Conditional Relative Frequency Distributions with Undefined Observations and Generalized Fuzzy Orthopartitions
Authors: Stefania Boffa, Davide Ciucci
JAIR 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | As a first goal, we introduce the so-called conditional relative frequency distributions with undefined observations for representing frequencies characterized by uncertainty. After that, we show that conditional relative frequency distributions with undefined observations can be identified with particular generalized fuzzy orthopartitions, which are mathematical models describing vague partitions where the membership of elements to classes is only partially known. Finally, we provide a sufficient and necessary condition to identify a generalized fuzzy orthopartition with a conditional frequency distribution with undefined observations. This article introduces novel models to describe conditional relative frequency distributions in case undefined observations are added to the initial data. |
| Researcher Affiliation | Academia | STEFANIA BOFFA , IULM University, Italy DAVIDE CIUCCI, University of Milano-Bicocca, Italy Authors Contact Information: Stefania Boffa, orcid: https://orcid.org/0000-0002-4171-3459, EMAIL, IULM University, Milan, Italy; Davide Ciucci, orcid: https://orcid.org/0000-0002-8083-7809, EMAIL, University of Milano-Bicocca, Milan, Italy. |
| Pseudocode | No | The paper describes mathematical models, definitions, propositions, and theorems, often accompanied by examples. It does not contain any explicitly labeled pseudocode or algorithm blocks with structured steps. |
| Open Source Code | No | The paper does not contain any explicit statement about making source code available or provide links to a code repository. |
| Open Datasets | Yes | T carries real data, which have been detected by the Italian National Institute of Statistics (ISTAT) 9. Such data are available on the ISTAT website (https://www.istat.it/). |
| Dataset Splits | No | The paper discusses conditional relative frequency distributions with undefined observations and how they relate to generalized fuzzy orthopartitions. It uses illustrative examples with real data, but it does not specify any training, validation, or test dataset splits, as it does not involve machine learning experiments that require such partitioning. |
| Hardware Specification | No | The paper is theoretical, focusing on mathematical models and their properties. It describes the framework and provides illustrative examples, but it does not detail any computational experiments that would require specific hardware specifications. |
| Software Dependencies | No | The paper focuses on mathematical theory and concepts. It does not mention any specific software libraries, frameworks, or programming languages with version numbers that would be required to replicate its findings. |
| Experiment Setup | No | The paper presents theoretical models and mathematical proofs, along with illustrative examples. It does not describe an experimental setup with hyperparameters, training configurations, or other system-level settings, as it does not involve empirical machine learning experiments. |