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New Operations on Interval-Valued Picture Fuzzy Set, Interval-Valued Picture Fuzzy Soft Set and Their Applications

Authors: Ahmed Mostafa Khalil; Sheng-Gang Li; Harish Garg; Hongxia Li; Shengquan Ma;

New Operations on Interval-Valued Picture Fuzzy Set, Interval-Valued Picture Fuzzy Soft Set and Their Applications

Abstract

An interval-valued picture fuzzy set (IVPFS) is one of the generalizations of an interval-valued fuzzy set to handle the uncertainties in the data during analysis. The aim of this paper is to introduce and study new operations of IVPFS, along with its properties, and examples. In addition, we present the notion of the interval-valued picture fuzzy soft set theory and investigated their properties. Several operations on such as subset, equal, complement, inf product, sup product, union, and intersection are defined over the interval-valued picture fuzzy soft set and discussed their basic properties. Furthermore, we construct an algorithm using an interval-valued picture fuzzy soft set to solve the decision-making problems and illustrate its applicability through a numerical example. From the study, we conclude that the proposed approach is viable in order to handle the uncertainties during the decision-making problems.

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Keywords

interval-valued picture fuzzy set, interval-valued picture fuzzy soft set, Picture fuzzy set, soft set, decision-making, Electrical engineering. Electronics. Nuclear engineering, TK1-9971

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    87
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    Top 1%
    influence
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    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
87
Top 1%
Top 10%
Top 1%
gold