Abstract
In this paper, the notions of m-polar picture fuzzy subalgebra (PFSA), m-polar picture fuzzy ideal (PFI) and m-polar picture fuzzy implicative ideal (PFII) of BCK algebra are introduced and some related basic results are presented. A relation between m-polar PFI and m-polar PFII is established. It is shown that an m-polar PFII of a BCK algebra is an m-polar PFI. But the converse of the proposition is not necessarily true. Converse is true only in implicative BCK algebra. The concept of m-polar picture fuzzy commutative ideal (PFCI) is also explored here and some related results are investigated.
Highlights
After the initiation of fuzzy set (FS) by Zadeh [1] in 1965, the notion of intuitionistic fuzzy set (IFS) was propounded by Atanassov [2] in 1986
We introduce the concept of m-polar picture fuzzy subalgebra (PFSA), m-polar picture fuzzy ideal (PFI) and m-polar picture fuzzy implicative ideal (PFII), m-polar picture fuzzy commutative ideal (PFII) of BCK algebra and explore some results related to these
We have initiated the notion of m-polar PFI and mpolar PFII of BCK algebra
Summary
After the initiation of fuzzy set (FS) by Zadeh [1] in 1965, the notion of intuitionistic fuzzy set (IFS) was propounded by Atanassov [2] in 1986. Later on a lot of works on BCK/BCI algebra and ideals in fuzzy set environment were done by several researchers [8,9,10,11,12]. Intuitionistic fuzzy subalgebra and intuitionistic fuzzy ideal (IFI) in BCK algebra were presented by Jun and Kim [13] in 2000 as an extension of FS concept in BCK algebra. Bipolar fuzzy set (BFS) [16] is the generalization of FS which involves the degree of positive membership (DPMS) and the degree of negative membership (DNegMS) of an element. In 2013, including the measure of neutral membership and generalizing the notion of IFS, the concept of picture fuzzy set (PFS) was initiated by Cuong [18]. After the initiation of PFS, different types of research works in context of PFS were performed by several researchers
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