzy Dominance-based Rough Set in Set-valued Information System

YANG Xi-bei,ZHANG Zai-yue,ZHANG Ming,

计算机科学 , 2011,
Abstract: The set valued information system was analyzed by dominanccbased rough set approach. By considering the dominance degree in terms of pair of objects, the concept of fuzzy dominance relation was proposed, the fuzzy technique was then employed in the dominanccbased rough set theory. hhe fuzzy dominanccbased rough set model was presented, then corresponding properties were discussed, from which we obtained new theory and practical approach to derive decision rules from the set valued decision system. Some numerical examples were employed to substantiate the conceptual arguments.
Dominance-based rough set approach as a paradigm of knowledge discovery and granular computing
Roman Slowinski,

重庆邮电大学学报(自然科学版) , 2010,
Abstract: Dominance-based rough set approach (DRSA) permits representation and analysis of all phenomena involving monotonicity relationship between some measures or perceptions. DRSA has also some merits within granular computing, as it extends the paradigm of granular computing to ordered data, specifies a syntax and modality of information granules which are appropriate for dealing with ordered data, and enables computing with words and reasoning about ordered data. Granular computing with ordered data is a very general paradigm, because other modalities of information constraints, such as veristic, possibilistic and probabilistic modalities, have also to deal with ordered value sets (with qualifiers relative to grades of truth, possibility and probability), which gives DRSA a large area of applications.
Rough Computational Methods Based on Tolerance Matrix

HUANG Bing,HE Xin,ZHOU Xian-Zhong,

自动化学报 , 2004,
Abstract: Rough set theory is a new mathematical tool to deal with vagueness and uncertainty. The classical rough set theory based on equivalence relation has made a great progress, while the equivalence relation is too harsh to meet and is extended to tolerance relation in real world. It is important to investigate rough computational methods for rough set theory, which is one of the bottleneck problems in the development of rough set theory. Matrix computation based on tolerance relation for information systems is discussed, and a one-to-one relationship between tolerance relation and tolerance matrix is constructed in this paper. Two algorithms for attribute re-duction in incomplete information system are presented with an example to illustrate their validity.
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