α-Dominance relation and rough sets in interval-valued information systems

Set-valued information systems are generalized models of single-valued information systems. Its semantic interpretation can be classified into two categories: disjunctive and conjunctive. We focus on the former in this paper. By introducing four types of dominance relations to the disjunctive set-valued information systems, we establish a dominance-based rough sets approach, which is mainly based on the substitution of the indiscernibility relation by the dominance relations. Furthermore, we develop a new approach to sorting for objects in disjunctive set-valued ordered information systems, which is based on the dominance class of an object induced by a dominance relation. Finally, we propose criterion reductions of disjunctive set-valued ordered information systems that eliminate only those information that are not essential from the ordering of objects. The approaches show how to simplify a disjunctive set-valued ordered information system. Throughout this paper, we establish in detail the interrelationships among the four types of dominance relations, which include corresponding dominance classes, rough sets approaches, sorting for objects and criterion reductions. These results give a kind of feasible approaches to intelligent decision making in disjunctive set-valued ordered information systems.

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Multi-Granulation Graded Rough Intuitionistic Fuzzy Sets Models Based on Dominance Relation

Symmetry ◽

10.3390/sym10100446 ◽

2018 ◽

Vol 10 (10) ◽

pp. 446 ◽

Cited By ~ 2

Author(s):

Zhan-ao Xue ◽

Min-jie Lv ◽

Dan-jie Han ◽

Xian-wei Xin

Keyword(s):

Information Systems ◽

Fuzzy Sets ◽

Rough Sets ◽

Intuitionistic Fuzzy Sets ◽

Dominance Relation ◽

Classification Error ◽

Type I ◽

Type Ii ◽

Intuitionistic Fuzzy ◽

Relation Type

From the perspective of the degrees of classification error, we proposed graded rough intuitionistic fuzzy sets as the extension of classic rough intuitionistic fuzzy sets. Firstly, combining dominance relation of graded rough sets with dominance relation in intuitionistic fuzzy ordered information systems, we designed type-I dominance relation and type-II dominance relation. Type-I dominance relation reduces the errors caused by single theory and improves the precision of ordering. Type-II dominance relation decreases the limitation of ordering by single theory. After that, we proposed graded rough intuitionistic fuzzy sets based on type-I dominance relation and type-II dominance relation. Furthermore, from the viewpoint of multi-granulation, we further established multi-granulation graded rough intuitionistic fuzzy sets models based on type-I dominance relation and type-II dominance relation. Meanwhile, some properties of these models were discussed. Finally, the validity of these models was verified by an algorithm and some relative examples.

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Probabilistic decision making based on rough sets in interval-valued fuzzy information systems

Granular Computing ◽

10.1007/s41066-018-0139-9 ◽

2018 ◽

Vol 4 (3) ◽

pp. 391-405

Author(s):

Derong Shi ◽

Xiaoyan Zhang

Keyword(s):

Decision Making ◽

Information Systems ◽

Rough Sets ◽

Fuzzy Information ◽

Interval Valued

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Intelligent reasoning and management decision making with grey rough influence diagrams

International Journal of Intelligent Computing and Cybernetics ◽

10.1108/ijicc-03-2016-0012 ◽

2016 ◽

Vol 9 (4) ◽

pp. 336-353 ◽

Cited By ~ 1

Author(s):

Haiqing Hu ◽

Bingqiang Liu ◽

Tao Shen

Keyword(s):

Information Systems ◽

Decision Analysis ◽

Rough Sets ◽

Grey System Theory ◽

Approximate Reasoning ◽

Influence Diagrams ◽

Uncertain Information ◽

Content Type ◽

Intelligent Decision ◽

Interval Valued

Purpose Influence diagrams (IDs) have been widely applied as a form of knowledge expression and a decision analysis tool in the management and engineering fields. Relationship measurements and expectation values are computed depending on probability distributions in traditional IDs, however, most information systems in the real world are nondeterministic, and data in information tables can be interval valued, multiple valued and even incomplete. Consequently, conventional numeric models of IDs are not suitable for information processing with respect to imprecise data whose boundaries are uncertain. The paper aims to discuss these issues. Design/methodology/approach The grey system theory and rough sets have proved to be effective tools in the data processing of uncertain information systems, approximate knowledge acquisition and representation are also the objectives in intelligent reasoning and decision analysis. Hence, this study proposes a new mathematical model by combining grey rough sets with IDs, and approximate measurements are used instead of probability distribution, an implicational relationship is utilized instead of an indiscernible relationship, and all of the features of the proposed approach contribute to deal with uncertain problems. Findings The focus of this paper is to provide a more comprehensive framework for approximate knowledge representation and intelligent decision analysis in uncertain information systems and an example of decision support in product management systems with the new approach is illustrated. Originality/value Collaboration of IDs and grey rough sets is first proposed, which provides a new mathematical and graphical tool for approximate reasoning and intelligent decision analysis within interval-valued information systems.

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Attribute significance based on inclusion degree for incomplete information systems and their applications to MADM problems

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-211046 ◽

2021 ◽

pp. 1-17

Author(s):

Zhanhong Shi ◽

Dinghai Zhang

Keyword(s):

Information System ◽

Information Systems ◽

Incomplete Information ◽

Dominance Relation ◽

General Description ◽

Fuzzy Information ◽

Inclusion Degree ◽

Attribute Weights ◽

Incomplete Information Systems ◽

Interval Valued

Attribute significance is very important in multiple-attribute decision-making (MADM) problems. In a MADM problem, the significance of attributes is often different. In order to overcome the shortcoming that attribute significance is usually given artificially. The purpose of this paper is to give attribute significance computation formulas based on inclusion degree. We note that in the real-world application, there is a lot of incomplete information due to the error of data measurement, the limitation of data understanding and data acquisition, etc. Firstly, we give a general description and the definition of incomplete information systems. We then establish the tolerance relation for incomplete linguistic information system, with the tolerance classes and inclusion degree, significance of attribute is proposed and the corresponding computation formula is obtained. Subsequently, for incomplete fuzzy information system and incomplete interval-valued fuzzy information system, the dominance relation and interval dominance relation is established, respectively. And the dominance class and interval dominance class of an element are got as well. With the help of inclusion degree, the computation formulas of attribute significance for incomplete fuzzy information system and incomplete interval-valued fuzzy information system are also obtained. At the same time, results show that the reduction of attribute set can be obtained by computing the significance of attributes in these incomplete information systems. Finally, as the applications of attribute significance, the attribute significance is viewed as attribute weights to solve MADM problems and the corresponding TOPSIS methods for three incomplete information systems are proposed. The numerical examples are also employed to illustrate the feasibility and effectiveness of the proposed approaches.

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Multiple Granulation Rough Set Approach to Interval-Valued Intuitionistic Fuzzy Ordered Information Systems

Symmetry ◽

10.3390/sym13060949 ◽

2021 ◽

Vol 13 (6) ◽

pp. 949

Author(s):

Zhen Li ◽

Xiaoyan Zhang

Keyword(s):

Information Theory ◽

Pattern Recognition ◽

Information System ◽

Information Systems ◽

Rough Set ◽

Fuzzy Set ◽

Equivalence Relation ◽

Target Concept ◽

Actual Case ◽

Interval Valued

As a further extension of the fuzzy set and the intuitive fuzzy set, the interval-valued intuitive fuzzy set (IIFS) is a more effective tool to deal with uncertain problems. However, the classical rough set is based on the equivalence relation, which do not apply to the IIFS. In this paper, we combine the IIFS with the ordered information system to obtain the interval-valued intuitive fuzzy ordered information system (IIFOIS). On this basis, three types of multiple granulation rough set models based on the dominance relation are established to effectively overcome the limitation mentioned above, which belongs to the interdisciplinary subject of information theory in mathematics and pattern recognition. First, for an IIFOIS, we put forward a multiple granulation rough set (MGRS) model from two completely symmetry positions, which are optimistic and pessimistic, respectively. Furthermore, we discuss the approximation representation and a few essential characteristics for the target concept, besides several significant rough measures about two kinds of MGRS symmetry models are discussed. Furthermore, a more general MGRS model named the generalized MGRS (GMGRS) model is proposed in an IIFOIS, and some important properties and rough measures are also investigated. Finally, the relationships and differences between the single granulation rough set and the three types of MGRS are discussed carefully by comparing the rough measures between them in an IIFOIS. In order to better utilize the theory to realistic problems, an actual case shows the methods of MGRS models in an IIFOIS is given in this paper.

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