Linear Diophantine fuzzy set and its applications towards multi-attribute decision-making problems

Fuzzy set theory, rough set theory and soft set theory are all generic mathematical tools for dealing with uncertainties. There has been some progress concerning practical applications of these theories, especially, the use of these theories in decision making problems. In the present article, we review some decision making methods based on (fuzzy) soft sets, rough soft sets and soft rough sets. In particular, we provide several novel algorithms in decision making problems by combining these kinds of hybrid models. It may be served as a foundation for developing more complicated soft set models in decision making.

A survey of decision making methods based on certain hybrid soft set models

Graphical abstractDisplay Omitted HighlightsA novel Z-soft fuzzy rough set model is constructed.Novel idea and new results are different from Meng-SFR-model and Sun-SFR-model.A kind of decision making method based on the Z-SFR-sets is investigated.The comparisons of numerical experimentation are given.An overview of techniques based on some types of soft set models are discussed. In this paper, a kind of novel soft set model called a Z-soft fuzzy rough set is presented by means of three uncertain models: soft sets, rough sets and fuzzy sets, which is an important generalization of Z-soft rough fuzzy sets. As a novel Z-soft fuzzy rough set, its applications in the corresponding decision making problems are established. It is noteworthy that the underlying concepts keep the features of classical Pawlak rough sets. Moreover, this novel approach will involve fewer calculations when one applies this theory to algebraic structures. In particular, an approach for the method of decision making problem with respect to Z-soft fuzzy rough sets is proposed and the validity of the decision making methods is testified by a given example. At the same time, an overview of techniques based on some types of soft set models is investigated. Finally, the numerical experimentation algorithm is developed, in which the comparisons among three types of hybrid soft set models are analyzed.

On a novel uncertain soft set model

Graphical abstractDisplay Omitted In this paper, we investigate the relationships among rough sets, soft sets and hemirings. The concept of soft rough hemirings is introduced, which is an extended notion of a rough hemiring. It is pointed out that in this paper, we first apply soft rough sets to algebraic structure-hemirings. Further, we first put forward the concepts of C-soft sets and CC-soft sets, which provide a new research idea for soft rough algebraic research. Moreover, we study roughness in hemirings with respect to MSR-approximation spaces. Some new soft rough operations over hemirings are explored. In particular, lower and upper MSR-hemirings (k-ideal and h-ideal) are investigated. Finally, we put forth an approach for multicriteria group decision making problem based on modified soft rough sets and offer an actual example.

A novel soft rough set

Three-way group decision making based on multigranulation fuzzy decision-theoretic rough set over two universes

The aim of this paper is to introduce the notion of a rough soft hemiring, which is an extended notion of a rough hemiring and a soft hemiring. We study roughness in soft hemirings with respect to Pawlak approximation spaces. Some new rough soft operations are explored. In particular, lower and upper rough soft hemirings and k-idealistic, h-idealistic, strong h-idealistic idealistic soft hemirings are investigated. Finally, an important result on an upper strong h-idealistic rough soft hemiring via Bourne's congruence relations are obtained.

A new rough set theory: rough soft hemirings

Combining rough sets and soft sets, a kind of novel rough soft hemirings with respect to a strong h-ideal of hemirings in Pawlak approximation spaces is introduced. The relationships between lower and upper rough soft hemirings are studied. In particular, lower and upper rough soft strong h-ideals with respect to strong h-ideals are investigated, respectively. Some good examples are given. Finally, we put forward two new kinds of decision-making methods in rough soft sets, and some related algebraic and applied examples are also given.

Another approach to rough soft hemirings and corresponding decision making

By means of Dubois and Prade’s idea, we apply rough fuzzy sets and fuzzy rough sets to algebraic structures. The concepts of rough fuzzy strong h-ideals (rough fuzzy prime ideals) and fuzzy rough strong h-ideals (fuzzy rough prime ideals) of hemirings are introduced, respectively. The relationships between them are investigated. Some characterizations of these two kinds of rough set theory of hemirings are explored. Keyword: rough set; strong h-ideal; rough fuzzy strong h-ideal; fuzzy rough strong h-ideal; rough fuzzy prime ideal; fuzzy rough prime ideal; hemiring. 2000 Mathematics Subject Classification: MSC 2010; 16Y60; 16Y99.

Rough fuzzy (fuzzy rough) strong h-ideals of hemirings

The aim of this paper is to introduce the concepts of IFP-intuitionistic fuzzy soft h-ideals and IFP-equivalent intuitionistic fuzzy soft h-ideals of hemirings. Some characterizations and properties of them are given. In particular, some good examples are explored. Finally, we investigate aggregate intuitionistic fuzzy h-ideals of hemirings based on decision making.

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Qi Liu

Papers

A survey of decision making methods based on certain hybrid soft set models

A new rough set theory: rough soft hemirings

Another approach to rough soft hemirings and corresponding decision making

Rough fuzzy (fuzzy rough) strong h-ideals of hemirings

IFP-Intuitionistic Fuzzy Soft $h$-Ideals of Hemirings and Its Decision Making