Soft sets and soft groups Aktaş, Hacı; Çağman, Naim
Information sciences,
07/2007, Volume:
177, Issue:
13
Journal Article
Peer reviewed
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.
•We define a intuitionistic fuzzy parameterized soft sets for dealing with uncertainties that is based on both soft sets and intuitionistic fuzzy sets.•We investigated their operations and ...properties.•We introduce a decision making method based on intuitionistic FP-soft sets.
In this work, we first define intuitionistic fuzzy parameterized soft sets (intuitionistic FP-soft sets) and study some of their properties. We then introduce an adjustable approaches to intuitionistic FP-soft sets based decision making. Finally, we give a numerical example which shows that this method successfully works.
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 set theory is an important tool for dealing with problems involving uncertainty. In a soft set, parameter set is a classical set. In this study, we introduce parameter trees by using mappings ...from parameter set into power set of parameter set and investigate some properties of them. We also define operations between two parameter trees and obtain some of their properties. Furthermore we give a similarity measure method between parameter trees.
In this study, concept of bipolar soft rough sets and set theoretical operations of bipolar soft rough sets are defined, and some of their properties are obtained. Also, a decision making method ...based on operations of bipolar soft rough sets is proposed to choose optimum element among alternatives. Finally, an illustrative example is given to show the method can be successfully applied to some problems.
In this work, we first defined the intuitionistic fuzzy soft sets (IFS-sets) and their operations. By using them, we then give some results and construct a decision making method. Finally, we give an ...application which shows that this approach is useful to handle several realistic uncertain problems.
In recent years, soft sets and neutrosophic sets have become a subject of great interest for researchers and have been widely studied based on decision-making problems. In this paper, we propose a ...new concept of the soft sets that is called interval-valued neutrosophic parameterized interval-valued neutrosophic soft sets (
ivnpivn
-soft sets). It is a generalization of the other soft sets such as fuzzy soft sets, intuitionistic fuzzy soft sets, neutrosophic soft sets, fuzzy parameterized soft sets, intuitionistic fuzzy parameterized soft sets, neutrosophic parameterized neutrosophic soft sets. Also, we proposed
ivnpivn
-soft matrices which are representative of the
ivnpivn
-soft sets. We then developed a decision-making method on the
ivnpivn
-soft sets and
ivnpivn
-soft matrices. Then, we proposed a numerical example to verify validity and feasibility of the developed method. Finally, the proposed method is compared with several different methods to verify its feasibility.
In this paper, we define a soft intersection group (soft int-group) on a soft set. This new concept functions as a bridge among soft set theory, set theory and group theory and shows the effect of ...soft sets on a group structure in the sense of intersection and inclusion of sets. We then derive the basic properties of soft int-groups and give its applications to group theory.
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