Complex & Intelligent Systems ( IF 5.8 ) Pub Date : 2021-02-17 , DOI: 10.1007/s40747-021-00271-7 B. Elavarasan , G. Muhiuddin , K. Porselvi , Y. B. Jun
Human endeavours span a wide spectrum of activities which includes solving fascinating problems in the realms of engineering, arts, sciences, medical sciences, social sciences, economics and environment. To solve these problems, classical mathematics methods are insufficient. The real-world problems involve many uncertainties making them difficult to solve by classical means. The researchers world over have established new mathematical theories such as fuzzy set theory and rough set theory in order to model the uncertainties that appear in various fields mentioned above. In the recent days, soft set theory has been developed which offers a novel way of solving real world issues as the issue of setting the membership function does not arise. This comes handy in solving numerous problems and many advancements are being made now-a-days. Jun introduced hybrid structure utilizing the ideas of a fuzzy set and a soft set. It is to be noted that hybrid structures are a speculation of soft set and fuzzy set. In the present work, the notion of hybrid ideals of a near-ring is introduced. Significant work has been carried out to investigate a portion of their significant properties. These notions are characterized and their relations are established furthermore. For a hybrid left (resp., right) ideal, different left (resp., right) ideal structures of near-rings are constructed. Efforts have been undertaken to display the relations between the hybrid product and hybrid intersection. Finally, results based on homomorphic hybrid preimage of a hybrid left (resp., right) ideals are proved.
中文翻译:
混合结构应用于理想的近环
人类的努力范围广泛,包括解决工程,艺术,科学,医学,社会科学,经济学和环境领域的引人入胜的问题。为了解决这些问题,经典的数学方法是不够的。现实世界中的问题涉及许多不确定因素,因此很难通过经典方法解决。世界各地的研究人员已经建立了新的数学理论,例如模糊集理论和粗糙集理论,以便对上述各个领域中出现的不确定性进行建模。近年来,由于没有出现设置隶属函数的问题,软集理论得到了发展,它提供了一种解决现实世界问题的新颖方法。这在解决众多问题时非常方便,并且如今正在取得许多进步。Jun引入了利用模糊集和软集思想的混合结构。要注意的是,混合结构是对软集和模糊集的推测。在当前的工作中,引入了近环混合理想的概念。已经进行了大量工作来研究其部分重要性能。这些概念已经过特征化,它们之间的关系也得以建立。对于混合的左(分别为右)理想,构造了不同的左环(分别为右)理想环结构。已经做出努力来显示混合产品和混合交叉点之间的关系。最后,证明了基于混合左(分别为右)理想的同构混合原像的结果。要注意的是,混合结构是对软集和模糊集的推测。在当前的工作中,引入了近环混合理想的概念。已经进行了大量工作来研究其部分重要性能。这些概念已经过特征化,它们之间的关系也得以建立。对于混合的左(理想,右)理想,构建了不同的左环理想(近,右)理想结构。已经做出努力以显示混合产品和混合交叉点之间的关系。最后,证明了基于混合左(分别为右)理想的同构混合原像的结果。要注意的是,混合结构是对软集和模糊集的推测。在当前的工作中,引入了近环混合理想的概念。已经进行了大量工作来研究其部分重要性能。这些概念已经过特征化,它们之间的关系也得以建立。对于混合的左(理想,右)理想,构建了不同的左环理想(近,右)理想结构。已经做出努力来显示混合产品和混合交叉点之间的关系。最后,证明了基于混合左(分别为右)理想的同构混合原像的结果。已经进行了大量工作来研究其部分重要性能。这些概念已经过特征化,它们之间的关系也得以建立。对于混合的左(理想,右)理想,构建了不同的左环理想(近,右)理想结构。已经做出努力来显示混合产品和混合交叉点之间的关系。最后,证明了基于混合左(分别为右)理想的同构混合原像的结果。已经进行了大量工作来研究其部分重要性能。这些概念已经过特征化,它们之间的关系也得以建立。对于混合的左(理想,右)理想,构建了不同的左环理想(近,右)理想结构。已经做出努力来显示混合产品和混合交叉点之间的关系。最后,证明了基于混合左(分别为右)理想的同构混合原像的结果。