Bipolar fuzzy relation equations systems based on the product t-norm

• URL: http://arxiv.org/abs/2410.02816v1
• Date: Tue, 24 Sep 2024 09:09:13 GMT
• Title: Bipolar fuzzy relation equations systems based on the product t-norm
• Authors: M. Eugenia Cornejo, David Lobo, Jesús Medina,
• Abstract summary: Bipolar fuzzy relation equations arise as a generalization of fuzzy relation equations considering unknown variables together with their logical connective negations. This paper focuses on the study of bipolar fuzzy relation equations systems based on the max-product t-norm composition.
• Score: 0.5735035463793009
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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 zero. As a consequence, this paper complements the contribution carried out by the authors on the solvability of bipolar max-product fuzzy relation equations.

Related papers

• Neural Differential Algebraic Equations [6.100037457394823]
  We present Neural Differential-Algebraic Equations (NDAEs) suitable for data-driven modeling of Differential-Algebraic Equations (DAEs) We show that the proposed NDAEs abstraction is suitable for relevant system-theoretic data-driven modeling tasks.
  arXiv  Detail & Related papers  (2024-03-19T17:43:57Z)
• Towards true discovery of the differential equations [57.089645396998506]
  Differential equation discovery is a machine learning subfield used to develop interpretable models. This paper explores the prerequisites and tools for independent equation discovery without expert input.
  arXiv  Detail & Related papers  (2023-08-09T12:03:12Z)
• The solution set of fuzzy relation equations with addition-min composition [5.327411221630033]
  This paper deals with the resolutions of fuzzy relation equations with addition-min composition. We first propose an algorithm to find all minimal solutions of the fuzzy relation equations and also supply an algorithm to find all maximal solutions of the fuzzy relation equations.
  arXiv  Detail & Related papers  (2022-10-29T05:39:04Z)
• Symbolic Recovery of Differential Equations: The Identifiability Problem [52.158782751264205]
  Symbolic recovery of differential equations is the ambitious attempt at automating the derivation of governing equations. We provide both necessary and sufficient conditions for a function to uniquely determine the corresponding differential equation. We then use our results to devise numerical algorithms aiming to determine whether a function solves a differential equation uniquely.
  arXiv  Detail & Related papers  (2022-10-15T17:32:49Z)
• Identifiability and Asymptotics in Learning Homogeneous Linear ODE Systems from Discrete Observations [114.17826109037048]
  Ordinary Differential Equations (ODEs) have recently gained a lot of attention in machine learning. theoretical aspects, e.g., identifiability and properties of statistical estimation are still obscure. This paper derives a sufficient condition for the identifiability of homogeneous linear ODE systems from a sequence of equally-spaced error-free observations sampled from a single trajectory.
  arXiv  Detail & Related papers  (2022-10-12T06:46:38Z)
• On the solvability of weakly linear systems of fuzzy relation equations [0.0]
  Systems of fuzzy relation equations and inequalities in which an unknown fuzzy relation is on the one side of the equation or inequality are linear systems. This paper describes the set of fuzzy relations that solve weakly linear systems to a certain degree and provides ways to compute them.
  arXiv  Detail & Related papers  (2022-05-25T16:59:48Z)
• Deformed Explicitly Correlated Gaussians [58.720142291102135]
  Deformed correlated Gaussian basis functions are introduced and their matrix elements are calculated. These basis functions can be used to solve problems with nonspherical potentials.
  arXiv  Detail & Related papers  (2021-08-10T18:23:06Z)
• Multi-objective discovery of PDE systems using evolutionary approach [77.34726150561087]
  In the paper, a multi-objective co-evolution algorithm is described. The single equations within the system and the system itself are evolved simultaneously to obtain the system. In contrast to the single vector equation, a component-wise system is more suitable for expert interpretation and, therefore, for applications.
  arXiv  Detail & Related papers  (2021-03-11T15:37:52Z)
• Disentangling Observed Causal Effects from Latent Confounders using Method of Moments [67.27068846108047]
  We provide guarantees on identifiability and learnability under mild assumptions. We develop efficient algorithms based on coupled tensor decomposition with linear constraints to obtain scalable and guaranteed solutions.
  arXiv  Detail & Related papers  (2021-01-17T07:48:45Z)
• Conditional independences and causal relations implied by sets of equations [1.847740135967371]
  We make use of Simon's causal ordering algorithm to construct a causal ordering graph. We prove that it expresses the effects of perfect interventions on the equations under certain unique solvability assumptions. We discuss how this approach reveals and addresses some of the limitations of existing causal modelling frameworks.
  arXiv  Detail & Related papers  (2020-07-14T17:00:28Z)
• Recent advances in the calculation of dynamical correlation functions [0.0]
  Time-dependent correlation functions play a central role in both the theoretical and experimental understanding of dynamic properties. The method of recurrence relation has, at its foundation, the solution of Heisenberg equation of motion of an operator in a many-body interacting system. In this work, we discuss the most relevant applications of the method of recurrence relations and numerical calculations based on exact diagonalizations.
  arXiv  Detail & Related papers  (2020-05-28T18:33:22Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.