Anjan Mukherjee

Completely induced fuzzy topological spaces

Abstract The object of this paper is to introduce and to study the concepts of completely induced fuzzy topological spaces and completely lower semi continuous functions. Completely lower semi continuous functions turn out to be the natural tool for studying the completely induced fuzzy topological spaces.

Fuzzy weakly completely continuous functions

Abstract A new class of functions, called fuzzy weakly completely continuous functions, is introduced as generalization of fuzzy completely continuous functions. The concepts of fuzzy R-map and fuzzy faintly continuous function are also introduced and their relationships with fuzzy weakly completely continuous functions are investigated. The composition of fuzzy weakly completely continuous functions and its properties are studied. The concept of fuzzy extremally disconnected space is also introduced.

Topological Structure Formed by Soft Multi-Sets and Soft Multi-Compact Spaces

The purpose of this chapter was to study the concept of topological structure formed by soft multi-sets. The notion of relative complement of soft multi-set, soft multi-point, soft multi-open set, soft multi-closed set, soft multi-basis, soft multi-sub-basis, neighbourhoods and neighbourhood system, interior and closure of a soft multi-set, etc., is to be introduced, and their basic properties are also to be investigated. It is seen that a soft multi-topological space gives a parameterised family of topological spaces. Lastly, the concept of soft multi-compact space is also introduced.

Interval-valued intuitionistic fuzzy soft rough sets

In this chapter, the concept of interval-valued intuitionistic fuzzy soft rough sets is introduced. Also interval-valued intuitionistic fuzzy soft rough set-based multi-criteria group decision-making scheme is presented, which refines the primary evaluation of the whole expert group and enables us to select the optimal object in a most reliable manner. The proposed scheme is illustrated by an example regarding the candidate selection problem.

Fuzzy completely continuous mappings

Abstract The object of this paper is to investigate further properties of fuzzy completely continuous mapping.

Some more results on completely induced fuzzy topological spaces

Abstract The object of the paper is to present some new results on completely induced fuzzy topological spaces and completely semi-induced spaces earlier introduced by the authors in this journal. When a fuzzy topological space becomes a completely induced space is discussed. Examples of completely induced space are also cited.

Soft Interval-Valued Intuitionistic Fuzzy Rough Sets

The vagueness or the representation of imperfect knowledge has been a problem for a long time for the mathematicians. There are many mathematical tools for dealing with uncertainties; some of them are fuzzy set theory, rough set theory, and soft set theory. In this chapter, the concept of soft interval-valued intuitionistic fuzzy rough sets is introduced. Also some properties based on soft interval-valued intuitionistic fuzzy rough sets are presented. Also a soft interval-valued intuitionistic fuzzy rough set-based multi-criteria group decision-making scheme is presented. The proposed scheme is illustrated by an example regarding the car selection problem.

Interval-Valued Intuitionistic Fuzzy Soft Topological Spaces

In this chapter, the concept of interval-valued intuitionistic fuzzy soft topological space (IVIFS topological space) together with intuitionistic fuzzy soft open sets (IVIFS open sets) and intuitionistic fuzzy soft closed sets (IVIFS closed sets) are introduced. We define neighbourhood of an IVIFS set, interior IVIFS set, interior of an IVIFS set, exterior IVIFS set, exterior of an IVIFS set, closure of a IVIFS set, IVIFS basis, and IVIFS subspace. Some examples and theorems regarding these concepts are presented.

Fuzzy completely irresolute and fuzzy weakly completely irresolute functions

Abstract The aim of this paper is to introduce two new classes of functions, called fuzzy completely irresolute and fuzzy weakly completely irresolute functions. Their characterizations, examples, compositions of these functions, their relationships with other functions, and preservations of some fuzzy spaces under these functions are studied.

A density-based clustering algorithm and experiments on student dataset with noises using Rough set theory

ST-DBSCAN is an extension of the traditional density based clustering algorithm DBSCAN. This algorithm is proposed for clustering spatio-temporal datasets. Spatio-temporal data refers to data which is stored as temporal slices of the spatial dataset. Here the spatial part of data identifies the location in data space and the temporal part of data represents the state in time. ST-DBSCAN can cluster data based on their spatial and temporal attributes and assigns data points to different clusters. ST-DBSCAN finds the clusters as crisp set. Since the crisp sets have a well-defined boundary, it becomes very difficult to find the accurate clusters. Our proposed algorithm, Rough-ST-DBSCAN, clusters data points as Rough Sets. Rough Sets are formal approximations of Crisp Sets in terms of a pair of sets which give the lower and the upper approximation of the original set. The lower approximation will be represented by a cluster that will contain the data points that must belong to the cluster and the upper approximation will be represented by a cluster boundary that will contain the data points that may belong to the cluster. So this proposed Rough-ST-DBSCAN algorithm can cluster data points based on their spatial and temporal density and also can determine the type of belongingness to a specific cluster.