R. B. Fajriya Hakim

N-soft sets and their decision making algorithms

In this paper, we motivate and introduce the concept of N-soft set as an extended soft set model. Some useful algebraic definitions and properties are given. We cite real examples that prove that N-soft sets are a cogent model for binary and non-binary evaluations in numerous kinds of decision making problems. Finally, we propose decision making procedures for N-soft sets.

Soft Solution of Soft Set Theory for Recommendation in Decision Making

Soft set theory is a new general mathematical method for dealing with uncertain data which proposed by Molodtsov in 1999 had been applied by researchers in decision making problems. However, most existing studies generated exact solution that should be soft solution because the determination of the initial problem only uses values ​​or language approach. This paper shows the use of soft set theory as a generic mathematical tool to describe the objects in the form of information systems and evaluate using multidimensional scaling techniques to find the soft solution and recommendation for making a decision.

Clustering based-on indiscernibility and indiscernibility level

The core concept of classical rough sets are clustering similarities and dissimilarities of objects based on the notions of indiscernibility and discernibility. In this paper, we present a new method of clustering data based on the combination of indiscernibility and its indiscernibility level. The indiscernibility level quantifies the indiscernibility of pairs of objects among other objects in information systems. The result of this paper show the dual notions of indiscernibility and its indiscernibility level play an important role in clustering information systems.

Reducing Hierarchical Clustering Instability Using Clustering Based on Indiscernibility and Indiscernibility Level

The notions of indiscernibility and discernibility are the core concept of classical rough sets to cluster similarities and differences of data objects. In this paper, we use a new method of clustering data based on the combination of indiscernibility (quantitative indiscernibility relations) and its indiscernibility level. The indiscernibility level quantify the indiscernibility of pair of objects among other objects in information systems and this level represent the granularity of pair of objects in information system. For comparison to the new method, the following four clustering methods were selected and evaluated on a simulation data set : average-, complete- and single-linkage agglomerative hierarchical clustering and Ward’s method. The result of this paper shows that the four methods of hierarchical clustering yield dendrogram instability that give different solution under permutation of input order of data object while the new method reduce dendrogram instability.

On If-Then Multi Soft Sets-Based Decision Making

Soft set theory as a new mathematical tool for dealing with uncertainties was first introduced by Molodtsov has experienced rapid growth. Various applications of soft set for the purpose of decision-making have been shown by several researchers. From various studies presented mostly shows the role of soft sets as a tool in the collection of the various attributes needed by a person to determine which decisions will be taken. In this paper, we show how soft set can play a role in the decision made by a person based on a history of decisions that have been made earlier and used as a reference for the next decision. Therefore, we introduce an (if-then) multi soft sets as a developments of application of soft set which is stated in the form if (antecedent) and then (consequence). The antecedent and consequence are derived from previously several decisions that have been made by people when using a soft set as a tool to help them for making a decision.

A social choice approach to graded soft sets

We establish a correspondence between ideas from soft computing and social choice. This connection permits to draw bridges between choice mechanisms in both frameworks. We prove that both Soft sets and the novel concept of Graded soft sets can be faithfully represented by well-established voting situations in Social Choice. To be precise, their decision making mechanism by choice values coincides with approval voting and the Borda rule respectively. This analysis lays the basis for new insights into soft-set-inspired decision making with a social choice foundation.

Ranked Clusterability Model of Dyadic Data in Social Network

The dyads relationship as a substantial portion of triads or larger structure formed a ranked clusterability model in social network. Ranked clusterability model of dyads postulates that the hierarchical clustering process starts from the mutual dyads which occur only within clusters then stop until all of the mutual dyads grouped. The hierarchy process continues to cluster the asymmetric dyads which occur between clusters but at different levels. Then the last process is clustering the null dyads, which is clustered at the end of the hierarchy after all of asymmetric dyads grouped and occur only between clusters at the same level of the hierarchy. This paper explores a ranked clusterability model of dyads from a simple example of social network and represents it to the new sociomatrix that facilitate to view a whole network and presents the result in a dendrogram network data. This model adds a new insight to the development of science in a clustering study of emerging social network.

Reducing dendrogram instability using clustering based on indiscernibility and indiscernibility level

The notions of indiscernibility and discernibility are the core concept of classical rough sets to cluster similarities and differences of data objects. In this paper, we use a new method of clustering data based on the combination of indiscernibility (quantitative indiscernibility relation) and its indiscernibility level. The indiscernibility level quantify the indiscernibility of pair of objects among other objects in information systems and this level represent the granularity of pair of objects in information system. For comparison to the new method, the following four clustering methods were selected and evaluated on a simulation dataset: average-, complete- and single-linkage agglomerative hierarchical clustering and Ward’s method. The result of this paper shows that the four methods of hierarchical clustering yield dendrogram instability that gives different solution under permutation of input order of data object while the new method reduces dendrogram instability.

The Concept of Indiscernibility Level of Rough Set to Reduce the Dendrogram Instability

The main concept of rough sets theory is clustering similarities of objects based on the notions of indiscernibility relation. In this paper, we develop the concept of indiscernibility level of rough set theory as an additional measurement for hierarchical clustering. The combination between indiscernibility (quantitative indiscernibility relation) and indiscernibility level are used as a new method for hierarchical clustering. The indiscernibility level quantifies the indiscernibility of pairs of objects among other objects in information system. For comparison, the following four clustering methods were selected and evaluated on a simulation data set : average-, complete- and single-linkage agglomerative hierarchical clustering and Ward’s method. The simulation shows that the hierarchical clustering yields dendrogram instability that gives different solutions under permutations of input order of data objects. The result of this paper shows that the new method plays an important role in clustering information system and compared to other method, clustering based on indiscernibility and its indiscernibility level reduces the dendrogram instability.