A glimpse of some common concepts in algebras of logic and uncertain environments

Daniela Danciulescu, Dana Piciu, Cristian Dinu, Sebastian Stefaniga, Florentina Boboc

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abstract_carpathian_2025_41_4_1061-1077

https://doi.org/10.37193/CJM.2025.04.14

Published on 16 September 2025

Issue no: Vol 41/2025 no. 4 Tags: Residuated lattice; $F$-ideal, Inventory model, Inventory game

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Abstract.

The aim of this paper is to investigate some concepts that appear both in algebras of logic and in various uncertain environments.
The first part of the paper is devoted to study $F$ -ideals in residuated lattices and some of their properties. If $L$ is a residuated lattice and $\mu$ is a $F$ -ideal in $L$ then the binary relation $\sim _{\mu _{\mu (0)}}$ is an equivalence relation on $L$ and we investigate the algebraic structure of the factor set.

In the second part of the paper, some applications of $FNs$ in uncertain environments are discussed. Inventory games are considered in the case of imprecise parameters of EOQ and EPQ models. Computing with $TrFNs$ is detailed and some formulas for solving games when players cooperate are presented. Computational details and numerical examples are included.