E-resources
Peer reviewed
-
Gao, Jie; Liang, Zhilei; Xu, Zeshui
IEEE transactions on cybernetics, 10/2020, Volume: 50, Issue: 10Journal Article
The <inline-formula> <tex-math notation="LaTeX">{q} </tex-math></inline-formula>-rung orthopair fuzzy set (<inline-formula> <tex-math notation="LaTeX">{q} </tex-math></inline-formula>-ROFS) is a powerful tool to deal with uncertainty and ambiguity in real life. The theoretical basis for processing the continuous <inline-formula> <tex-math notation="LaTeX">{q} </tex-math></inline-formula>-rung orthopair fuzzy information is <inline-formula> <tex-math notation="LaTeX">{q} </tex-math></inline-formula>-rung orthopair fuzzy calculus (<inline-formula> <tex-math notation="LaTeX">{q} </tex-math></inline-formula>-ROFC) and the main object is <inline-formula> <tex-math notation="LaTeX">{q} </tex-math></inline-formula>-rung orthopair fuzzy functions (<inline-formula> <tex-math notation="LaTeX">{q} </tex-math></inline-formula>-ROFFs). Recently, the authors proposed derivatives and differentials of <inline-formula> <tex-math notation="LaTeX">{q} </tex-math></inline-formula>-ROFFs in the framework of <inline-formula> <tex-math notation="LaTeX">{q} </tex-math></inline-formula>-ROFC. In this paper, we aim to further study the <inline-formula> <tex-math notation="LaTeX">{q} </tex-math></inline-formula>-rung orthopair fuzzy integral (<inline-formula> <tex-math notation="LaTeX">{q} </tex-math></inline-formula>-ROFI). It is the most important and fundamental part of the <inline-formula> <tex-math notation="LaTeX">{q} </tex-math></inline-formula>-ROFC theoretical system with direct and powerful applications. Our contribution is the indefinite and definite integrals, and bridges the fuzzy calculus theoretical gap of the nonlinear <inline-formula> <tex-math notation="LaTeX">{q} </tex-math></inline-formula>-ROFFs. In particular, we begin with the indefinite integral of <inline-formula> <tex-math notation="LaTeX">{q} </tex-math></inline-formula>-ROFFs, which can be regarded as the anti-derivatives operations of our previous work. Some of their basic properties are discussed. Next, we give the accurate concept of definite integrals of <inline-formula> <tex-math notation="LaTeX">{q} </tex-math></inline-formula>-ROFFs under additive operations, and obtain the explicit integral formula. Some properties of <inline-formula> <tex-math notation="LaTeX">{q} </tex-math></inline-formula>-ROFIs, such as comparison, algebraic operations, and mean value theorem are analyzed. Finally, we generalize the <inline-formula> <tex-math notation="LaTeX">{q} </tex-math></inline-formula>-ROFI to the case when membership and nonmembership functions are allowed to be correlated. After the theoretical results have been established, we present some numerical examples to demonstrate the rationality and effectiveness of integrating continuous <inline-formula> <tex-math notation="LaTeX">{q} </tex-math></inline-formula>-rung orthopair fuzzy data with the <inline-formula> <tex-math notation="LaTeX">{q} </tex-math></inline-formula>-ROFIs.
![loading ... loading ...](themes/default/img/ajax-loading.gif)
Shelf entry
Permalink
- URL:
Impact factor
Access to the JCR database is permitted only to users from Slovenia. Your current IP address is not on the list of IP addresses with access permission, and authentication with the relevant AAI accout is required.
Year | Impact factor | Edition | Category | Classification | ||||
---|---|---|---|---|---|---|---|---|
JCR | SNIP | JCR | SNIP | JCR | SNIP | JCR | SNIP |
Select the library membership card:
If the library membership card is not in the list,
add a new one.
DRS, in which the journal is indexed
Database name | Field | Year |
---|
Links to authors' personal bibliographies | Links to information on researchers in the SICRIS system |
---|
Source: Personal bibliographies
and: SICRIS
The material is available in full text. If you wish to order the material anyway, click the Continue button.