Optimal allocation problem under uncertainty modeled by extended fuzzy intervals

In this paper we deal with well known Optimal Allocation Problem (OAP) and its solution under uncertainty. We define a special interval uncertainty by extending the well known concept of fuzzy intervals (or, fuzzy numbers), defining a new concept of extended fuzzy interval and its subspace: extended linear fuzzy interval. Then we present some examples and derive basic properties. We formulate the corresponding optimization problem with the extended fuzzy interval coefficients and, in particular, extended fuzzy interval variables and derive its optimal solution in the form of extended fuzzy intervals. Some numerical examples are presented in order to illustrate particular problems and solution concepts.& COPY; 2023 Elsevier B.V. All rights reserved.

Automated summary

This paper studies the Optimal Allocation Problem (OAP) and its solution under uncertainty. A special interval uncertainty is defined by extending the concept of fuzzy intervals, creating the concept of extended fuzzy intervals and its subspace: extended linear fuzzy intervals. The optimization problem with extended fuzzy interval coefficients and variables is formulated, and its optimal solution is derived in the form of extended fuzzy intervals. Numerical examples are provided to illustrate specific problems and solution concepts.