# Relations of granular worlds

Witold Pedrycz; George Vukovich

International Journal of Applied Mathematics and Computer Science (2002)

- Volume: 12, Issue: 3, page 347-357
- ISSN: 1641-876X

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topPedrycz, Witold, and Vukovich, George. "Relations of granular worlds." International Journal of Applied Mathematics and Computer Science 12.3 (2002): 347-357. <http://eudml.org/doc/207592>.

@article{Pedrycz2002,

abstract = {In this study, we are concerned with a two-objective development of information granules completed on a basis of numeric data. The first goal of this design concerns revealing and representing a structure in a data set. As such it is very much oriented towards coping with the underlying it relational aspects of the experimental data. The second goal deals with a formation of a mapping between information granules constructed in two spaces (thus it concentrates on the it directional aspect of information granulation). The quality of the mapping is directly affected by the information granules over which it operates, so in essence we are interested in the granules that not only reflect the data but also contribute to the performance of such a mapping. The optimization of information granules is realized through a collaboration occurring at the level of the data and the mapping between the data sets. The operational facet of the problem is cast in the realm of fuzzy clustering. As the standard techniques of fuzzy clustering (including a well-known approach of FCM) are aimed exclusively at the first objective identified above, we augment them in order to accomplish sound mapping properties between the granules. This leads to a generalized version of the FCM (and any other clustering technique for this matter). We propose a generalized version of the objective function that includes an additional collaboration component to make the formed information granules in rapport with the mapping requirements (that comes with a it directional component captured by the information granules). The additive form of the objective function with a modifiable component of collaborative activities makes it possible to express a suitable level of collaboration and to avoid a phenomenon of potential competition in the case of incompatible structures and the associated mapping. The logic-based type of the mapping (that invokes the use of fuzzy relational equations) comes as a consequence of the logic framework of information granules. A complete optimization method is provided and illustrated with several numeral studies.},

author = {Pedrycz, Witold, Vukovich, George},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {granular modeling; models of collaborative computing; collaboration and competition; clustering; fuzzy models; granular computing; FCM; fuzzy clustering},

language = {eng},

number = {3},

pages = {347-357},

title = {Relations of granular worlds},

url = {http://eudml.org/doc/207592},

volume = {12},

year = {2002},

}

TY - JOUR

AU - Pedrycz, Witold

AU - Vukovich, George

TI - Relations of granular worlds

JO - International Journal of Applied Mathematics and Computer Science

PY - 2002

VL - 12

IS - 3

SP - 347

EP - 357

AB - In this study, we are concerned with a two-objective development of information granules completed on a basis of numeric data. The first goal of this design concerns revealing and representing a structure in a data set. As such it is very much oriented towards coping with the underlying it relational aspects of the experimental data. The second goal deals with a formation of a mapping between information granules constructed in two spaces (thus it concentrates on the it directional aspect of information granulation). The quality of the mapping is directly affected by the information granules over which it operates, so in essence we are interested in the granules that not only reflect the data but also contribute to the performance of such a mapping. The optimization of information granules is realized through a collaboration occurring at the level of the data and the mapping between the data sets. The operational facet of the problem is cast in the realm of fuzzy clustering. As the standard techniques of fuzzy clustering (including a well-known approach of FCM) are aimed exclusively at the first objective identified above, we augment them in order to accomplish sound mapping properties between the granules. This leads to a generalized version of the FCM (and any other clustering technique for this matter). We propose a generalized version of the objective function that includes an additional collaboration component to make the formed information granules in rapport with the mapping requirements (that comes with a it directional component captured by the information granules). The additive form of the objective function with a modifiable component of collaborative activities makes it possible to express a suitable level of collaboration and to avoid a phenomenon of potential competition in the case of incompatible structures and the associated mapping. The logic-based type of the mapping (that invokes the use of fuzzy relational equations) comes as a consequence of the logic framework of information granules. A complete optimization method is provided and illustrated with several numeral studies.

LA - eng

KW - granular modeling; models of collaborative computing; collaboration and competition; clustering; fuzzy models; granular computing; FCM; fuzzy clustering

UR - http://eudml.org/doc/207592

ER -

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