Rough Intuitionistic Fuzzy Research Articles

The equilibrium of maritime transport under disaster effects: The case of COVID-19

Ensuring traffic flows remain in equilibrium is crucial in preventing congestion and disruptions in maritime transport chains. Using the fuzzy linear programming method, this article examines how COVID-19 risks have affected the concentration and capacity of maritime cargo flows. The study presents the model, the computational process, and its applications, assessing the transport system's degree of imbalance in 2020-2021 compared to 2018-2019. The model allows for the evaluation of multiple dimensions to obtain an aggregative result. The model provides insights into the dynamics of changes in maritime traffic under the influence of COVID-19. Keywords: Intuitionistic Fuzzy Rough, maritime transport, transport equilibrium, seaborne trade, port calls

Attribute reduction based on observational consistency in intuitionistic fuzzy multi-covering decision systems

Attribute reduction is an important issue in data mining, machine learning and other applications of big data processing. Covering-based rough set and intuitionistic fuzzy (IF) set models are both the effective theoretical tools of uncertainty or imprecise computation, and thus IF covering rough set model has been acknowledged as a positive approach to attribute reduction. Based on IF covering rough set model, this study explores a kind of parameterized IF observational consistency in IF multi-covering decision system, and proposes an attribute reduction method. This article firstly defines the concepts of regular IF β-covering, parameterized IF observational sets on the regular IF β-covering approximation space. Secondly, the parameterized IF observational consistency is defined to be the principal of attribute reduction in the IF multi-covering decision system, and the related IF discernibility matrix is developed to provide a way of attribute reduction. For multi-observational consistency corresponding to an observational parameters set, an unified multi-observational discernibility matrix is constructed, which avoids the disadvantage of needing to construct multiple corresponding discernibility matrices separately. Furthermore, an attribute reduction algorithm based on iterative dissolving of unified multi-observational discernibility matrix is proposed, and the experiment to demonstrate effectiveness of algorithm is presented. Experiments with UCI datasets shows that, the proposed method is a good way for improving both the rates of attribute-reduced and the classification accuracy of reduced datasets.

Kernelised Rough Sets Based Clustering Algorithms Fused With Firefly Algorithm for Image Segmentation

Data clustering methods have been used extensively for image segmentation in the past decade. In one of the author's previous works, this paper has established that combining the traditional clustering algorithms with a meta-heuristic like the Firefly Algorithm improves the stability of the output as well as the speed of convergence. It is well known now that the Euclidean distance as a measure of similarity has certain drawbacks and so in this paper we replace it with kernel functions for the study. In fact, the authors combined Rough Fuzzy C-Means (RFCM) and Rough Intuitionistic Fuzzy C-Means (RIFCM) with Firefly algorithm and replaced Euclidean distance with either Gaussian or Hyper-tangent or Radial basis Kernels. This paper terms these algorithms as Gaussian Kernel based rough Fuzzy C-Means with Firefly Algorithm (GKRFCMFA), Hyper-tangent Kernel based rough Fuzzy C-Means with Firefly Algorithm (HKRFCMFA), Gaussian Kernel based rough Intuitionistic Fuzzy C-Means with Firefly Algorithm (GKRIFCMFA) and Hyper-tangent Kernel based rough Intuitionistic Fuzzy C-Means with Firefly Algorithm (HKRIFCMFA), Radial Basis Kernel based rough Fuzzy C-Means with Firefly Algorithm (RBKRFCMFA) and Radial Basis Kernel based rough Intuitionistic Fuzzy C-Means with Firefly Algorithm (RBKRIFCMFA). In order to establish that these algorithms perform better than the corresponding Euclidean distance-based algorithms, this paper uses measures such as DB and Dunn indices. The input data comprises of three different types of images. Also, this experimentation varies over different number of clusters.

Covering-Based Rough Fuzzy, Intuitionistic Fuzzy and Neutrosophic Nano Topology and Applications

In recent years, “mathematical orientations on real-life problems”, which continue to increase, began to make a significant impact. Information systems for many decision-making problems consist of uncertain, incomplete, indeterminate and indiscernible structures and components. Classical set theory and interpretation methods fail to represent, express and solve the problems of these types or cause to make wrong decisions. For this reason, in this study, we provide definitions and methods to present information and problem representations in more detail and precision. This paper introduces three new topologies called covering-based rough fuzzy, covering-based rough intuitionistic fuzzy and covering-based rough neutrosophic nano topology. Some fundamental definitions such as open set, closed set, interior, closure and basis are given. Neutrosophic definitions and properties are mainly investigated. We give some real life applications of covering-based rough neutrosophic nano topology in the final part of the paper and an explanatory example of decision making application by defining core point.

Novel Three-Way Decisions Models with Multi-Granulation Rough Intuitionistic Fuzzy Sets

The existing construction methods of granularity importance degree only consider the direct influence of single granularity on decision-making; however, they ignore the joint impact from other granularities when carrying out granularity selection. In this regard, we have the following improvements. First of all, we define a more reasonable granularity importance degree calculating method among multiple granularities to deal with the above problem and give a granularity reduction algorithm based on this method. Besides, this paper combines the reduction sets of optimistic and pessimistic multi-granulation rough sets with intuitionistic fuzzy sets, respectively, and their related properties are shown synchronously. Based on this, to further reduce the redundant objects in each granularity of reduction sets, four novel kinds of three-way decisions models with multi-granulation rough intuitionistic fuzzy sets are developed. Moreover, a series of concrete examples can demonstrate that these joint models not only can remove the redundant objects inside each granularity of the reduction sets, but also can generate much suitable granularity selection results using the designed comprehensive score function and comprehensive accuracy function of granularities.

Multi-Granulation Graded Rough Intuitionistic Fuzzy Sets Models Based on Dominance Relation

From the perspective of the degrees of classification error, we proposed graded rough intuitionistic fuzzy sets as the extension of classic rough intuitionistic fuzzy sets. Firstly, combining dominance relation of graded rough sets with dominance relation in intuitionistic fuzzy ordered information systems, we designed type-I dominance relation and type-II dominance relation. Type-I dominance relation reduces the errors caused by single theory and improves the precision of ordering. Type-II dominance relation decreases the limitation of ordering by single theory. After that, we proposed graded rough intuitionistic fuzzy sets based on type-I dominance relation and type-II dominance relation. Furthermore, from the viewpoint of multi-granulation, we further established multi-granulation graded rough intuitionistic fuzzy sets models based on type-I dominance relation and type-II dominance relation. Meanwhile, some properties of these models were discussed. Finally, the validity of these models was verified by an algorithm and some relative examples.

Algorithms on Rough-Intuitionistic Fuzzy Classification with a Threshold and Implementations

Hybridization of Rough Sets with intuitionistic fuzzy sets is commonly in use for deriving several real time applications. In this aspect, we describe three types of algorithms namely lower, upper and rough indexing algorithms to index the records of decision table with intuitionistic fuzzy decision attributes and the same are implemented using C Programming.

A Comparative Analysis of Depth Computation of Leukaemia Images using a Refined Bit Plane and Uncertainty Based Clustering Techniques

Abstract Several image segmentation techniques have been developed over the years to analyze the characteristics of images. Among these, the uncertainty based approaches and their hybrids have been found to be more efficient than the conventional and individual ones. Very recently, a hybrid clustering algorithm, called Rough Intuitionistic Fuzzy C-Means (RIFCM) was proposed by the authors and proved to be more efficient than the conventional and other algorithms applied in this direction, using various datasets. Besides, in order to remove noise from the images, a Refined Bit Plane (RBP) algorithm was introduced by us. In this paper we use a combination of the RBP and RIFCM to propose an approach and apply it to leukemia images. The aim of the paper is twofold. First, it establishes the superiority of our approach in medical diagnosis in comparison to most of the conventional, as well as uncertainty based approaches. The other objective is to provide a computer-aided diagnosis system that will assist the doctors in evaluating medical images in general, and also in easy and better assessment of the disease in leukaemia patients. We have applied several measures like DB-index, D-index, RMSE, PSNR, time estimation in depth computation and histogram analysis to support our conclusions.

The Rough Intuitionistic Fuzzy Ideals of Intuitionistic Fuzzy Subrings in a Commutative Ring

The aim of this paper is to give some definitions of rough intuitionistic fuzzy ideal, rough intuitionistic fuzzy radical, rough prime (primary) intuitionistic fuzzy ideal and rough semiprime intuitionistic fuzzy ideal of an intuitionistic fuzzy subring, and also to give some properties of such ideals. Moreover, we give their nature under homomorphism.

An interval-valued rough intuitionistic fuzzy set model

Rough set theory is a powerful tool for dealing with uncertainty, granuality and incompleteness of knowledge in information systems. This paper presents an interval-valued rough intuitionistic fuzzy (IF) set model by means of integrating the classical Pawlak rough set theory with the interval-valued IF set theory. In this paper, we first introduce some concepts and properties of interval-valued IF set theory. Then, the rough approximations of an interval-valued IF set in the classical Pawlak approximation space and the generalised Pawlak approximation space are respectively defined, and some fundamental properties of the approximation operators are studied. Furthermore, by employing cut sets of interval-valued IF sets, classical representations of interval-valued rough IF approximation operators are presented, and the connections between special binary relations and interval-valued rough IF approximation operators are constructed. Finally, we discuss the knowledge reduction and knowledge discovery of the interval-valued IF information systems.