Bipolar fuzzy relation equations systems based on the product t-norm
This research addresses a theoretical problem in fuzzy logic for domains involving human reasoning, but it is incremental as it builds on existing contributions.
The paper tackles the problem of solving bipolar fuzzy relation equations systems based on the max-product t-norm, studying their solvability and algebraic structure of solutions, including cases with zero independent terms, as a complement to prior work on bipolar max-product fuzzy relation equations.
Bipolar fuzzy relation equations arise as a generalization of fuzzy relation equations considering unknown variables together with their logical connective negations. The occurrence of a variable and the occurrence of its negation simultaneously can give very useful information for certain frameworks where the human reasoning plays a key role. Hence, the resolution of bipolar fuzzy relation equations systems is a research topic of great interest. This paper focuses on the study of bipolar fuzzy relation equations systems based on the max-product t-norm composition. Specifically, the solvability and the algebraic structure of the set of solutions of these bipolar equations systems will be studied, including the case in which such systems are composed of equations whose independent term be equal to zero. As a consequence, this paper complements the contribution carried out by the authors on the solvability of bipolar max-product fuzzy relation equations.