An Approach to Bilevel Multi-Objective Linear Fractional Probabilistic Optimization in Neutrosophic Environments with Applications

Abstract

In real-life organization sectors, decision-makers (DMs) always encounter several complexi
ties like hierarchical decision-process with multiple conflict ratio goals, constraints associated with probabil
ity and uncertainty parameter with hesitance scope. Despite the important role of optimization method for
real-life problem, a very few success has been achieved to deal with this applicable complex problem. Thus,
the current study has focused on investigating an efficient method consisting of a goal-programming (GP),
chance-constrained optimization (CCO) and intuitionistic fuzzy mathematical (IFM) approach for solv
ing hierarchical multi-objective linear fractional probabilistic optimization (HMOLFPO) problems under
neutrosophic environment. Here each hierarchical decision-making optimize numerous conflict affain-ratio
objective functions under chance constraints with uncertain coefficients and quantity defined as neutro
sophic linear numbers of the form γ +ωI where γ,ω ∈ R and I represents indeterminacy. In the proposed
method, first the crisp linear model of neutrosophic HMOLFPO problem is formulated using the concept
of interval ratio, CCO and linearized strategy. Then, the membership and non-memberships are investi
gated to measure the degree of satisfaction and dissatisfaction for each imprecise goal of DMs. Finally,
GP with an IFM method is developed to generate a non-dominant solution for all DMs at both levels.
Unlike existing methods, these strategy helps to avoid a decision-locks between upper and lower DMs.
The applicability and efficiency of the suggested method are illustrated by solving numerical examples and
industrial production real-life problem

DOI 10.5281/zenodo.20975534