Concise granule descriptions for definable granules and approaching descriptions for indefinable granules are challenging and important issues in granular computing. The concept with only common attributes has been intensively studied. To investigate the granules with some special needs, we propose a novel type of compound concepts in this paper, i.e., common-and-necessary concept. Based on the definitions of concept-forming operations, the logical formulas are derived for each of the following types of concepts: formal concept, object-induced three-way concept, object oriented concept and common-and-necessary concept. Furthermore, by utilizing the logical relationship among various concepts, we have derived concise and unified equivalent conditions for definable granules and approaching descriptions for indefinable granules for all four kinds of concepts.
翻译:在颗粒计算中,对可确定颗粒的精密颗粒描述和对不可确定颗粒的接近描述是具有挑战性和重要问题。对仅具有共同属性的概念进行了深入研究。为了调查具有某些特殊需要的颗粒,我们在本文件中提出了新型的复合概念,即共同和必要概念。根据概念形成作业的定义,为下列各类概念分别得出了逻辑公式:正式概念、物体引发的三向概念、对象导向概念和共同和必要概念。此外,通过利用各种概念之间的逻辑关系,我们为可确定颗粒制定了简明和统一的等同条件,并接近了所有四种概念的不可确定性颗粒的描述。