Concrete Example of Plithogenic Fuzzy Set

Florentin Smarandache

Concrete Example of Plithogenic Fuzzy Set

Florentin Smarandache

Let U = {a, b, c, d, e} be a universe of discourse, and let P = {b, c, e} be a plithogenic set included in U.

Let the attributes be: — color (c), — weight (w), — size (s), whose attribute values are respectively: — c = {white, yellow, blue};

with the degree of contradiction – c_c (white, yellow) = 0.20, – c_c (white, blue) = 0.40, – c_c (yellow, blue) = 0.20; — w = {thin, fat};

with the degree of contradiction – c_w (thin, fat) = 1. — s = {small, medium, big, verybig},

with the degree of contradiction – c_s (small, medium) = 0.25, – c_s (medium, big) = 0.25, – c_s (big, verybig) = 0.25.

Then:

P = { b (white, yellow, blue; thin, fat; small, medium, big, verybig), c (white, yellow, blue; thin, fat; small, medium, big, verybig), e (white, yellow, blue; thin, fat; small, medium, big, verybig) }, and because we use the plithogenic "fuzzy" set, each element b, c, e will have a "fuzzy" degree of membership to the set P with respect to each of its attribute values.