基于扩张的模糊软集运算

利用映射扩张给出了模糊软集的新的定义,并且验证了在新运算下所有模糊软集构成有界分配格。     

Algebraic structures of soft sets associated with new operations

Recently new operations have been defined for soft sets. In this paper, we study some important properties associated with these new operations. A collection of all soft sets with respect to new operations give rise to four idempotent monoids. Then with the help of these monoids we can study semiring (hemiring) structures of soft sets. Some of these semirings (hemirings) are actually lattices. Finally, we show that soft sets with a fixed set of parameters are MV algebras and BCK algebras.     

On lattice ordered soft sets

Certain type of linguistic terms such as satisfactory, good, very good and excellent have an order among them. In this paper we introduce a new concept of soft sets with some order among the parameters. Some properties of lattice ordered soft sets are given. Lattice ordered soft sets are very useful in particular type of decision making problems where some order exists among the elements of parameters set.     

On some new operations in soft module theory

In this paper, we introduce the notions of sum and direct sum of soft submodules, small soft submodules and radical of a soft module. Moreover, we obtain basic properties of such soft submodules.     

Soft sets and soft rough sets

In this study, we establish an interesting connection between two mathematical approaches to vagueness: rough sets and soft sets. Soft set theory is utilized, for the first time, to generalize Pawlak’s rough set model. Based on the novel granulation structures called soft approximation spaces, soft rough approximations and soft rough sets are introduced. Basic properties of soft rough approximations are presented and supported by some illustrative examples. We also define new types of soft sets such as full soft sets, intersection complete soft sets and partition soft sets. The notion of soft rough equal relations is proposed and related properties are examined. We also show that Pawlak’s rough set model can be viewed as a special case of the soft rough sets, and these two notions will coincide provided that the underlying soft set in the soft approximation space is a partition soft set. Moreover, an example containing a comparative analysis between rough sets and soft rough sets is given.     

The relationship among soft sets,soft rough sets and topologies

Molodtsov’s soft set theory is a newly emerging tool to deal with uncertain problems. Based on the novel granulation structures called soft approximation spaces, Feng et al. initiated soft rough approximations and soft rough sets. Feng’s soft rough sets can be seen as a generalized rough set model based on soft sets, which could provide better approximations than Pawlak’s rough sets in some cases. This paper is devoted to establishing the relationship among soft sets, soft rough sets and topologies. We introduce the concept of topological soft sets by combining soft sets with topologies and give their properties. New types of soft sets such as keeping intersection soft sets and keeping union soft sets are defined and supported by some illustrative examples. We describe the relationship between rough sets and soft rough sets. We obtain the structure of soft rough sets and the topological structure of soft sets, and reveal that every topological space on the initial universe is a soft approximating space.     

Entropy-based operations on fuzzy sets

By using a fuzzy entropy approach, three sets of new generalized operators are presented. After a general discussion on fuzzy entropy, the concept of an elementary entropy function of a fuzzy set is introduced. Using this mapping, the generalized intersections and unions are defined as mappings that assign the least and the most fuzzy membership grade to each of the elements of the domain of the operators, respectively. It is shown that these operators can be constructed from the conventional min and max operations. Next, two modified sets of operations are introduced. The second part of the paper investigates the applicability of the new operators in fuzzy logic controllers. Simulations have been carried out so as to determine the effects of the operators on the performance of the fuzzy controllers. It is concluded that the first set of operators does not provide stable control, but the performance of the fuzzy controller can be improved by using the modified operations for a class of plants     

犹豫模糊软集

犹豫模糊集是对模糊集的一种推广,它是一类关于域中每个元素所含隶属度的集合,常应用于群决策中,但由于其本身在参数工具上的缺乏使得难于处理不确定数据。为了提高决策的精确性,将软集与犹豫模糊集结合起来,提出犹豫模糊软集的概念,并给出犹豫模糊软集的基本运算法则和性质。     

多值直觉模糊软集

将多值直觉模糊集和软集相结合,提出了多值直觉模糊软集的概念。给出了多值直觉模糊软集的补、交、并“、且”“、或”运算的概念,并基于这些概念研究了若干性质。     

双极值模糊软集

提出了双极值模糊软集的概念,给出双极值模糊软集的补、并、交、"且"及"或"运算,并讨论了它们的性质。     

Exclusive disjunctive soft sets

Soft sets theory, initiated by Molodtsov, is an emerging tool to deal with uncertain problems and has been studied by scholars in both theory and practice. This paper proposes the notion of exclusive disjunctive soft sets and studies some of its operations, such as, restricted/relaxed AND operations, dependency between exclusive disjunctive soft sets and bijective soft sets, exclusive disjunctive soft decision systems, reduction of exclusive disjunctive soft decision systems, core of exclusive disjunctive soft decision systems, decision rules in exclusive disjunctive decision soft sets. Moreover, this study gives an application of exclusive disjunctive soft sets, which shows that it can be applied to attribute reduction of incomplete information system.     

对偶软集和对偶软子坡代数

借助软集对偶的概念,补充了软集对偶所保持的两个重要性质,引入了软子坡代数对偶的定义,主要研究了坡代数上软理想、软滤子对偶的若干性质,给出了软坡代数对偶之间的同态、同构的定义,证明了若两个软坡代数同构,且它们的对偶软坡代数均存在,在一定的条件下,它们也是同构的。     

Generalised fuzzy soft sets

In this paper, we define generalised fuzzy soft sets and study some of their properties. Application of generalised fuzzy soft sets in decision making problem and medical diagnosis problem has been shown.     

软集与软RSL-代数

将Molodtsov提出的软集理论应用于RSL-代数。为此,提出了软 RSL-代数和软 RSL-子代数的概念,讨论了它们的基本性质。同时,给出了关于RSL-代数的同态映射,刻画了同态映射的基本特性。     

软集与软格

将Molodtsov于1999年提出的软集理论应用到格论中,提出了软格和软子格的概念,讨论了它们相关的性质。另外,基于[∈]-软集和q-软集的概念,讨论了理想软格和滤子软格的一些性质。     

软集合和软MV-代数

通过将Molodtsov在1999年提出的软集合理论应用于MV-代数理论,提出了软MV-代数和软MV-子代数的概念,并且得到了相关的一些性质。     

Soft sets and soft rings

Molodtsov (1999) introduced the concept of soft sets in [1]. Then, Maji et al. (2003) defined some operations on soft sets in [2]. Akta? and Ça?man (2007) defined the notion of soft groups in [3]. Finally, soft semirings are defined by Feng et al. (2008) in [5]. In this paper, we have introduced initial concepts of soft rings.     

Soft sets and soft groups

Molodtsov introduced the concept of soft set theory, which can be used as a generic mathematical tool for dealing with uncertainty. In this paper we introduce the basic properties of soft sets, and compare soft sets to the related concepts of fuzzy sets and rough sets. We then give a definition of soft groups, and derive their basic properties using Molodtsov’s definition of the soft sets.     

Soft rough fuzzy sets and soft fuzzy rough sets

Fuzzy set theory, soft set theory and rough set theory are mathematical tools for dealing with uncertainties and are closely related. Feng et al. introduced the notions of rough soft set, soft rough set and soft rough fuzzy set by combining fuzzy set, rough set and soft set all together. This paper is devoted to the further discussion of the combinations of fuzzy set, rough set and soft set. A new soft rough set model is proposed and its properties are derived. Furthermore, fuzzy soft set is employed to granulate the universe of discourse and a more general model called soft fuzzy rough set is established. The lower and upper approximation operators are presented and their related properties are surveyed.