Fragile Watermarking of Decision System Using Rough Set Theory

Continuous attribute discretization based on rough set is to got possibly minimum number of cuts, and at the same time it should not weaken the indiscernibility ability of the original decision system. In order to obtain the optimal cut set of the continuous attribute system, based on research the choice of candidate cut set, this paper presents a heuristic genetic algorithm for continuous attribute discretization to decision tables. In this algorithm making the importance of the continuous cut as heuristic message, a new operator is constructed to not only maintain the discernibility of the cuts selected, but also improve local search ability of the algorithm. Compared the performance of this method with the others’, this method is proved effective and superiority.

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Decision systems in rough set theory: A set operatorial perspective

Journal of Algebra and Its Applications ◽

10.1142/s021949881950004x ◽

2019 ◽

Vol 18 (01) ◽

pp. 1950004 ◽

Cited By ~ 10

Author(s):

G. Chiaselotti ◽

T. Gentile ◽

F. Infusino

Keyword(s):

Set Theory ◽

Rough Set ◽

Rough Set Theory ◽

Decision Table ◽

Decision System ◽

Local Consistency ◽

Algebraic Set ◽

Decision Systems ◽

Set Systems ◽

Decision Attributes

In rough set theory (RST), the notion of decision table plays a fundamental role. In this paper, we develop a purely mathematical investigation of this notion to show that several basic aspects of RST can be of interest also for mathematicians who work with algebraic and discrete methods.In this abstract perspective, we call decision system a sextuple [Formula: see text] [Formula: see text], where [Formula: see text], [Formula: see text], [Formula: see text] are non-empty sets whose elements are called, respectively, objects, condition attributes, values, [Formula: see text] is a (possibly empty) set whose elements are called decision attributes, [Formula: see text] and [Formula: see text] is a map.The basic tool of our analysis is the equivalence relation [Formula: see text] on [Formula: see text], depending on the choice of a condition attribute subset [Formula: see text] and defined as follows: [Formula: see text] We denote by [Formula: see text] the equivalence class of [Formula: see text] with respect to [Formula: see text]. We interpret the classical RST notions of consistency and inconsistency for a decision table in an abstract algebraic set operatorial perspective and, in such a context, we introduce and investigate a kind of local consistency in any decision system [Formula: see text]. More specifically, we fix [Formula: see text], [Formula: see text] and try to determine in what cases all objects [Formula: see text] satisfy the condition [Formula: see text]. Then, we build a formal general framework whose basic tools are two local consistency set operators and a global closure operator, the condition attribute set [Formula: see text]. This paper provides a detailed study of these set operators, of the induced set systems and of the most relevant links between them.

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The use of rough rules in the selection of topographic objects for generalizing geographical information

Polish Cartographical Review ◽

10.2478/pcr-2020-0001 ◽

2020 ◽

Vol 52 (1) ◽

pp. 1-15

Author(s):

Anna Fiedukowicz

Keyword(s):

Set Theory ◽

Rough Set ◽

Rough Set Theory ◽

Visual Assessment ◽

Geographical Information ◽

Measurement Scales ◽

Decision System ◽

Current Form ◽

Selection Of

AbstractSelection is a key element of the cartographic generalisation process, often being its first stage. On the other hand it is a component of other generalisation operators, such as simplification. One of the approaches used in generalization is the condition-action approach. The author uses a condition-action approach based on three types of rough logics (Rough Set Theory (RST), Dominance-Based Rough Set Theory (DRST) and Fuzzy-Rough Set Theory (FRST)), checking the possibility of their use in the process of selecting topographic objects (buildings, roads, rivers) and comparing the obtained results. The complexity of the decision system (the number of rules and their conditions) and its effectiveness are assessed, both in terms of quantity and quality – through visual assessment. The conducted research indicates the advantage of the DRST and RST approaches (with the CN2 algorithm) due to the quality of the obtained selection, the greater simplicity of the decision system, and better refined IT tools enabling the use of these systems. At this stage, the FRST approach, which is characterised by the highest complexity of created rules and the worst selection results, is not recommended. Particular approaches have limitations resulting from the need to select appropriate measurement scales for the attributes used in them. Special attention should be paid to the selection of network objects, in which the use of only a condition-action approach, without maintaining consistency of the network, may not produce the desired results. Unlike approaches based on classical logic, rough approaches allow the use of incomplete or contradictory information. The proposed tools can (in their current form) find an auxiliary use in the selection of topographic objects, and potentially also in other generalisation operators.

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