A fuzzy soft set theoretic approach to decision making problems

Soft sets and soft rough sets

In this work, we define soft matrices and their operations which are more functional to make theoretical studies in the soft set theory We then define products of soft matrices and their properties We finally construct a soft max-min decision making method which can be successfully applied to the problems that contain uncertainties

Soft matrix theory and its decision making

In this paper, we review the definition and basic properties of the different types of fuzzy sets that have appeared up to now in the literature. We also analyze the relationships between them and enumerate some of the applications in which they have been used.

/pdf/a-historical-account-of-types-of-fuzzy-sets-and-their-jtvbgqsyj5.pdf

A Historical Account of Types of Fuzzy Sets and Their Relationships

Link prediction finds missing links (in static networks) or predicts the likelihood of future links (in dynamic networks). The latter definition is useful in network evolution (Wang et al., 2011; Barabasi and Albert, 1999; Kleinberg, 2000; Leskovec et al., 2005; Zhang et al., 2015). Link prediction is a fast-growing research area in both physics and computer science domain. There exists a wide range of link prediction techniques like similarity-based indices, probabilistic methods, dimensionality reduction approaches, etc., which are extensively explored in different groups of this article. Learning-based methods are covered in addition to clustering-based and information-theoretic models in a separate group. The experimental results of similarity and some other representative approaches are tabulated and discussed. To make it general, this review also covers link prediction in different types of networks, for example, directed, temporal, bipartite, and heterogeneous networks. Finally, we discuss several applications with some recent developments and concludes our work with some future works.

Link prediction techniques, applications, and performance: A survey

We further contribute to the properties of fuzzy soft sets as defined and studied in the work of Maji et al. (2001), Roy and Maji (2007), and Yang et al. (2007) and support them with examples and counterexamples. We improve Proposition 3.3 by Maji et al., (2001). Finally we define arbitrary fuzzy soft union and fuzzy soft intersection and prove DeMorgan Inclusions and DeMorgan Laws in Fuzzy Soft Set Theory.

On fuzzy soft sets

In this paper, we define the notion of a mapping on soft classes and study several properties of images and inverse images of soft sets supported by examples and counterexamples. Finally, these notions have been applied to the problem of medical diagnosis in medical expert systems.

Mappings on soft classes

Several properties of fuzzy semiclosure and fuzzy semi-interior of fuzzy sets defined by Yalvac (1988), have been established and supported by counterexamples. We also study the characterizations and properties of fuzzy semi-open and fuzzy semi-closed sets. Moreover, we define fuzzy s-open and fuzzy s-closed mappings and give some interesting characterizations.

/pdf/fuzzy-sets-fuzzy-s-open-and-s-closed-mappings-45769mbjun.pdf

Fuzzy sets, fuzzy S-open and S-closed mappings

We present several properties of fuzzy boundary and fuzzy semiboundary which have been supported by examples. Properties of fuzzy semi-interior, fuzzy semiclosure, fuzzy boundary, and fuzzy semiboundary have been obtained in product-related spaces. We give necessary conditions for fuzzy continuous (resp., fuzzy semicontinuous, fuzzy irresolute) functions. Moreover, fuzzy continuous (resp., fuzzy semicontinuous, fuzzy irresolute) functions have been characterized via fuzzy-derived (resp., fuzzy-semiderived) sets.

/pdf/fuzzy-boundary-and-fuzzy-semiboundary-28jmjkb26p.pdf

Fuzzy boundary and fuzzy semiboundary

Mappings on Soft Classes

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