Hesitant Bifuzzy Set (an introduction): A new approach to assess the reliability of the systems

All the available knowledge related to the Fuzzy Sets (FS) is constricted to express the circumstances when the sum of the degrees of membership and non-membership of any element exceeds one. To keep in mind that in real life there are many ill-defined or too inordinately complex situations, in this...

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Bibliographic Details
Published in:Mathematics and computers in simulation 2023-03, Vol.205, p.98-107
Main Authors: Chaube, Shshank, Joshi, Dheeraj Kumar, Ujarari, Chandan Singh
Format: Article
Language:English
Subjects:
Fuzzy reliability
Hesitant bifuzzy score function
Hesitant Bifuzzy Set
System reliability
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Summary:All the available knowledge related to the Fuzzy Sets (FS) is constricted to express the circumstances when the sum of the degrees of membership and non-membership of any element exceeds one. To keep in mind that in real life there are many ill-defined or too inordinately complex situations, in this article, we propose the concept of Hesitant Bifuzzy Set (HBFS), which appraises Fuzzy Set (FS), Intuitionistic Fuzzy Sets (IFS), Hesitant Fuzzy Set (HFS), Conflicting Bifuzzy Set (CBFS) and Dual Hesitant Fuzzy Set (DHFS) as particular cases. Here we discuss the fundamental operations along with the basic properties of HBFSs. A descriptive example is used to illustrate the proposed concept and method. The supremacy of this study is that all the existing methods only provide the reliability of the system in the form of a fuzzy element while the method introduced in this study always provides a crisp value for the reliability of the system.
ISSN:0378-4754
1872-7166
DOI:10.1016/j.matcom.2022.09.019