Fuzzy Approximation Space Research Articles

Some Algebraic Properties of Generalized Fuzzy Rough Approximations Derived by Fuzzy Set-Valued Homomorphism of LA-G-Semigroups

In this paper we define the concept of fuzzy set valued homomorphism of LA- G-semigroups and mention some features of them. We also investigate the approximations of a generalized fuzzy approximation space constructed on LA-G-semigroups and derived by fuzzy set valued homomorphisms of LA-G-semigroups. Especially, we focus on some algebraic properties of fuzzy subsets in terms of protection of some properties under these approximations.

Rough segmentation of coherent local intensity for bias induced 3-D MR brain images

Segmentation of brain MR volumes into different meaningful tissue classes is an essential prerequisite for many clinical analyses. However, intensity inhomogeneity or bias field, present in MR volumes, considerably degrades the quality of segmentation. In this regard, the paper presents a new segmentation algorithm, termed as CoLoRS (Coherent Local Intensity Rough Segmentation), for brain MR volumes corrupted with bias field artifact. It judiciously integrates the merits of coherent local intensity clustering and the theory of rough sets for simultaneous segmentation and bias field correction of brain MR volumes. The proposed algorithm partitions the entire image space into a number of small overlapping neighborhood regions. The bias, in each neighborhood region, is assumed to be constant. For each individual region, an objective function is defined for coherent local intensity rough segmentation. The voxels near the center point have similar influences on local objective function. In addition, the smaller distance between center and neighboring voxels yields more contribution on the voxel of interest. The proposed algorithm uses the dual-region concept to represent the neighborhood structure more efficiently. It makes possible of separate modeling of the voxels within neighborhood, according to their locations. Each region is considered to have several tissue classes, where each tissue class consists of a core region and an overlapping region. The segmentation in fuzzy approximation spaces provides an effective mean for brain MR volume analysis, as it handles overlapping partitions and addresses vagueness in tissue class definition. The effectiveness of the proposed algorithm, along with a comparison with existing approaches, is demonstrated on several publicly available brain MR data.

On novel hesitant fuzzy rough sets

This paper presents a novel framework for the study of hesitant fuzzy rough sets by integrating rough sets with hesitant fuzzy sets. Lower and upper approximations of hesitant fuzzy sets with respect to a hesitant fuzzy approximation space are first defined. Properties of hesitant fuzzy approximation operators are examined. Relationships between hesitant fuzzy approximation spaces and hesitant fuzzy topological spaces are then established. It is proved that the set of all lower approximation sets based on a hesitant fuzzy reflexive and transitive approximation space forms a hesitant fuzzy topology. And conversely, for a hesitant fuzzy rough topological space, there exists a hesitant fuzzy reflexive and transitive approximation space such that the topology in the hesitant fuzzy rough topological space is exactly the set of all lower approximation sets in the hesitant fuzzy reflexive and transitive approximation space. That is to say, there exists a one-to-one correspondence between the set of all hesitant fuzzy reflexive and transitive approximation spaces and the set of all hesitant fuzzy rough topological spaces.

Notes on [B. Yang, B.Q. Hu, On some types of fuzzy covering-based rough sets, Fuzzy Sets Syst. 312 (2017) 36–65

In this paper, we show by counterexamples that the six propositions about the fuzzy β-core in the fuzzy β-covering approximation space in Yang and Hu (2017) [3] are incorrect, and interpret the cause of errors.

(1704-3630) MULTI-GRANULATION FUZZY PROBABILISTIC ROUGH SETS AND THEIR CORRESPONDING THREE-WAY DECISIONS OVER TWO UNIVERSES

This article introduces a general framework of multi-granulation fuzzy probabilistic roughsets (MG-FPRSs) models in multi-granulation fuzzy probabilistic approximation space over twouniverses. Four types of MG-FPRSs are established, by the four different conditional probabilitiesof fuzzy event. For different constraints on parameters, we obtain four kinds of each type MG-FPRSsover two universes. To find a suitable way of explaining and determining these parameters in eachkind of each type MG-FPRS, three-way decisions (3WDs) are studied based on Bayesian minimum-riskprocedure, i.e., the decision-theoretic rough set (DTRS) approach. The main contribution of this paperis twofold. One is to extend the fuzzy probabilistic rough set (FPRS) to MG-FPRS model over two universes.Another is to present an approach to select parameters in MG-FPRS modeling by using the process ofdecision-making under conditions of risk.

Topological Properties of Multigranular Rough sets on Fuzzy Approximation Spaces

One of the extensions of the basic rough set model introduced by Pawlak in 1982 is the notion of rough sets on fuzzy approximation spaces. It is based upon a fuzzy proximity relation defined over a Universe. As is well known, an equivalence relation provides a granularization of the universe on which it is defined. However, a single relation defines only single granularization and as such to handle multiple granularity over a universe simultaneously, two notions of multigranulations have been introduced. These are the optimistic and pessimistic multigranulation. The notion of multigranulation over fuzzy approximation spaces were introduced recently in 2018. Topological properties of rough sets are an important characteristic, which along with accuracy measure forms the two facets of rough set application as mentioned by Pawlak. In this article, the authors introduce the concept of topological property of multigranular rough sets on fuzzy approximation spaces and study its properties.

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.

(1706-3718) CATEGORIES OF LATTICE-VALUED CLOSURE (INTERIOR) OPERATORS AND ALEXANDROFF L-FUZZY TOPOLOGIES

Galois connection in category theory play an important role inestablish the relationships between different spatial structures. Inthis paper, we prove that there exist many interesting Galoisconnections between the category of Alexandroff $L$-fuzzytopological spaces, the category of reflexive $L$-fuzzyapproximation spaces and the category of Alexandroff $L$-fuzzyinterior (closure) spaces. This indicates that there is a closeconnection between the three structures.

Properties of Multigranular Rough Sets on Fuzzy Approximation Spaces and their Application to Rainfall Prediction

Properties of Multigranular Rough Sets on Fuzzy Approximation Spaces and their Application to Rainfall Prediction

Probabilistic decision making based on rough sets in interval-valued fuzzy information systems

At present, the representative and hot research is three-way decision based on rough set theory. In addition, this topic has been applied in wide variety of specific. In the article, we aim to discuss the rough set method of decision theory in the background of interval-valued fuzzy information systems (IVFIS). First, the main work is to transform the IVFIS into two kinds of approximate spaces by the defined relations, which are fuzzy approximation space and interval-valued fuzzy approximation space, respectively. Simultaneously, fuzzy probability and IVF probability are considered in the whole process. Second, we study two kinds of decision-theoretic rough set methods by combining the Bayesian decision process. Finally, based on the above decision-making models, some illustrative examples about the credit evaluation of enterprises are introduced to deal with the real value and interval-valued data. These results show that the rough set method of decision theory we proposed has wider applications than decision-theoretic rough sets (DTRS).

Multi-granulation fuzzy decision-theoretic rough sets and bipolar-valued fuzzy decision-theoretic rough sets and their applications

This paper investigates the decision-theoretic rough set (DTRS) approach in the frameworks of multi-granulation fuzzy and bipolar-valued fuzzy (BVF) probabilistic approximation spaces, respectively. By integrating fuzzy probability and BVF probability into the Bayesian decision procedure, we get four types of model of multi-granulation fuzzy decision-theoretic rough set (MG-FDTRS) approach and multi-granulation bipolar-valued fuzzy decision-theoretic rough set (MG-BVF-DTRS) approach. Our four types of model of the MG-FDTRS and the MG-BVF-DTRS approaches are mainly based on computation of the four different conditional probabilities within the frameworks of multi-granulation fuzzy and BVF probabilistic approximation spaces, respectively. The main contribution of this paper is twofold. One is to extend the fuzzy decision-theoretic rough set (FDTRS) approach to the MG-FDTRS and the MG-BVF-DTRS approaches. Another is to address its applicable ability as it is applied to deal with the multi-source fuzzy and BVF probabilistic decision systems. An example is included to show the feasibility and potential results obtained.

Order based hierarchies on hesitant fuzzy approximation space

Granular computing which focuses on everyday and commonly used concepts and notions is a new field of multi-disciplinary study in dealing with theories, methodologies and techniques. As an important role in granular computing, hierarchy has attracted considerable attention. We are usually hesitant and irresolute for one thing when making decisions, which leads to a set of possible membership degrees. However, the existing hierarchies focus on crisp environment or fuzzy environment in which each element of the set has only one membership degree. To fill this gap, we research the hierarchies on hesitant fuzzy information granulations whose information granule has at least one membership degree of one object to the reference set. Firstly, we put forward new orders on hesitant fuzzy sets to characterize the hierarchies on hesitant fuzzy sets, the relationships of these orders are also researched. Moreover, we characterize the hierarchies on hesitant fuzzy information granulations from the viewpoint of granular computing. And then, new orders are presented to characterize the hierarchies on hesitant fuzzy information granulations. The order based hierarchies on hesitant fuzzy approximation space provide us with a more comprehensible perspective for the study of granular computing. Finally, two examples are given. One example is employed to compare the differences among the proposed orders on hesitant fuzzy sets, the other example is illustrated to show the orders on hesitant fuzzy sets that can be applied to hesitant fuzzy multi-attribute decision making. The results show that the orders proposed in this paper are effective to characterize the hierarchies on hesitant fuzzy approximation space.

Labeled fuzzy approximations based on bisimulations

This paper focuses on the labeled fuzzy approximation space, which is considered as a relational structure consisting of a nonempty universal set and some fuzzy relations. To deduce knowledge hidden in the labeled fuzzy approximation space, based on the notion of bisimulations, lower and upper fuzzy rough approximation operators are constructed. Then basic properties of the fuzzy rough approximation operators are investigated. When the largest bisimulation is a trivial identity relation in some cases, the concept of simulations is proposed. Moreover, the lower and upper fuzzy rough relation approximation operators are first proposed and properties of the new operators are examined. Finally, the relationships between two kinds of approximations are discussed.

Novel soft fuzzy rough rings (ideals) of rings and their application in decision making

In this paper, we investigate the relationship among soft sets, rough sets, fuzzy sets and rings. The notion of soft fuzzy rough rings (ideals) of rings is introduced, which is an extended notion of soft rough fuzzy rings (ideals) of rings. It is pointed out that in this paper, we first apply soft fuzzy rough sets to rings. Moreover, we study roughness in rings with respect to a pseudo-soft fuzzy approximation space. Some new soft fuzzy rough operations over rings are explored. In particular, lower and upper soft fuzzy rough rings (ideals) of rings are investigated. Finally, as an application, we put forth an approach to decision making based on soft fuzzy rough sets and offer an actual example.

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.

Crop suitability prediction in Vellore District using rough set on fuzzy approximation space and neural network

In Indian economy, agriculture is the prime vocation that avails in the overall development of the country. Tamil Nadu occupies approximately 7% of the nation's population, with 3% of water resources and 4% of land resources at the country level. The crop suitability prediction is of prime importance to enhance the nutritional security to the developing country. Based on several crops grown in a particular place, and the availability of natural resources, one can identify the suitability of crops that can be grown in a particular place. To this end, many mathematical tools were developed, but they failed to include processing of uncertainties present in the accumulated data. Therefore, in this paper an effort has been made to process the uncertainties by hybridizing rough set on fuzzy approximation space and neural network. The rough set on fuzzy approximation space identifies the almost indiscernibility among the natural resources and helps in minimizing the computational procedure on employing data reduction techniques, whereas neural network helps in prediction process. The proposed model is analysed on agriculture data of Vellore District of Tamil Nadu, India, and achieved 93% of classification accuracy in validation. The model is compared with an earlier model and achieved 8% more accuracy while predicting unseen associations.

Applications of a kind of novel Z-soft fuzzy rough ideals to hemirings

In this paper, we propose the notion of Z-soft fuzzy rough ideals of hemirings, which is an extended concept of Z-soft rough fuzzy ideals proposed by Zhan [J. Zhan, K. Zhu, A novel soft rough fuzzy set: Z-soft rough fuzzy ideals of hemirings and corresponding decision making, Soft Comput., 2016, DO I 10.1007/s00500-016-2119-9]. By two novel pseudo fuzzy soft sets, we investigate some kinds of Z-soft fuzzy rough ideals in hemirings with respect to a soft fuzzy approximation space. Some new soft fuzzy rough operations over hemirings are explored. Some Z-lower and Z-upper soft fuzzy rough ideals (k-ideals, h-ideals, strong h-ideals) of hemirings are investigated.

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.