A fuzzy soft set theoretic approach to decision making problems

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

The soft set theory, proposed by Molodtsov, can be used as a general mathematical tool for dealing with uncertainty. By combining the interval-valued fuzzy set and soft set models, the purpose of this paper is to introduce the concept of the interval-valued fuzzy soft set. The complement, ''AND'' and ''OR'' operations are defined on the interval-valued fuzzy soft sets. The DeMorgan's, associative and distribution laws of the interval-valued fuzzy soft sets are then proved. Finally, a decision problem is analyzed by the interval-valued fuzzy soft set. Some numerical examples are employed to substantiate the conceptual arguments.

Combination of interval-valued fuzzy set and soft set

The first aim of this study is to define soft topological spaces and to define soft continuity of soft mappings. Second is to introduce soft product topology and study properties of soft projection mappings. Third is to define soft compactness and generalize Alexander subbase theorem and Tychonoff theorem to the soft topological spaces.

Some notes on soft topological spaces

The traditional soft set is a mapping from a parameter to the crisp subset of universe. Molodtsov introduced the theory of soft sets as a generalized tool for modeling complex systems involving uncertain or not clearly defined objects. In this paper the concepts of soft set relations are introduced as a sub soft set of the Cartesian product of the soft sets and many related concepts such as equivalent soft set relation, partition, composition, function etc. are discussed.

Soft set relations and functions

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

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.

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Mappings on fuzzy soft classes

This work presents a method of multi-criteria decision making (MCDM) using neutrosophic sets. Besides studying some interesting mathematical properties of the method, algorithm viz neut-MCDM is presented. The work also furnishes the fundamentals of neutrosophic set theory succinctly, to provide a first introduction of neutrosophic sets for the MCDM community. To illustrate the computational details, neut-MCDM has been applied to the problem of university faculty selection against a given set of criteria.

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Athar Kharal

Papers

On fuzzy soft sets

Mappings on soft classes

Mappings on fuzzy soft classes

A Neutrosophic Multi-Criteria Decision Making Method

Homeopathic drug selection using Intuitionistic fuzzy sets.