Bipolar fuzzy i-convergent sequence spaces

It has been seen in literature reviews that many studies have been done on convergent sequence spaces, ideal convergence, ideal convergent sequence spaces, fuzzy convergent sequence spaces and fuzzy ideal convergent sequence spaces. However, it has been observed that there is a gap in the literature regarding bipolar fuzzy ideal convergent sequence spaces, and this study aims to eliminate the gap. Convergence, fuzzy numbers, ideal, suitable ideal, ideal convergence, statistical convergence, relationship between ideal and statistical convergence, bipolar fuzzy sets, bipolar fuzzy convergent sequence spaces, fuzzy ideal convergence, fuzzy ideal convergent sequence spaces, fuzzy ideal convergent sequence to zero spaces, fuzzy I-Cauchy sequence and the relationship between fuzzy I-convergence and fuzzy I-Cauchy sequence are examined. The definitions of fuzzy ideal convergent sequence space, fuzzy zero-ideal convergent sequence space and fuzzy I-Cauchy sequence are extended for bipolar fuzzy sets, and bipolar fuzzy ideal convergence, bipolar fuzzy ideal convergent sequence space, bipolar fuzzy ideal zero convergent sequence space and double polar fuzzy I-Cauchy series definitions have been made. It has been investigated whether the bipolar fuzzy ideal convergent sequence space and the fuzzy zero ideal convergent sequence space are linear spaces. The uniqueness of the limit of a bipolar fuzzy ideal convergent sequence and the relationship between the bipolar I-convergent sequence space and the bipolar fuzzy I-Cauchy sequence are given. Additionally, theorems related to bipolar fuzzy I-convergence and bipolar fuzzy I-Cauchy sequences are included.