Pythagorean m-polar fuzzy sets and TOPSIS method for the selection of advertisement mode

The prevailing structures like intuitionistic fuzzy sets, Pythagorean fuzzy sets and m-polar fuzzy sets etc. have their own deficiencies and limitations. There are many real life situations where multi-polar information is available and these structures fail to work due to their limitations e.g. in medical diagnosis sometimes some tests are repeated time and again to get multiple readings about symptoms to get a better diagnosis of a diseases. The motivation behind this article is to overcome these deficiencies by introducing a novel sort of set entitled Pythagorean m-polar fuzzy set (PmFS) as hybrid structure of Pythagorean fuzzy set and m-polar fuzzy set, m being some cardinal number. For m = 1, this set dwindles to Pythagorean fuzzy set and becomes Pythagorean bipolar fuzzy set for m = 2. We take the advantage to present a number of algebraic operations and some characteristics of PmFSs. We define some linguistic terms using the notion of product of PmFSs (circle times) by assigning different numeric values to the constant k is an element of [0, infinity [ and present an illustration to determine the values of membership and non-membership functions of PmFSs for lower, middle and upper class regarding economic position. We render an application of PmFSs in decision making problem (DMP) of selection of most appropriate mode of advertisement using the well-known tool TOPSIS.