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It is well known that crisp graph theory is saturated. However, saturation in a fuzzy environment has only lately been created and extensively researched. It is necessary to consider <i>m</i> components for each node and edge in an <i>m</i>-polar fuzzy graph. Since there is only one component for this idea, we are unable to manage this kind of circumstance using the fuzzy model since we take into account <i>m</i> components for each node as well as edges. Again, since each edge or node only has two components, we are unable to apply a bipolar or intuitionistic fuzzy graph model. In contrast to other fuzzy models, <i>m</i>PFG models produce outcomes of fuzziness that are more effective. Additionally, we develop and analyze these kinds of <i>m</i>PFGs using examples and related theorems. Considering all those things together, we define saturation for a <i>m</i>-polar fuzzy graph (<i>m</i>PFG) with multiple membership values for both vertices and edges; thus, a novel approach is required. In this context, we present a novel method for defining saturation in <i>m</i>PFG involving <i>m</i> saturations for each element in the membership value array of a vertex. This explains <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>-saturation and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula>-saturation. We investigate intriguing properties such as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>-vertex count and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula>-vertex count and establish upper bounds for particular instances of <i>m</i>PFGs. Using the concept of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>-saturation and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>-saturation, block and bridge of <i>m</i>PFG are characterized. To identify the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>-saturation and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula>-saturation <i>m</i>PFGs, two algorithms are designed and, using these algorithms, the saturated <i>m</i>PFG is determined. The time complexity of these algorithms is <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>O</mi><mo>(</mo><mo>|</mo><mi>V</mi><msup><mo>|</mo><mn>3</mn></msup><mo>)</mo></mrow></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>|</mo><mi>V</mi><mo>|</mo></mrow></semantics></math></inline-formula> is the number of vertices of the given graph. In addition, we demonstrate a practical application where the concept of saturation in <i>m</i>PFG is applicable. In this application, an appropriate location is determined for the allocation of a facility point.