A generalized algebraic approach to finding rough set approximations and generating logic rules

Sitnikov, D.; Ryabov, Oleg; Titova, O.; Romanenko, O. V.

doi:10.2495/data070011

Cited by 3 publications

(6 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…in our series of papers [2][3][4][5] we try to give the rough set ideology a bit different perspective by avoiding the usage of the knowledge granularity concept. Whereas the classical rough set theory is based on the indiscernibility relation (which can be equivalence, tolerance or other types of relations), we do not use such a notion and try to consider uncertainty from a logic-algebraic viewpoint.…”

Section: Algebraic Approach Versus Knowledge Granularitymentioning

confidence: 99%

A rough set based algebraic approach to modelling complex systems

Sitnikov¹,

Ryabov²,

Mishcheriakov³

et al. 2018

Int. J. DNE

Self Cite

View full text Add to dashboard Cite

A complex system is considered as an algebraic structure having specific properties that do not allow expressing precisely the meaning of information objects included in the system. An algebraic definition of complexity has been given. the complexity has been considered from two viewpoints. A system can be considered to be a complex one if (a) boundary regions for system's objects and processes are broad; (b) possibilities for system's decompositions are limited. difficulties associated with complex system description and decomposition have been discussed in the framework of rough set methodology. A method for extracting salient features of information objects available in the system has been outlined. some theoretical aspects of rough set based analysis of complex systems have been discussed. All the operations designated to obtaining new knowledge or data patterns in complex systems are algebraically described from the viewpoint of algebraic systems including predicates (in particular, finite ones) and operations on them. thus, a system is considered to be complex if there is a great degree of uncertainty in the data and/or there are some serious problems with system's decomposition."

show abstract

Section: Algebraic Approach Versus Knowledge Granularitymentioning

confidence: 99%

A rough set based algebraic approach to modelling complex systems

Sitnikov¹,

Ryabov²,

Mishcheriakov³

et al. 2018

Int. J. DNE

Self Cite

View full text Add to dashboard Cite

show abstract

“…A method for quick finding the upper and lower approximations of a rough set with the help of manipulating Boolean strings has been suggested in [4]. It allows finding approximations for a given set using only Boolean operations.…”

Section: A Methods For Finding Local Reductsmentioning

confidence: 99%

“…Elements a 1 , a 2 , a 3 , a 4 , and a 5 are described with the help of features P 1 , P 2 , P 3 . The set X consists of elements a 2 , a 4 , a 5 (Table 5).…”

Section: A Methods For Finding Local Reductsmentioning

confidence: 99%

“…For finding approximations of a rough set various approaches can be used, including the algebraic approach developed by the authors earlier [4]. The suggested approach uses only comparison and Boolean operations, which makes the process of searching approximations and building approximation-based logic rules quite quick from the computational viewpoint.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An approach to finding reduced sets of information features describing discrete objects based on rough sets theory

Sitnikov

Titova

Romanenko³

et al. 2008

WIT Transactions on Information and Communication Technologies

Self Cite

View full text Add to dashboard Cite

Modern Data Mining methods allow discovering non-trivial dependencies in large information arrays. Since these methods are used for processing and analysis of huge information volumes, reducing the number of features necessary for describing a discrete object is one of the most important problems.One of the classical problems in intelligent data analysis is the problem of classifying new objects based on some a-priori information. This information might not allow us to exactly classify an object as one belonging to a certain set. In such cases using rough sets theory may be an effective solution as this theory operates with the concept of "indiscernible" elements and ambiguous information.In this paper we introduce a concept of a local reduct as a reduced set of features allowing us to describe a particular subset of the original set with the same precision as with the help of the full set of features. A method has been suggested which allows finding reduced sets of features adequately describing a rough set without losing necessary information (so-called reducts), and also assessing the importance of each feature. The suggested method is based on the algebraic approach to finding rough set approximations developed by the authors earlier. The main idea of the developed approach is as follows: if the algebraic approximations of a rough set do not change substantially in the process of excluding features the resulting reduced set of features can be used instead of the original full set. Also the greater changes eliminating a particular feature causes in the approximations, the more important this feature is.

show abstract

“…We earlier suggested an original algebraic approach for determining the upper and lower approximations for a given set [2]. This approach allows using only logic operations for calculating approximations, which substantially speeds up the process of generating logic rules reflecting dependencies in discrete data.…”

Section: Introductionmentioning

confidence: 99%

A method for finding minimal sets of features adequately describing discrete information objects

et al. 2009

Self Cite

View full text Add to dashboard Cite

One of the classical Data Mining problems is the problem of classifying new objects on the basis of available information when the information associated with these objects does not allow identifying them unambiguously as elements of some set. In such cases using rough sets theory is often an effective solution. This theory operates with such concepts as "indiscernible" elements and relations. A rough set is characterized by lower and upper approximations for finding which the authors earlier suggested an original algebraic method. The given method uses only logic operations, which makes the process of searching logic rules very quick and efficient.The upper and lower approximations of a rough set allow describing elements of this set as completely as it is possible from the viewpoint of available information. In this connection it seems interesting and important to find irreducible sets of features describing a rough set with the same "precision" as with the help of a full set of features (so called reducts). This problem is quite difficult and complicated and at present it does not have good solutions. Our paper continues research carried out by the authors earlier and we suggest a method for finding reducts based on eliminating non-salient features in the reverse order of their importance. The suggested procedure allows us to avoid exhaustive searching by extracting a predefined number of most significant reducts. In this paper we consider arbitrary features taking on their values from finite sets.

show abstract

A generalized algebraic approach to finding rough set approximations and generating logic rules

Cited by 3 publications

References 3 publications

A rough set based algebraic approach to modelling complex systems

A rough set based algebraic approach to modelling complex systems

An approach to finding reduced sets of information features describing discrete objects based on rough sets theory

A method for finding minimal sets of features adequately describing discrete information objects

Contact Info

Product

Resources

About