Abstract
In this paper, the idea of ∈ , ∈ ∨ q ˘ -bipolar fuzzy b -ideals and an ∈ , ∈ ∨ q ˘ -bipolar fuzzy ideals of BCK / BCI -algebras is delivered, and their related properties are investigated with the aid of some examples. We also provide the connection between ∈ , ∈ ∨ q ˘ -bipolar fuzzy ideals and bipolar fuzzy ideals and ∈ , ∈ ∨ q ˘ -bipolar fuzzy b -ideals and bipolar fuzzy b -ideals by way of counterexamples.
Highlights
In the real world, there are several difficult problems in engineering, medical science, economics, environment, social science, and other various fields involving incalculable data
There are several difficult problems in engineering, medical science, economics, environment, social science, and other various fields involving incalculable data. Problems of this nature which are frequently encountered in our daily lives cannot be solved by classical mathematical methods
In 1965, the belief of fuzzy sets turned into was first delivered with the aid of Zadeh [1], which is an effective hand set for modelling indecision and elusiveness in numerous issues springing up inside the field of technology
Summary
There are several difficult problems in engineering, medical science, economics, environment, social science, and other various fields involving incalculable data. Jana et al [16, 17] introduced generalizations of ð∈, ∈ ∨qÞ -intuitionistic fuzzy subalgebras and ideals of BCK/BCI-algebras with thresholds. Jana et al [18] introduced the concept of ð∈, ∈ ∨qÞ-bipolar fuzzy BCK/BCI-subalgebras and ð∈, ∈ ∨qÞ-bipolar fuzzy ideals of BCK/BCI-algebras. These works are enough to motivate us, and, to the best of our knowledge, no other works are available on ð∈, ∈ ∨qÞ-bipolar fuzzy ideals and b-ideals in BCK/BCI-algebras and other fuzzy algebraic structures. Ð∈, ∈ ∨qÞ-bipolar fuzzy b-ideals of BCI/BCK-algebras are proposed, and their properties are examined in detail
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