A Gradient Descent Approach for Multi-Objective Picture-Fuzzy Stochastic Programming Problems

EasyChair Preprint 15707

Abstract

This paper explores multi-objective stochastic fuzzy linear programming problems using picture-fuzzy theory to model parameter uncertainty and fuzziness. Picture-fuzzy theory provides a flexible way to handle uncertain data by representing acceptance, rejection, and hesitation degrees. The study introduces a method to transform the initial stochastic fuzzy problem into a quasiconvex programming problem. The study enhances computational efficiency and ensures algorithm convergence by applying a gradient descent approach rather than conventional heuristic methods. The paper provides theoretical proof using quasiconvex optimization to validate the proposed method, establishing a foundation for its convergence and effectiveness. To illustrate the method's feasibility and efficacy, the paper presents computational examples demonstrating its correctness and potential applications, particularly in economics and finance where uncertainty and fuzziness in market data are significant. This research opens new pathways for solving complex programming problems in uncertain environments.

Keyphrases: Hanoi University of Science and Technology, Multiobjective stochastic linear programming, Picture Fuzzy Sets, Picture Fuzzy decision, Probability maximization, Variance covariance matrices, convex set, fuzzy decision making, gradient descent, multi objective stochastic linear optimization, objective picture fuzzy stochastic programming, picture fuzzy stochastic programming problems, probability maximization model

@booklet{EasyChair:15707,
  author    = {Tuan Khang Truong and Son Ta Anh and Ngoc Thang Tran},
  title     = {A Gradient Descent Approach for Multi-Objective Picture-Fuzzy Stochastic Programming Problems},
  howpublished = {EasyChair Preprint 15707},
  year      = {EasyChair, 2025}}