Algebraic approaches to granular computing

Mao, Hua; Hu, Mengjun; Yao, Yiyu

doi:10.1007/s41066-019-00178-2

Cited by 9 publications

(4 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…• Primitive Granular Computing Paradigm: PGCP (see [3]) • Classical Granular Computing Paradigms: CGCP including precision based approaches, GrC model approach [11], and definite object approaches [15,16]. • Axiomatic Granular Computing Paradigm: AGCP due to the present author…”

Section: Granules and Granulationsmentioning

confidence: 99%

“…In actual semantics a number of concepts of definiteness is possible. In some approaches, as in [15,16], these are taken as granules. Related theory has a direct connection with closure algebras and operators as indicated in [3].…”

Section: Meaning Of Termsmentioning

confidence: 99%

“…Most semantics in these contexts correspond to the classical domain. GT03 is an approach suggested in [15,16] -the idea that all granules should be definite objects has a long history, but requiring the converse falls within debatable territory.…”

Section: Contamination and Granular Operator Spacesmentioning

confidence: 99%

See 2 more Smart Citations

Algebraic Semantics of Generalized RIFs

Mani

2021

Preprint

View full text Add to dashboard Cite

A number of numeric measures like rough inclusion functions (RIFs) are used in general rough sets and soft computing. But these are often intrusive by definition, and amount to making unjustified assumptions about the data. The contamination problem is also about recognizing the domains of discourses involved in this, specifying errors and reducing data intrusion relative to them. In this research, weak quasi rough inclusion functions (wqRIFs) are generalized to general granular operator spaces with scope for limiting contamination. New algebraic operations are defined over collections of such functions, and are studied by the present author. It is shown by her that the algebras formed by the generalized wqRIFs are ordered hemirings with additional operators. By contrast the generalized rough inclusion functions lack similar structure. This potentially contributes to improving the selection (possibly automatic) of such functions, training methods, and reducing contamination (and data intrusion) in applications. The underlying framework and associated concepts are explained in some detail as they are relatively new.

show abstract

Section: Granules and Granulationsmentioning

confidence: 99%

Section: Meaning Of Termsmentioning

confidence: 99%

See 1 more Smart Citation

Algebraic Semantics of Generalized RIFs

Mani

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Since the basic notions in Pawlak classical rough set model (Pawlak 1982(Pawlak , 1991 asked the requirement to be an equivalence relation which restricted the applied fields of rough set, many authors have hoped to change the equivalence relation in order to extend the approximation operators of Pawlak classical rough set model. And some extended approximation operators are provided by the combining of rough set with some other theories and some other mathematical structures, for example, fuzzy theory (Cattanco 1998;Mi et al 2008;Yao 1998aYao , 2001Yao et al 2019), covering theory (Bonikowski et al 1998;Yao 1998b;Yao and Yao 2012;Zhang et al 2019), lattice (Li et al 2016;Pawlak and Skowron 2007c;Wang et al 2019;Yao 1998b), matroid theory (Li and Liu 2012;Marek and Skowron 2014), three-way decisions (Huang and Zhu 2016;Zhao and Hu 2020), and some others (Li et al 2019;Mao et al 2021;Xu and Wang 2018;Zhang et al 2016).…”

mentioning

confidence: 99%

Approximation operators via TD-matroids on two sets

Wang

Mao

2022

Soft Comput

Self Cite

View full text Add to dashboard Cite

Rough set theory is an extension of set theory with two additional unary set-theoretic operators known as approximation in order to extract information and knowledge. It needs the basic, or say definable, knowledge to approximate the undefinable knowledge in a knowledge space using the pair of approximation operators. Many existed approximation operators are expressed with unary form. How to mine the knowledge which is asked by binary form with rough set has received less research attention, though there are strong needs to reveal the answer for this challenging problem. There exist many information with matroid constraints since matroid provides a platform for combinatorial algorithms especially greedy algorithm. Hence, it is necessary to consider a matroidal structure on two sets no matter the two sets are the same or not. In this paper, we investigate the construction of approximation operators expressed by binary form with matroid theory, and the constructions of matroidal structure aided by a pair of approximation operators expressed by binary form. First, we provide a kind of matroidal structure—TD-matroid defined on two sets as a generalization of Whitney classical matroid. Second, we introduce this new matroidal construction to rough set and construct a pair of approximation operators expressed with binary form. Third, using the existed pair of approximation operators expressed with binary form, we build up two concrete TD-matroids. Fourth, for TD-matroid and the approximation operators expressed by binary form on two sets, we seek out their properties with aspect of posets, respectively. Through the paper, we use some biological examples to explain and test the correct of obtained results. In summary, this paper provides a new approach to research rough set theory and matroid theory on two sets, and to study on their applications each other.

show abstract

Rough set approximations based on a matroidal structure over three sets

Wang

Mao²,

Liu³

et al. 2022

Appl Intell

Self Cite

View full text Add to dashboard Cite

Pawlak’s classical model of rough set approximations provides an efficient tool for extracting information exactly by employing available knowledge (i.e., known knowledge) in an information system, since many problems in rough set theory are NP-hard and their solution process is therefore greedy and approximate. Many extensions of Pawlak’s classical model have been proposed in recent years. Most of them are considered over one or two sets, that is, one- or two-dimensional space or one- or two-dimensional data. Aided by relation-based rough set models, a few of these extensions are considered over three sets. However, the real world is in three-dimensional space. Therefore, it is necessary to solve these problems with other models, such as covering rough set models. For this purpose, we propose the TP-matroid—a matroidal structure over three sets. Employing the family of feasible sets of a TP-matroid as the available knowledge, a pair of rough set approximations—lower and upper approximations—is provided. In addition, for an information system defined over three sets, assisted by formal concept analysis, we establish a pair of rough set approximations. Furthermore, two TP-matroids are established based on the above pair of rough set approximations. The integration between the two pairs of rough set approximations presented here is discussed. The results show that for an information system in three-dimensional space, the rough set approximations provided here can effectively explore unknown knowledge by using available knowledge based on the family of feasible sets of a TP-matroid.

show abstract

Algebraic approaches to granular computing

Cited by 9 publications

References 33 publications

Algebraic Semantics of Generalized RIFs

Algebraic Semantics of Generalized RIFs

Approximation operators via TD-matroids on two sets

Rough set approximations based on a matroidal structure over three sets

Contact Info

Product

Resources

About