On some optimisation models in a fuzzy-stochastic environment

Abstract

This paper is on Fuzzy Stochastic Optimisation, an area that is quickly coming to the forefront of mathematical programming under uncertainty. An even stronger motivating factor for the growing interest in this area can be found in the ubiquitous nature of decision problems involving hybrid undeterminacy. More precisely, we consider a range of situations in which random factors and fuzzy information co-occur in an optimisation setting. Related hybrid optimisation models are discussed and converted into deterministic terms through appropriate tools like probabilistic set, uncertain probability, and fuzzy random variable, making good use of uncertainty principles. We also discuss ways to deal with the resulting problems. Numerical examples carried out using class optimisation software demonstrate the efficiency of the proposed approaches. We shall end this article by pointing out some of the challenges that currently occupy researchers in this emerging field.

A Kaleodoscopic View of Fuzzy Stochastic Optimization*

“…For the proof of this result, we invite the reader to consult [33]. We must also stress the fact that several methods have been developed over the past few decades due to the efforts of many researches, e.g.…”

A novel fuzzy stochastic multi-objective linear programming for multi-level capacitated lot-sizing problem: a real case study of a furniture company

“…Many scholars believe that randomness and fuzziness are complementary [39][40][41]. On the other side, increasing the complexity of real production planning problem needs actuarial methods capable of managing complex problems manipulating heterogeneous data, variety of definitions and measurements, high degree of imprecision and vagueness to input data, and changeable assumption lead to develop interest in situations where fuzziness and randomness are merged in an optimization framework [42]. [43] addressed ML-CLSP in a mixed assembly shop.…”

“…Several methods have been developed in the literature to deal with the fuzzy stochastic models involving both ambiguousness and randomness of the coefficients and parameters in objective functions and constraints [42]. Van Hop [47] converts the multi-objective FS-MILP model into the corresponding deterministic one by using superiority and inferiority measures of the FSV.…”

“…System uncertainty includes the uncertainties within the production system such as uncertainty in production cost and actual capacity or consumption of resources. We reviewed the literature and explored four main issues as the major reasons of using the FSV instead of deterministic, fuzzy, or stochastic variable in the proposed ML-CLSP model as follows [42,46,58,59]:…”

Chance-constrained programming with fuzzy stochastic coefficients

“…These works are surveyed again in Luhandjula (2006). Luhandjula and Joubert (2010) further investigate optimisation models in a fuzzy stochastic environment and approaches to convert them into deterministic problems, focusing on the Gaussian case.…”