Abstract
Recent trends in modern information processing have focused on polarizing information, and and bipolar fuzzy sets can be useful. Bipolar fuzzy sets are one of the important tools that can be used to distinguish between positive information and negative information. Positive information, for example, already observed or experienced, indicates what is guaranteed to be possible, and negative information indicates that it is impossible, prohibited, or certainly false. The purpose of this paper is to apply the bipolar fuzzy set to BCK/BCI-algebras. The notion of (translated) k-fold bipolar fuzzy sets is introduced, and its application in BCK/BCI-algebras is discussed. The concepts of k-fold bipolar fuzzy subalgebra and k-fold bipolar fuzzy ideal are introduced, and related properties are investigated. Characterizations of k-fold bipolar fuzzy subalgebra/ideal are considered, and relations between k-fold bipolar fuzzy subalgebra and k-fold bipolar fuzzy ideal are displayed. Extension of k-fold bipolar fuzzy subalgebra is discussed.
Highlights
A fuzzy set is introduced in [1], and it deals with uncertainty connected with perceptions, preferences, and imprecision of states
We introduce the notion of k-fold bipolar fuzzy subalgebra and k-fold bipolar fuzzy ideal and investigate several properties
If a set expression can express this kind of difference, it will be more beneficial than a traditional fuzzy set expression
Summary
A fuzzy set is introduced in [1], and it deals with uncertainty connected with perceptions, preferences, and imprecision of states. Mathematics 2019, 7, 1036 the concept of bipolar fuzzy subalgebras/ideals of a BCK/BCI-algebra, and investigated several properties. Lee and Jun [6] introduced the notion of bipolar fuzzy a-ideals of BCI-algebras and investigated their properties. They discussed relations between bipolar fuzzy subalgebras, bipolar fuzzy ideals, and bipolar fuzzy a-ideals. Akram et al [12] introduced certain notions of bipolar fuzzy soft graphs and investigated some of their properties They presented several applications of the bipolar fuzzy soft graphs in a multiple criteria decision-making problem. We introduce the notion of k-fold bipolar fuzzy subalgebra and k-fold bipolar fuzzy ideal and investigate several properties. We introduce the extension of k-fold bipolar fuzzy set and discuss their properties
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