Correlation of interval-valued intuitionistic fuzzy sets

doi:10.1016/0165-0114(94)00343-6

Fuzzy Sets and Systems

Volume 74, Issue 2, 15 September 1995, Pages 237-244

https://doi.org/10.1016/0165-0114(94)00343-6 Get rights and content

Abstract

In this paper we introduce the concepts of correlation and correlation coefficient of interval-valued intuitionistic fuzzy sets and we study their first properties. We also introduce two decomposition theorems of the correlation of interval-valued intuitionistic fuzzy sets, one in terms of the correlation of interval-valued fuzzy sets and the entropy of the intuitionistic fuzzy sets, and the other theorem in terms of the correlation of intuitionistic fuzzy sets.

References (8)

K. Atanassov
Intuitionistic fuzzy sets
Fuzzy Sets and Systems
(1986)
K. Atanassov et al.
Interval valued intuitionistic fuzzy sets
Fuzzy Sets and Systems
(1989)
T. Gerstenkorn et al.
Correlation of intuitionistic fuzzy sets
Fuzzy Sets and Systems
(1991)
M.B. Gorzalczany
A method of inference in approximate reasoning based on interval-valued fuzzy sets
Fuzzy Sets and Systems
(1987)

There are more references available in the full text version of this article.

Cited by (367)

Optimal cloud service provider selection: An MADM framework on correlation-based TOPSIS with interval-valued q-rung orthopair fuzzy soft set
2024, Engineering Applications of Artificial Intelligence
The interaction between two factors significantly measures the results' exactness. But, acquiring information for statistical computation is frequent, and the data obtained could be challenging to interpret. To predict how a particular factor will fluctuate regarding another as well, the correlation coefficient (CC) is usually employed. But this approach is rarely utilized for interval-valued q-rung orthopair fuzzy soft set (IVq-ROFSS). The situation in which IVq-ROFSS grows as it is modern, along with a broad depiction of the q-rung orthopair fuzzy soft set (q-ROFSS), engaging for a more reflective and precise assessment. The current study explores the CC and weighted correlation coefficient (WCC) for IVq-ROFSS and their fundamental characteristics. This research is designed to improve the prioritization technique for order preference by similarity to the ideal solution (TOPSIS) with expanded measures. Also, to check the linearity of the intended approach, we integrated mathematical formulations of correlation constrictions. This study demonstrates that the suggested methodology is a robust multi-attribute decision-making (MADM) tool for intricate information set interpretation and prioritizing. We presented a numerical illustration demonstrating the actual application of our recommended decision-making strategy for choosing Cloud Service Providers (CSPs) in cloud service management. The approach developed in this research is superior to conventional models in maintaining the precise structure of the determined studies. Thus, the algorithm produces more reliable and consistent decisions. The influence of our studies grows within the scope of this research, as the originated algorithm can enhance the ability to analyze realities and make informed decisions in light of the information provided. Therefore, this study can significantly impact data analysis and decision-making by revealing the importance of the proposed TOPSIS approach and the vitality of perpetual development in methods for making decisions to get more reliable and precise outcomes.
Data analysis for panoramic X-ray selection: Fermatean fuzzy type correlation coefficients approach
2023, Engineering Applications of Artificial Intelligence
An interval-valued Fermatean hesitant fuzzy set (IVFHFS) not only can be regarded as the union of some interval-valued Fermatean fuzzy sets (IVFFSs) but also represent the Fermatean hesitant fuzzy elements (FHFEs) in the form of interval values. So IVFHFSs are extensions of FHFSs and IVFFSs, which are powerful tools to represent more complicated, uncertain, and vague information. This paper focuses on the four kinds of correlation coefficients for FHFSs and extends them to the correlation coefficients and the weighted correlation coefficients for IVFHFSs. In the processing, we develop the least common multiple expansion (LCME) methods to solve the problem that the cardinalities of Fermatean hesitant fuzzy elements (FHFEs) (or interval-valued Fermatean hesitant fuzzy elements (IVPHFEs)) are different. In addition, we propose score functions and accuracy functions of FFEs (or IVFFEs) to rank all the FFEs (or IVFFEs) in an FHFE (or an IVFHFE). Especially, score functions and accuracy functions of IVFFEs are both presented as interval numbers. Then use the comparison method of interval numbers to compare two revised IVFHFEs in order to keep the original fuzzy information as far as possible. What is more, we define the local correlations and local informational energies which can depict the similarity between two IVFHFEs more meticulously and completely. At last, the numerical examples show the feasibility and applicability of the proposed methods in multiple criteria decision-making (MCDM) and clustering analysis.
Uncertain probability, regular probability interval and relative proximity
2023, Fuzzy Sets and Systems
This work firstly discusses two layers of meanings about uncertain information from which the uncertain probability information is naturally introduced which can generalize some other uncertain information such as interval information, intuitionistic fuzzy information and vague information. Two decision making models are presented, called relative opinion and selected opinions. To model their high dimensional counterparts, we introduce the concepts of uncertain probability matrix, regular probability interval and BUI of probability vector mainly based on some barycentric coordinates expressions. Some related properties, remarks, high dimensional cases of relative opinion and selected opinions with numerical examples are presented. Further, we technically define the concept of relative proximity for probability vector by which it is possible to define a type of unimodal function on the space of probability vectors, which otherwise is difficult to be done. Finally, some properties of relative proximity in relation to BUI of probability vector are analyzed. This work is suitable for both practitioners and theorists devoted to uncertain models.
Interval-valued intuitionistic fuzzy rough set system over a novel conflict distance measure with application to decision-making
2023, MethodsX
Conflict analysis is one of the most critical application domains whose importance is increasing rapidly nowadays. Attributes involving conflicts frequently occur with opinion, negotiations, and collaborators in decision-making. Taking advantage of the uncertainty present in decision-making, in this paper, we have proposed a system that can solve the problems involving conflicts more adequately.
- •
  A new interval-valued intuitionistic fuzzy rough set (IVIFRS) system is introduced to handle a decision-making problem involving a conflict of interests.
- •
  The proposed system exploits both the notions of rough set and interval-valued intuitionistic fuzzy set theories in sharpening the boundaries of conflicts.
- •
  In the IVIFRS system, the disputes amongst the objectives are measured by the novel conflict distance measure. Further, an interval-valued intuitionistic fuzzy conflict analysis system formulated on the IVIFRS is designed for deciding the conflicting attributes
The formulated system is then studied for weight vectors too. The intended conflict analysis system is studied with reference to the well-known existing intuitionistic fuzzy rough set system. The real-life socio-economic problems are dealt with, and the experimental results validate the efficacy of the proposed system.
A fair bed allocation during COVID-19 pandemic using TOPSIS technique based on correlation coefficient for interval-valued pythagorean fuzzy hypersoft set
2024, Scientific Reports
A Novel Correlation Coefficient for Spherical Fuzzy Sets and its Application in Pattern Recognition, Medical Diagnosis and Mega Project Selection
2024, SSRN

View all citing articles on Scopus

View full text