This paper is devoted to an exposition of the idea of using granular structures obtained from data in the classification tasks of these data into decision classes. Classifiers are induced from granular reflections of data sets.

Let P and Q be bounded posets. In this note, a lemma is introduced that provides a set of sufcient conditions for the proper part of P being homotopy equivalent to the suspension of the proper part of Q. An application of this lemma is a uniied proof of the sphericity of the higher Bruhat orders under both inclusion order (which is a known result by ZIEGLER) and single step inclusion order (whi...

It is shown that the numbers ci of chains of length i in the proper part L \ {0, 1} of a distributive lattice L of length l + 2 satisfy the inequalities c0 < . . . < c⌊l/2⌋ and c⌊3l/4⌋ > . . . > cl. This proves 75 % of the inequalities implied by the Neggers unimodality conjecture.

henceforth PC) undertakes a fundamental re-examination of the relationship between merelogy, the general theory of parts, and set theory, the general theory of collections. He assumes a certain minimum background familiarity with both subjects, and limitations of space make the same assumption inevitable in the present account. Varzi (2011) is recommended as a clear, concise survey of mereology...

When describing a mereological relationship, the use of the word “part” to whole hides the intended semantics of the parthood relations. Existing studies in mereology usually present part of as a general top level mereology relation, and all other mereological relations are sub-relations under it. We present an alternative approach of mereological pluralism, in which each mereological relation ...