Plithogenic Quasigroups with Application to Decision Making

Abstract

 In this paper, we extend the concept of neutrosopic sets by introducing plithogenic quasigroups
by associating a quasigroup (Q,·) with a plithogenic structure: attributes V , dominant vD, contradiction de
grees ci ∈ [0,1], and neutrosophic degrees d(x,vi). The plithogenic product ·P aggregates componentwise via
(1−ci)tN +cisN with tN = min, sN = max. We prove that (P(Q),·P) is a quasigroup and its parastrphes; the
Latin square property lifts, guaranteeing unique solvability of a·P x = b. Solvability holds iff each component bi
lies in the ci-weighted interval between ai and xi: ci = 1 forces bi ≥ ai while ci = 0 forces bi ≤ ai. We character
ize isotopies, homomorphisms, and nuclei, showing 0 < ci < 1 yields trivial nuclei and contradicts associativity.
We applied plithogenic quasigroup properties to portfolio selection with V = {Risk,Return,Liquidity}, setting
cRisk = 0.9 blocks buy signals whereas cRisk = 0.1 enables solvability, where ci functions as a parameter con
necting algebraic feasibility to risk policy in decision making

DOI 10.5281/zenodo.21981733