Bipolar fuzzy relation equations systems based on the product t‐norm. (2nd May 2019)

• Record Type: Journal Article
• Authors: Cornejo, M. Eugenia; Lobo, David; Medina, Jesús
• Other Names: Vigo-Aguiar Jesus guestEditor.; Kumam Poom guestEditor.
• Is Part Of: Mathematical methods in the applied sciences. Volume 42:Number 17(2019)
• Page Start: 5779
• Page End: 5793
• Publication Date: 2019-05-02
• Subjects: bipolar fuzzy relation equation -- fuzzy set -- max‐product t‐norm composition -- negation operator; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.5646
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : 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 0. As a consequence, this paper complements the contribution carried out by the authors on the solvability of bipolar max‐product fuzzy relation equations.