Intuitionistic Fuzzy Approximation Space Research Articles

On Covering-Based Rough Intuitionistic Fuzzy Sets

Intuitionistic Fuzzy Sets (IFSs) and rough sets depending on covering are important theories for dealing with uncertainty and inexact problems. We think the neighborhood of an element is more realistic than any cluster in the processes of classification and approximation. So, we introduce intuitionistic fuzzy sets on the space of rough sets based on covering by using the concept of the neighborhood. Three models of intuitionistic fuzzy set approximation space based on covering are defined by using the concept of neighborhood. In the first and second model, we approximate IFS by rough set based on one covering (C) by defining membership and non-membership degree depending on the neighborhood. In the third mode, we approximate IFS by rough set based on family of covering (Ci) by defining membership and non-membership degree depending on the neighborhood. We employ the notion of the neighborhood to prove the definitions and the features of these models. Finlay, we give an illustrative example for the new covering rough IF approximation structure.

Topological properties of multigranular rough sets on intuitionistic fuzzy approximation spaces

Two of the extensions of the basic rough set model introduced by Pawlak in 1982 is the rough sets on fuzzy approximation spaces introduced by De et al. in 2003 and its extension rough sets on intuitionistic fuzzy approximation spaces in 2006 by Tripathy. The model of Tripathy is dependent upon an intuitionistic fuzzy proximity relation. In an attempt to handle multiple granulations simultaneously two types of multigranulations called the optimistic and pessimistic multigranulation were introduced by Qian et al. in 2006 and 2010 respectively. The notion of multigranular rough sets over intuitionistic fuzzy approximation spaces were introduced by Tripathy et al. in 2018. Topological properties of rough sets, introduced by Pawlak have been studied extensively for different types of rough sets by Tripathy et al. Continuing this, here we introduce and study the concept of topological properties of multigranular rough sets on intuitionistic fuzzy approximation spaces.

Topological properties of multigranular rough sets on intuitionistic fuzzy approximation spaces

Two of the extensions of the basic rough set model introduced by Pawlak in 1982 is the rough sets on fuzzy approximation spaces introduced by De et al. in 2003 and its extension rough sets on intuitionistic fuzzy approximation spaces in 2006 by Tripathy. The model of Tripathy is dependent upon an intuitionistic fuzzy proximity relation. In an attempt to handle multiple granulations simultaneously two types of multigranulations called the optimistic and pessimistic multigranulation were introduced by Qian et al. in 2006 and 2010 respectively. The notion of multigranular rough sets over intuitionistic fuzzy approximation spaces were introduced by Tripathy et al. in 2018. Topological properties of rough sets, introduced by Pawlak have been studied extensively for different types of rough sets by Tripathy et al. Continuing this, here we introduce and study the concept of topological properties of multigranular rough sets on intuitionistic fuzzy approximation spaces.

A knowledge elicitation framework in ranking healthcare providers using rough set with formal concept analysis

A comparison of healthcare institutions by ranking involves generating their relative scores based on the infrastructure, process and other quality dynamics. Being a top-ranking institute depends on the overall score secured against the hospital quality parameters that are being assessed for ranking. However, each of the parameters is not equally important when it comes to ranking. Hence, the objective of this research is to explore the parameters which are vital as they significantly influence the ranking score. In this paper, a hybrid model is presented for knowledge extraction, which employs techniques of rough set on intuitionistic fuzzy approximation space (RSIFAS) for classification, learning from examples module 2 (LEM2) algorithm for generating decision rules, and formal concept analysis (FCA) for attribute exploration. The model is discussed using AHA US News score data for cancer specialisation. The result signifies the connection between quality attributes and ranking. Finally, the leading attribute and its particular values are identified for different states of ranking.

Agriculture Crop Suitability Prediction Using Rough Set on Intuitionistic Fuzzy Approximation Space and Neural Network

Agriculture plays a vital role in Indian economy. On considering the overall geographical space verses population in India, 7% of population is chronicled in Tamilnadu, with 3% of water and 4% of land resources. Thus an automated prediction system becomes essential for predicting the crop based on the nutritional security of the country. In this paper, effort has been made to process the uncertainties by hybridizing rough set on intuitionistic fuzzy approximation space (RSIFAS) [Acharjya DP, Tripathy BK. Rough sets on intuitionistic fuzzy approximation spaces and knowledge representation. Int J Artif Int Comput Res. 2009;1 (1):29–36.] and neural network [Hecht NR. Theory of the backpropagation neural network. Proceedings of the international Joint Conference on neural networks, 1 (1989), 593–605.]. RSIFAS identifies the almost indiscernibility among the natural resources, and helps in reducing the computational procedure on employing data reduction techniques whereas neural network helps in prediction process. It helps to find the crops that may be cultivated based on the available natural resources. The proposed model is analyzed on data accumulated from Vellore district of Tamilnadu, India and achieved 93.7% of average classification accuracy. The model is compared with earlier models and found 6.9% better accuracy while prediction.

A Novel Rough Set Model in Generalized Single Valued Neutrosophic Approximation Spaces and Its Application

In this paper, we extend the rough set model on two different universes in intuitionistic fuzzy approximation spaces to a single-valued neutrosophic environment.

A Novel Rough Set Model in Generalized Single Valued Neutrosophic Approximation Spaces and Its Application

In this paper, we extend the rough set model on two different universes in intuitionistic fuzzy approximation spaces to a single-valued neutrosophic environment. Firstly, based on the ( α , β , γ ) -cut relation R ˜ { ( α , β , γ ) } , we propose a rough set model in generalized single-valued neutrosophic approximation spaces. Then, some properties of the new rough set model are discussed. Furthermore, we obtain two extended models of the new rough set model—the degree rough set model and the variable precision rough set model—and study some of their properties. Finally, we explore an example to illustrate the validity of the new rough set model.

A framework for attribute selection in marketing using rough computing and formal concept analysis

Marketing management employs various tools and techniques, including market research, to perform accurate marketing analysis. Information and communication technology provided a new dimension in marketing research to maximise the revenues and profits of the firm by identifying the chief attributes affecting decisions. In this paper, we present a hybrid approach for attribute selection in marketing based on rough computing and formal concept analysis. Our approach is aimed at handling an information system that contains numerical attribute values that are “almost similar” instead of “exact similar”. To handle such an information system we use two processes—pre-process and post-process. In pre-process, we use rough set on intuitionistic fuzzy approximation space with ordering rules to find knowledge and associations, whereas in post-process we use formal concept analysis to identify the chief attributes affecting decisions.

Privacy preservation in fuzzy association rules using rough set on intuitionistic fuzzy approximation spaces and DSR

The present age of internet and the rising of business have resulted into many folds of increase in the volume of data which are to be used for various applications on a day to day basis. Therefore, it is an obvious challenge to reduce the dataset and find useful information pertaining to the interest of the organisation. But another challenge lies in hiding sensitive information in order to provide privacy. Thus, attribute reduction and privacy preservation are two major challenges in privacy preserving data mining. In this paper, we propose a sensitive rule hiding model to hide sensitive fuzzy association rules. Proposed model uses rough set on intuitionistic fuzzy approximation spaces with ordering to reduce the dataset dimensionality. We use triangular and trapezoidal membership function to get the fuzzified information system. Finally, decreasing the support of right hand side of the rule is used to hide sensitive fuzzy association rules.

Intuitionistic Fuzzy Topologies Induced by Intuitionistic Fuzzy Approximation Spaces

In this paper, we obtain some basic results of intuitionistic fuzzy topological spaces induced by given intuitionistic fuzzy approximation spaces. In addition, we introduce the concept of pseudo-constant intuitionistic fuzzy relation, and obtain topological structures of an intuitionistic fuzzy approximation space by using them.

Hierarchical structures and uncertainty measures for intuitionistic fuzzy approximation space

The hierarchical structures and uncertainty measures in granular computing are the two main aspects for investigating the structure and uncertainty of all types of approximation spaces. Although several hierarchical structures and uncertainty measures have been proposed to represent and analyze different granular structures, these structures and uncertainty measures are studied under crisp or fuzzy conditions. Hierarchical structures and uncertainty measures for the intuitionistic fuzzy (IF) approximation space are addressed in this paper. First, we propose the representation and operations of IF granular structures, as well as examine four hierarchical structures and a lattice structure of IF approximation space. Second, the natural extensions of fuzzy information granularity, fuzzy information entropy, fuzzy rough entropy, and fuzzy information Shannon entropy, namely, IF granularity, IF information entropy, IF rough entropy, and IF information Shannon entropy, are developed and adopted to characterize the uncertainty of IF granular structures in the IF approximation space. Third, we provide the multi-granulation IF approximation space and study its four hierarchical structures. Furthermore, we discuss the relationships between the presented hierarchical structures and multi-granulation IF rough sets in the multi-granulation IF approximation space. Fourth, we propose four types of IF uncertainty measures to depict the uncertainty of the multi-granulation IF knowledge base in the multi-granulation IF approximation space with respect to optimistic and pessimistic multi-granulation IF rough sets, which is more reasonable compared with previous work conducted in a crisp context.

Rough set over dual-universes in intuitionistic fuzzy approximation space and its application

In this paper we generalize the rough set model over dual-universes in fuzzy approximation space to intuitionistic fuzzy case. Concretely, based on the cut set of intuitionistic fuzzy relation, the rough set model over dual-universes in intuitionistic fuzzy approximation space is first presented. Then, some properties of the rough set model are discussed. Two extended models of the rough set model are given, and some principal results are obtained. Finally, by three-way decision theory, two examples are applied to illustrate the application of the rough set model presented in this paper.

On intuitionistic fuzzy topologies based on intuitionistic fuzzy reflexive and transitive relations

Topologies and rough set theory are widely used in the research field of machine learning and cybernetics. An intuitionistic fuzzy rough set, which is the result of approximation of an intuitionistic fuzzy set with respect to an intuitionistic fuzzy approximation space, is an extension of fuzzy rough sets. For further studying the theories and applications of intuitionistic fuzzy rough sets, in this paper, we investigate the topological structures of intuitionistic fuzzy rough sets. We show that an intuitionistic fuzzy rough approximation space can induce an intuitionistic fuzzy topological space in the sense of Lowen if and only if the intuitionistic fuzzy relation in the approximation space is reflexive and transitive. We also examine the sufficient and necessary conditions that an intuitionistic fuzzy topological space can be associated with an intuitionistic fuzzy reflexive and transitive relation such that the induced lower and upper intuitionistic fuzzy rough approximation operators are, respectively, the intuitionistic fuzzy interior and closure operators of the given topology.

On intuitionistic fuzzy rough sets and their topological structures

In this paper, lower and upper approximations of intuitionistic fuzzy sets with respect to an intuitionistic fuzzy approximation space are first defined. Properties of intuitionistic fuzzy approximation operators are examined. Relationships between intuitionistic fuzzy rough set approximations and intuitionistic fuzzy topologies are then discussed. It is proved that the set of all lower approximation sets based on an intuitionistic fuzzy reflexive and transitive approximation space forms an intuitionistic fuzzy topology; and conversely, for an intuitionistic fuzzy rough topological space, there exists an intuitionistic fuzzy reflexive and transitive approximation space such that the topology in the intuitionistic fuzzy rough topological space is just the set of all lower approximation sets in the intuitionistic fuzzy reflexive and transitive approximation space. That is to say, there exists an one-to-one correspondence between the set of all intuitionistic fuzzy reflexive and transitive approximation spaces and the set of all intuitionistic fuzzy rough topological spaces. Finally, intuitionistic fuzzy pseudo-closure operators in the framework of intuitionistic fuzzy rough approximations are investigated.

On characterization of intuitionistic fuzzy rough sets based on intuitionistic fuzzy implicators

This paper presents a general framework for the study of relation-based ( I , T ) -intuitionistic fuzzy rough sets by using constructive and axiomatic approaches. In the constructive approach, by employing an intuitionistic fuzzy implicator I and an intuitionistic fuzzy triangle norm T , lower and upper approximations of intuitionistic fuzzy sets with respect to an intuitionistic fuzzy approximation space are first defined. Properties of ( I , T ) -intuitionistic fuzzy rough approximation operators are examined. The connections between special types of intuitionistic fuzzy relations and properties of intuitionistic fuzzy approximation operators are established. In the axiomatic approach, an operator-oriented characterization of ( I , T ) -intuitionistic fuzzy rough sets is proposed. Different axiom sets characterizing the essential properties of intuitionistic fuzzy approximation operators associated with various intuitionistic fuzzy relations are explored.