Molodtsov introduced the theory of soft sets, which can be used as a general mathematical tool for dealing with uncertainty. This paper aims to introduce the concept of the type-2 fuzzy soft set by integrating the type-2 fuzzy set theory and the soft set theory. Some operations on the type-2 fuzzy soft sets are given. Furthermore, we investigate the decision making based on type-2 fuzzy soft se...

Maji et al. introduced the concept of intuitionistic fuzzy soft sets, which is an extension to the soft set and intuitionistic fuzzy set. In this paper, we apply the concept of intuitionistic fuzzy soft sets to semigroup theory. The notion of intuitionistic fuzzy soft ideals over a semigroup is introduced and their basic properties are investigated. Some lattice structures of the set of all int...

Recommended by Krzysztof Pietrusewicz We define the concept of a mapping on classes of fuzzy soft sets and study the properties of fuzzy soft images and fuzzy soft inverse images of fuzzy soft sets, and support them with examples and counterexamples.

Generalized intuitionistic fuzzy soft set theory, proposed by Park et al. [Journal of Korean Institute of Intelligent Systems 21(3) (2011) 389-394], has been regarded as an effective mathematical tool to deal with uncertainties. In this paper, we prove that certain De Margan’s law hold in generalized intuitionistic fuzzy soft set theory with respect to union and intersection operations on gener...

The goal of this paper is to bring a new approach to the computation of the decision making problems by using inverse (fuzzy) soft sets instead of (fuzzy) soft sets which makes the algorithms easier and faster than the existed methods. For this purpose, we first define inverse soft sets and inverse fuzzy soft sets. Then we use them to solve decision making problems in a slightly modified way. c...

The main goal of this publication is to show that the basic constructions in theories fuzzy sets, soft hesitant sets or intuitionistic have a common background, based on theory monads categories. It proven ad hoc defined concepts individual theories, such as power set structures these relations approximation operators by are only special examples applications monad This makes it possible, one h...