Clustering based-on indiscernibility and indiscernibility level

Abstract

The core concept of classical rough sets are clustering similarities and dissimilarities of objects based on the notions of indiscernibility and discernibility. In this paper, we present a new method of clustering data based on the combination of indiscernibility and its indiscernibility level. The indiscernibility level quantifies the indiscernibility of pairs of objects among other objects in information systems. The result of this paper show the dual notions of indiscernibility and its indiscernibility level play an important role in clustering information systems.

Reducing Hierarchical Clustering Instability Using Clustering Based on Indiscernibility and Indiscernibility Level

“…Hakim et al [2] have introduced the new method of clustering based on Indiscernibility and Indiscernibility Level. The indiscernibility here is motivated by quantitative indiscernibility relations presented in Zhao et al [1].…”

“…The denominator of that level was indiscernibility and discernibility a pair of objects, unlike the above indiscernibility level, Hakim et al [2] proposed a new quantity of indiscernibility level as a ratio of the indiscernibility of a pair of objects to the total indiscernibility object pairs in information system. This level show how strong an indiscernibility of a pair of objects to the all objects in information system.…”

“…The connection between quantitative indiscernibility relation and indiscernibility level and also the definition for quantitative discernibility relations and discernibility level could be read in detail at [2]. …”

“…We here introduce indiscernibility level, a novel measure that solves the instability problems and make it possible to represent the granularity of objects while keeping the use of independently defined binary classifications. The indiscernibility level [2], γ(x i , x j ), defined as a j a i a j a i a j a i a x I x I x I A a x I x I A a x I x I A …”

“…Quantitative indiscernibility relations as an indiscernibility relation with binary attribute value on information system which is reflexive and symmetric [1] creates similarity measure of indiscernible classes among pairs of objects in information system. Quantitative indiscernibility relation and indiscernibility level have been used as a new method for hierarchical clustering introduced by Hakim et al [2]. Indiscernibility level is the ratio of quantitative indiscernibility relations among pair of objects to the total quantitative indiscernibility relations of objects pairs on the information system.…”