scholarly journals An Intelligent and Robust Framework towards Anomaly Detection, Medical Diagnosis, and Shortest Path Problems Based on Interval-Valued T-Spherical Fuzzy Information

2020 ◽  
Vol 2020 ◽  
pp. 1-23
Author(s):  
Huanhuan Jin ◽  
Syed Khurram Jah Rizvi ◽  
Tahir Mahmood ◽  
Naeem Jan ◽  
Kifayat Ullah ◽  
...  
Keyword(s):  
Anomaly Detection ◽  
Fuzzy Sets ◽  
Shortest Path ◽  
Fuzzy Set ◽  
Medical Diagnosis ◽  
Shortest Path Problem ◽  
Information Modeling ◽  
Research Trend ◽  
Shortest Path Problems ◽  
Interval Valued

The recent emerging advancements in the domain of the fuzzy sets are the framework of the T-spherical fuzzy set (TSFS) and interval valued T-spherical fuzzy set (IVTSFS). Keeping in view the promising significance of the latest research trend in the fuzzy sets and the enabling impact of IVTSFS, we proposed a novel framework for decision assembly using interval valued TSFS based upon encompassing the four impressive dimensions of human judgement including favor, abstinence, disfavor, and refusal degree. Another remarkable contribution is the optimization of information modeling and prevention of information loss by redefining the concept of each membership in interval. Moreover, the proposed research made a worthy contribution work by demonstrating the effective utilization of the interval valued TSFS based framework in anomaly detection, medical diagnosis, and shortest path problem. The proposed work demonstrates the effective remedial measure for the anomaly detection problem based on several parameters using the aggregation operators of IVTSFS. Moreover, the interval valued T-spherical fuzzy relations and their composition are illustrated to investigate the medical diagnosis problem. Furthermore, the notion of interval valued T-spherical fuzzy graph is also presented and fundamental notions of graph theory are also demonstrated with the help of real world instances. In the context of interval valued T-spherical fuzzy graphs (IVTSFGs), a modified Dijkstra Algorithm (DA) is developed and applied to the shortest path problem. The in-depth quantitative assessment and comparative analysis revealed that the proposed notion outpaces contemporary progressive approaches.

scholarly journals An Improved Correlation Coefficient of Intuitionistic Fuzzy Sets

2019 ◽  
Vol 28 (2) ◽  
pp. 231-243 ◽  
Author(s):  
Han-Liang Huang ◽  
Yuting Guo
Keyword(s):  
Fuzzy Sets ◽  
Correlation Coefficient ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Medical Diagnosis ◽  
Intuitionistic Fuzzy Set ◽  
Intuitionistic Fuzzy Sets ◽  
Intuitionistic Fuzzy ◽  
Interval Valued

Abstract The intuitionistic fuzzy set is a useful tool to deal with vagueness and uncertainty. Correlation coefficient of the intuitionistic fuzzy sets is an important measure in intuitionistic fuzzy set theory and has great practical potential in a variety of areas, such as decision making, medical diagnosis, pattern recognition, etc. In this paper, an improved correlation coefficient of the intuitionistic fuzzy sets is defined, and it can overcome some drawbacks of the existing ones. The properties of this correlation coefficient are discussed. Then, the generalization of the coefficient of interval-valued intuitionistic fuzzy sets is also introduced. Finally, two examples about the application of the proposed correlation coefficient of the intuitionistic fuzzy sets in medical diagnosis and clustering are shown to illustrate the advantages over the existing methods.

scholarly journals Interval Valued Neutrosophic Shortest Path Problem by A* Algorithm

2020 ◽  
pp. 53-61
Author(s):  
admin admin ◽  
◽  
◽  
◽  
Said Broumi ◽  
...  
Keyword(s):  
Shortest Path ◽  
Score Function ◽  
Shortest Path Problem ◽  
Destination Node ◽  
A Algorithm ◽  
Shortest Path Problems ◽  
Different Types ◽  
The Cost ◽  
Arc Lengths ◽  
Interval Valued

Many researchers have been proposing various algorithms to unravel different types of fuzzy shortest path problems. There are many algorithms like Dijkstra’s, Bellman-Ford,Floyd-Warshall and kruskal’s etc are existing for solving the shortest path problems. In this work a shortest path problem with interval valued neutrosophic numbers is investigated using the proposed algorithm. A* algorithm is extensively applied in pathfinding and graph traversal.Unlike the other algorithms mentioned above, A* algorithm entails heuristic function to uncover the cost of path that traverses through the particular state. In the structured work A* algorithm is applied to unravel the length of the shortest path by utilizing ranking function from the source node to the destination node. A* algorithm is executed by applying best first search with the help of this search, it greedily decides which vertex to investigate subsequently. A* is equally complete and optimal if an acceptable heuristic is concerned. The arc lengths in interval valued neutrosophic numbers are defuzzified using the score function. A numerical example is used to illustrate the proposed approach.

A novel approach for solving all-pairs shortest path problem in an interval-valued fuzzy network: Suggested modifications

2021 ◽  
pp. 1-18
Author(s):  
Tanveen Kaur Bhatia ◽  
Amit Kumar ◽  
S.S. Appadoo
Keyword(s):  
Shortest Path ◽  
Fuzzy Number ◽  
Fuzzy Systems ◽  
Shortest Path Problem ◽  
Shortest Path Problems ◽  
Novel Approach ◽  
Shortest Distance ◽  
All Pairs Shortest Path ◽  
Fuzzy Network ◽  
Interval Valued

Enayattabr et al. (Journal of Intelligent and Fuzzy Systems 37 (2019) 6865– 6877) claimed that till now no one has proposed an approach to solve interval-valued trapezoidal fuzzy all-pairs shortest path problems (all-pairs shortest path problems in which distance between every two nodes is represented by an interval-valued trapezoidal fuzzy number). Also, to fill this gap, Enayattabr et al. proposed an approach to solve interval-valued trapezoidal fuzzy all-pairs shortest path problems. In this paper, an interval-valued trapezoidal fuzzy shortest path problem is considered to point out that Enayattabr et al.’s approach fails to find correct shortest distance between two fixed nodes. Hence, it is inappropriate to use Enayattabr et al.’s approach in its present from. Also, the required modifications are suggested to resolve this inappropriateness of Enayattabr et al.’s approach.

Width-based distance measures on interval-valued intuitionistic fuzzy sets

2021 ◽  
pp. 1-13
Author(s):  
Xi Li ◽  
Chunfeng Suo ◽  
Yongming Li
Keyword(s):  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Medical Diagnosis ◽  
Intuitionistic Fuzzy Sets ◽  
Distance Measures ◽  
Intuitionistic Fuzzy ◽  
Interval Valued ◽  
Dissimilarity Function ◽  
Better Than

An essential topic of interval-valued intuitionistic fuzzy sets(IVIFSs) is distance measures. In this paper, we introduce a new kind of distance measures on IVIFSs. The novelty of our method lies in that we consider the width of intervals so that the uncertainty of outputs is strongly associated with the uncertainty of inputs. In addition, better than the distance measures given by predecessors, we define a new quaternary function on IVIFSs to construct the above-mentioned distance measures, which called interval-valued intuitionistic fuzzy dissimilarity function. Two specific methods for building the quaternary functions are proposed. Moreover, we also analyzed the degradation of the distance measures in this paper, and show that our measures can perfectly cover the measures on a simpler set. Finally, we provide illustrative examples in pattern recognition and medical diagnosis problems to confirm the effectiveness and advantages of the proposed distance measures.

scholarly journals Generalised Interval-Valued Fuzzy Soft Set

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Shawkat Alkhazaleh ◽  
Abdul Razak Salleh
Keyword(s):  
Decision Making ◽  
Similarity Measure ◽  
Fuzzy Set ◽  
Medical Diagnosis ◽  
Soft Set ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Decision Making Problem ◽  
Fuzzy Soft Sets ◽  
Interval Valued

We introduce the concept of generalised interval-valued fuzzy soft set and its operations and study some of their properties. We give applications of this theory in solving a decision making problem. We also introduce a similarity measure of two generalised interval-valued fuzzy soft sets and discuss its application in a medical diagnosis problem: fuzzy set; soft set; fuzzy soft set; generalised fuzzy soft set; generalised interval-valued fuzzy soft set; interval-valued fuzzy set; interval-valued fuzzy soft set.

Multi-criteria decision making and pattern recognition based on similarity measures for Fermatean fuzzy sets

2021 ◽  
pp. 1-17
Author(s):  
Changlin Xu ◽  
Juhong Shen
Keyword(s):  
Decision Making ◽  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Medical Diagnosis ◽  
Intuitionistic Fuzzy Set ◽  
Similarity Measures ◽  
New Method ◽  
Fuzzy Decision Making ◽  
Multi Criteria Decision Making

 Higher-order fuzzy decision-making methods have become powerful tools to support decision-makers in solving their problems effectively by reflecting uncertainty in calculations better than crisp sets in the last 3 decades. Fermatean fuzzy set proposed by Senapati and Yager, which can easily process uncertain information in decision making, pattern recognition, medical diagnosis et al., is extension of intuitionistic fuzzy set and Pythagorean fuzzy set by relaxing the restraint conditions of the support for degrees and support against degrees. In this paper, we focus on the similarity measures of Fermatean fuzzy sets. The definitions of the Fermatean fuzzy sets similarity measures and its weighted similarity measures on discrete and continuous universes are given in turn. Then, the basic properties of the presented similarity measures are discussed. Afterward, a decision-making process under the Fermatean fuzzy environment based on TOPSIS method is established, and a new method based on the proposed Fermatean fuzzy sets similarity measures is designed to solve the problems of medical diagnosis. Ultimately, an interpretative multi-criteria decision making example and two medical diagnosis examples are provided to demonstrate the viability and effectiveness of the proposed method. Through comparing the different methods in the multi-criteria decision making and the medical diagnosis application, it is found that the new method is as efficient as the other methods. These results illustrate that the proposed method is practical in dealing with the decision making problems and medical diagnosis problems.

scholarly journals Random assignment and shortest path problems

2006 ◽  
Vol DMTCS Proceedings vol. AG,... (Proceedings) ◽  
Author(s):  
Johan Wästlund
Keyword(s):  
Limit Theorem ◽  
Shortest Path ◽  
Complete Graph ◽  
Assignment Problem ◽  
Shortest Path Problem ◽  
Random Assignment ◽  
Shortest Path Problems ◽  
Parisi Formula ◽  
International Audience ◽  
Random Assignment Problem

International audience We explore a similarity between the $n$ by $n$ random assignment problem and the random shortest path problem on the complete graph on $n+1$ vertices. This similarity is a consequence of the proof of the Parisi formula for the assignment problem given by C. Nair, B. Prabhakar and M. Sharma in 2003. We give direct proofs of the analogs for the shortest path problem of some results established by D. Aldous in connection with his $\zeta (2)$ limit theorem for the assignment problem.

Note on “Optimal path selection approach for fuzzy reliable shortest path problem”

2020 ◽  
Vol 39 (5) ◽  
pp. 7653-7656
Author(s):  
Ranjan Kumar ◽  
SA Edalatpanah ◽  
Hitesh Mohapatra
Keyword(s):  
Shortest Path ◽  
Fuzzy Systems ◽  
Optimal Path ◽  
Vital Role ◽  
Path Selection ◽  
Shortest Path Problem ◽  
Shortest Path Problems ◽  
Fuzzy Environment ◽  
Selection Approach ◽  
Arc Lengths

There are different conditions where SPP play a vital role. However, there are various conditions, where we have to face with uncertain parameters such as variation of cost, time and so on. So to remove this uncertainty, Yang et al. [1] “[Journal of Intelligent & Fuzzy Systems, 32(1), 197-205”] have proposed the fuzzy reliable shortest path problem under mixed fuzzy environment and claimed that it is better to use their proposed method as compared to the existing method i.e., “[Hassanzadeh et al.; A genetic algorithm for solving fuzzy shortest path problems with mixed fuzzy arc lengths, Mathematical and Computer Modeling, 57(2013) 84-99” [2]]. The aim of this note is, to highlight the shortcoming that is carried out in Yang et al. [1] article. They have used some mathematical incorrect assumptions under the mixed fuzzy domain, which is not true in a fuzzy environment.

Interval-Valued Fuzzy H-Ideals on ß-Algebra

2020 ◽  
pp. 244-274
Author(s):  
Prakasam Muralikrishna ◽  
Tapan Senapati ◽  
Perumal Hemavathi
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Cartesian Product ◽  
Algebraic Structures ◽  
Interval Valued

The notion of interval valued fuzzy set was first introduced by Zadeh as a generalization of fuzzy sets. Using interval valued fuzzy set, various algebraic structures and related topics were discussed. This chapter extends fuzzy H-ideal into interval valued fuzzy H-ideals of β-algebra and deals some related results. It also provides the study on homomorphic images of an interval valued fuzzy H-ideals of β-algebra and the idea of Cartesian product of interval valued fuzzy H-ideals of β-algebra.

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