A novel soft set approach in selecting clustering attribute

Emerging trends in soft set theory and related topics.

Soft rough fuzzy sets and soft fuzzy rough sets

Fuzzy set theory, rough set theory and soft set theory are all generic mathematical tools for dealing with uncertainties. There has been some progress concerning practical applications of these theories, especially, the use of these theories in decision making problems. In the present article, we review some decision making methods based on (fuzzy) soft sets, rough soft sets and soft rough sets. In particular, we provide several novel algorithms in decision making problems by combining these kinds of hybrid models. It may be served as a foundation for developing more complicated soft set models in decision making.

Theories of fuzzy sets and rough sets are powerful mathematical tools for modelling various types of uncertainty. Dubois and Prade investigated the problem of combining fuzzy sets with rough sets. Soft set theory was proposed by Molodtsov as a general framework for reasoning about vague concepts. The present paper is devoted to a possible fusion of these distinct but closely related soft computing approaches. Based on a Pawlak approximation space, the approximation of a soft set is proposed to obtain a hybrid model called rough soft sets. Alternatively, a soft set instead of an equivalence relation can be used to granulate the universe. This leads to a deviation of Pawlak approximation space called a soft approximation space, in which soft rough approximations and soft rough sets can be introduced accordingly. Furthermore, we also consider approximation of a fuzzy set in a soft approximation space, and initiate a concept called soft---rough fuzzy sets, which extends Dubois and Prade's rough fuzzy sets. Further research will be needed to establish whether the notions put forth in this paper may lead to a fruitful theory.

The concept of soft set is fundamentally important in almost every scientific field. Soft set theory is a new mathematical tool for dealing with uncertainties and is a set associated with parameters and has been applied in several directions. Since Molodtsov originated the idea of soft sets, some research on soft sets has been done in the literature. This theory represents a promising technique in imperfect data analysis which has found interesting extensions and various applications that handle imperfect knowledge, such as Bayesian inference, fuzzy set etc. In this paper, define the notion of soft sets, and the study that are interesting and valuable in the theory of soft sets, which emphasis on a series of applications especially in decision making problems. Also presents comprehensive study, development and survey of its existing literature. Keywords—BCI; BCK; FCM; Fuzzy Set; Fuzzy Soft Set; Soft Rough Set; Soft Semi Rings; Soft Set; Uncertainty.

Soft set theory and rough set theory are mathematical tools for dealing with uncertainties and are closely related. The main purpose of soft rough set is reducing the soft boundary region by increasing the lower approximation and decreasing the upper approximation. This paper is devoted to the further generalization of the soft rough set theory by using the ideal notion to reduce the soft boundary region. A new soft rough set model, called soft ideal approximation space, is proposed and its properties are derived. The new soft ideal lower and upper approximation operators are presented and their related properties are surveyed.

Association rule mining is an active data mining research area. In recent years, association rules from large databases have received considerable attention and have been applied to various areas such as marketing, retail and finance, etc. The traditional algorithms for mining frequent association patterns suffer from the problems of under prediction and over prediction of patterns. The main aim of the present paper is to develop a soft set approach for mining fuzzy quantitative association patterns in order to address the issues of under prediction and over prediction of these patterns. The proposed approach is illustrated with the help of a suitable example and experiment on a real world data set of air pollution. The transactional dataset is represented as soft set(fuzzy) using the concept of parameter co-occurrences in the transaction. The quantitative attributes are dealt with by fine -partitioning the value of each attributes and then creating new tables which represent each (fine) partition as a field. The results obtained by soft set approach, soft set fuzzy approach are compared with those obtained by Apriori algorithm without soft set approach. The significant differences have been observed in support and confidence levels of patterns obtained by three approaches.

The classical soft rough set theory offers a formal theoretical framework for solving the uncertainty under a single granulation environment. However, it is noticeable that the soft rough set theory cannot be applied in the situation of multigranulation in the real world. To address this issue, in this paper we firstly present two types of multigranulation soft rough sets, which are the optimistic multigranulation soft rough set and the pessimistic multigranulation soft rough set. Then the basic and important properties of these multigranulation soft rough sets are studied. Finally, we investigate the relationships among single granulation soft rough set, namely classical soft rough set, optimistic multigranulation soft rough set and pessimistic multigranulation soft rough set. These results will enrich the soft set theory and multigranulation rough set theory, and also extend their application scopes.

After the paper of Molodtsov [Molodtsov D. Soft set theory — First results, Computers and Mathematics with Applications, 1999, vol. 37, no. 4-5, pp. 19-31.] first appeared, soft set theory grew at a breakneck pace. Several authors have introduced various operations, relations, results, etc. as well as other aspects in soft set theory and hybrid structures incorrectly, despite their widespread use in mathematics and allied areas. In his paper [Molodtsov D.A. Equivalence and correct operations for soft sets, International Robotics and Automation Journal, 2018, vol. 4, no. 1, pp. 18-21.], Molodtsov, the father of soft set theory, pointed out several wrong results and notions. Molodtsov [Molodtsov D.A. Structure of soft sets, Nechetkie Sistemy i Myagkie Vychisleniya, 2017, vol. 12, no. 1, pp. 5-18.] also stated that the concept of soft set had not been fully understood and used everywhere. As a result, it is important to revisit the quirks of those conceptions and provide a formal account of the notion of soft set equivalency. Molodtsov already explored many correct operations on soft sets. We use some notions and results of Molodtsov [Molodtsov D.A. Structure of soft sets, Nechetkie Sistemy i Myagkie Vychisleniya, 2017, vol. 12, no. 1, pp. 5-18.] to create matrix representations as well as related operations of soft sets, and to quantify the similarity between two soft sets.

Extending fuzzy soft sets with fuzzy description logics

Feature selection is an important preprocess for data mining. The soft set theory is a new mathematical tool to deal with uncertainties. Merging the soft set theory into the feature selection process based on rough sets facilitates the computation with equivalence classes and improves the efficiency. We propose a paired relation soft set model based on equivalence classes of the information system. Then we use it to present the lower approximate set in the form of soft sets and calculate the degree of dependency between relations. Furthermore, we give a new mapping to obtain equivalence classes of indiscernibility relations and propose a feature selection algorithm based on the paired relation soft set model. Compared to the algorithm based NSS, this algorithm shows 18.17% improvement on an average. Meantime, both of the algorithms show a good scalability.

Theories of fuzzy sets and rough sets are powerful mathematical tools for modelling various types of uncertainty. Molodtsov (Comput Math Appl 37:19–31, 1999 [6]) initiated a novel concept called soft sets, a new mathematical tool for dealing with uncertainties. It has been found that fuzzy sets, rough sets, and soft sets are closely related concepts (Aktas and Cagman in Inf Sci 1(77):2726–2735, 2007 [1]). Research works on soft sets are very active and progressing rapidly in these years. In 2001, Maji et al. (J Fuzzy Math 9(3):589–602, 2001 [5]) proposed the idea of intuitionistic fuzzy soft set theory and established some results on them. Based on an equivalence relation on the universe of discourse, Dubois and Prade (Int J Gen Syst 17:191–209, 1990 [3]) introduced the lower and upper approximation of fuzzy sets in a Pawlak approximation space and obtained a new notion called rough fuzzy sets. Feng et al. (Soft Compt 14:899–911, 2009 [4]) introduced lower and upper soft rough approximation of fuzzy sets in a soft approximation space and obtained a new hybrid model called soft rough fuzzy sets which is the extension of Dubois and Prade’s rough fuzzy sets. The aim of this chapter is to consider lower and upper soft rough intuitionistic fuzzy approximation of intuitionistic fuzzy sets in intuitionistic fuzzy soft approximation space (IF soft approximation space) and obtain a new hybrid model called soft rough intuitionistic fuzzy sets which can be seen as extension of both the previous work by Dubois and Prade and Feng et al.

A rough set approach to intuitionistic fuzzy soft set based decision making

Neutrosophic sets (NSs) handle uncertain information while fuzzy sets (FSs) and intuitionistic fuzzy sets (IFs) fail to handle indeterminate information. Soft set theory, neutrosophic set theory, and rough set theory are different mathematical models for handling uncertainties and they are mutually related. The neutrosophic soft rough set (NSRS) model is a hybrid model by combining neutrosophic soft sets with rough sets. We apply neutrosophic soft rough sets to graphs. In this research paper, we introduce the idea of neutrosophic soft rough graphs (NSRGs) and describe different methods of their construction. We consider the application of NSRG in decision-making problems. In particular, we develop efficient algorithms to solve decision-making problems.

Association analysis of amino acids in molecular sequences can reveal crucial information and knowledge for understanding structure, function and interaction of proteins. The traditional methods of association rule mining like apriori, F-P Growth etc. fail to generate appropriate patterns due to inherent uncertainty present in data. The uncertainty in sequence data caused by variation in the length of sequences and lack of parameterization lead to under prediction and over prediction of the results. In this paper an attempt has been made to develop a soft set based approach for mining fuzzy association patterns in peptide sequences of dengue virus. The fuzzy set approach is employed to incorporate the degree of relationships among amino acids due to variation in length of the sequences. The soft set approach is employed to incorporate the relationship of parameters with amino acid association patterns. The 12,581 sequences of dengue virus are downloaded from NCBI and screened for redundancy to obtain non redundant 6995 sequences. The amino acid associations are explored and analyzed using soft fuzzy approach. Also the results obtained by soft fuzzy approach are compared with the results obtained individually by ordinary, fuzzy and soft set approaches. The soft fuzzy approach is able to overcome the issue of under prediction and over prediction of the results obtained by other approaches. Also the interesting association rules have been generated to predict the structure and physico chemical properties of the peptide sequences.