Author
Yong Li
Bio: Yong Li is an academic researcher from Jiangnan University. The author has contributed to research in topics: Type (model theory) & Soft set. The author has co-authored 5 publications.
Papers
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12 Sep 2016
TL;DR: In this article, the concept of soft subincline is introduced and some equivalent conditions of it and two operations "RESTRICTED INTERSECT" and "AND" on it are discussed.
Abstract: Firstly, this paper presents the new concept of soft subincline. Then some equivalent conditions of it and two operations “RESTRICTED INTERSECT” and “AND” on it are discussed. After that the relationship between soft subincline and the dual of soft set based on the method of the dual of soft set are studied. In addition, the concepts and properties of maps between soft subincline are given. Finally, the chain condition of H which consists of all of the soft subinclines is introduced and obtain a necessary and sufficient condition for H is Artinian or Noetherian.
20 Jul 2017
TL;DR: This paper gives the equivalent descriptions of the new type soft prime ideal of KU-algebras and investigates its properties, and defines the new concept of the projection of AND operation of soft set, and obtains that the projected projection of And operation of two soft set is also the newTypesoft prime ideal.
Abstract: Through combining the soft set with KU-algebras, this paper introduces the concept of a new type soft prime ideal of KU-algebras and investigates its properties. Firstly, we give the equivalent descriptions of the new type prime soft ideal of KU-algebras. Then, we show the differences between the new type soft prime ideal of KU-algebras and the common soft prime ideal of KU-algebras by giving examples. After then, studies about the equivalent description of the new type soft prime ideal and the new type soft ideal prove that the algebraic structure of dual soft set is different from the algebraic structure of \(\alpha \)-level set. Besides, we define the new concept of the projection of AND operation of soft set, and the obtain that the projection of AND operation of two soft set is also the new type soft prime ideal, if the AND operation is a new type soft prime ideal of KU-algebras. Finally, we explore the properties of the new type soft prime ideal of KU-algebras about the image and inverse image.
20 Jul 2017
TL;DR: Methods of pointwise are used to discuss some basic properties of homomorphic image and homomorphic preimage of the fuzzy subalgebra of a \(KU - \) algebra from the following aspects.
Abstract: In this paper, we carry out a detailed investigation into the \(( \in , \in \vee {q_{_{\left( {\lambda ,\mu } \right) }}}) - \) fuzzy subalgebra of a \(KU - \) algebra from the following aspects. Firstly, the concepts of the pointwise \(( \in , \in \vee {q_{_{\left( {\lambda ,\mu } \right) }}}) - \) fuzzy subalgebra and generalized fuzzy subalgebra of KU-algebras are introduced. Secondly, the equivalent descriptions of the \(( \in , \in \vee {q_{_{\left( {\lambda ,\mu } \right) }}}) - \) fuzzy subalgebra are given, including the level set, the \(( \in , \in \vee {q_{_{\left( {\lambda ,\mu } \right) }}}) - \) fuzzy subalgebra is better than \(( \in , \in ) - \) fuzzy subalgebra and \(( \in , \in \vee q) - \) fuzzy subalgebra, which has rich hierarchy structure. Once more, we use methods of pointwise to discuss some basic properties of homomorphic image and homomorphic preimage of the \(( \in , \in \vee {q_{_{\left( {\lambda ,\mu } \right) }}}) - \) fuzzy subalgebra. Finally, we discuss the related properties about direct product and projection.
20 Jul 2017
TL;DR: A new concept of the descending (ascending) chain conditions of the ideals of KU-algebras is introduced and is studied using the properties of \(( \in , \in \vee {q_{(\lambda ,\mu )}})\)-fuzzy ideals.
Abstract: First, new concepts of pointwise \(( \in , \in \vee {q_{(\lambda ,\mu )}})\)-fuzzy ideals and generalized fuzzy ideals of KU-algebras are defined. By using inequalities, level sets and characteristic functions, some equivalent characterizations of \(( \in , \in \vee {q_{(\lambda ,\mu )}})\)-fuzzy ideals of KU-algebras are studied, a richer hierarchical structure of this fuzzy ideal is presented, and some properties are discussed using the partial order of KU-algebras. Second, it is proven that the intersections, unions (under certain conditions), homomorphic image and homomorphic preimage of \(( \in , \in \vee {q_{(\lambda ,\mu )}})\)-fuzzy ideals of KU-algebras are also \(( \in , \in \vee {q_{(\lambda ,\mu )}})\)-fuzzy ideals. Then, the direct product and projection of the \(( \in , \in \vee {q_{(\lambda ,\mu )}})\)-fuzzy ideals of KU-algebras are also investigated. Finally, a new concept of the descending (ascending) chain conditions of the ideals of KU-algebras is introduced and is studied using the properties of \(( \in , \in \vee {q_{(\lambda ,\mu )}})\)-fuzzy ideals.
20 Jul 2017
TL;DR: In this paper, a new type of derivations on FI-algebras is introduced and the existence of it is verified by an example and a program, and the properties of the derivations are investigated.
Abstract: In this paper, firstly, the concept of a new type of derivations on FI-algebras is introduced. The existence of it is verified by an example and a program. Then, the concepts of different kinds of derivations on FI-algebras are given. The properties of derivations on FI-algebras and the relationship between derivations and ideal are investigated. The equivalent conditions of identity derivation and the equivalent conditions of isotone derivation are proved. Finally, the concept of \(a-\)principal derivations on DFI-algebras is given. The existence of \(a-\)principal derivations is verified by an example and a program.