Representing fuzzy decision tables in a fuzzy relational database environment.

In this paper the representation of decision tables in a relational database environment is discussed. First, crisp decision tables are defined. Afterwards a technique to represent decision tables in a relational system is presented. Next, fuzzy extensions are made to crisp decision tables in order to deal with imprecision and uncertainty. As a result, with crisp decision tables as special cases fuzzy decision tables are defined which include fuzziness in the conditions as well as in the actions. Analogous to the crisp case, it is demonstrated how fuzzy decision tables can be stored in a fuzzy relational database environment. Furthermore, consultation of these tables is discussed using fuzzy queries.Decision making;

Modelling decision tables from data.

On most datasets induction algorithms can generate very accurate classifiers. Sometimes, however, these classifiers are very hard to understand for humans. Therefore, in this paper it is investigated how we can present the extracted knowledge to the user by means of decision tables. Decision tables are very easy to understand. Furthermore, decision tables provide interesting facilities to check the extracted knowledge on consistency and completeness. In this paper, it is demonstrated how a consistent and complete DT can be modelled starting from raw data. The proposed method is empirically validated on several benchmarking datasets. It is shown that the modelling decision tables are sufficiently small. This allows easy consultation of the represented knowledge.Data;

An overview of decision table literature.

The present report contains an overview of the literature on decision tables since its origin. The goal is to analyze the dissemination of decision tables in different areas of knowledge, countries and languages, especially showing these that present the most interest on decision table use. In the first part a description of the scope of the overview is given. Next, the classification results by topic are explained. An abstract and some keywords are included for each reference, normally provided by the authors. In some cases own comments are added. The purpose of these comments is to show where, how and why decision tables are used. Other examined topics are the theoretical or practical feature of each document, as well as its origin country and language. Finally, the main body of the paper consists of the ordered list of publications with abstract, classification and comments.

A branch and bound algorithm to optimize the representation of tabular decision processe.

Decision situations have various aspects: knowledge acquisition and structuring, knowledge representation, knowledge validation and decision making. It has been recognized in literature that decision tables can play an important role in each of these stages. It is however not necessary to use only one representation formalism during the whole life cycle of an intelligent system. Likewise it is possible that different formats of the same formalism serve different purposes in the development process.Important in this respect is the search for automated and, if possible, optimized transitions between different formats of a formalism and between various formalisms. In this paper a branch and bound algorithm is presented that transforms expanded decision tables, that, because of their explicit enumeration of all decision cases primarily serve an acquisition and verification function, into optimized contracted decision tables, primarily used as target representation of a decision process. An optimal contracted decision table is a contracted decision table with a condition order which results in the minimum number of contracted decision columns.

On the decomposition of tabular knowledge systems.

Recently there has been a growing interest in the decomposition of knowledge based systems and decision tables. Much work in this area has adopted an informal approach. In this paper, we first formalize the notion of decomposition, and then we study some interesting classes of decompositions. The proposed classification can be used to formulate design goals to master the decomposition of large decision tables into smaller components. Importantly, carrying out a decomposition eliminates redundant information from the knowledge base, thereby taking away -right from the beginning- a possible source of inconsistency. This, in turn, renders subsequent verification and validation more smoothly.Knowledge; Systems;

An overview of decision table literature 1982-1995.

This report gives an overview of the literature on decision tables over the past 15 years. As much as possible, for each reference, an author supplied abstract, a number of keywords and a classification are provided. In some cases own comments are added. The purpose of these comments is to show where, how and why decision tables are used. The literature is classified according to application area, theoretical versus practical character, year of publication, country or origin (not necessarily country of publication) and the language of the document. After a description of the scope of the interview, classification results and the classification by topic are presented. The main body of the paper is the ordered list of publications with abstract, classification and comments.

Applications of Formal Methods to Specification and Safety of Avionics Software

This report treats several topics in applications of formal methods to avionics software development. Most of these topics concern decision tables, an orderly, easy-to-understand format for formally specifying complex choices among alternative courses of action. The topics relating to decision tables include: generalizations fo decision tables that are more concise and support the use of decision tables in a refinement-based formal software development process; a formalism for systems of decision tables with behaviors; an exposition of Parnas tables for users of decision tables; and test coverage criteria and decision tables. We outline features of a revised version of ORA's decision table tool, Tablewise, which will support many of the new ideas described in this report. We also survey formal safety analysis of specifications and software

Optimal Decision Trees for Local Image Processing Algorithms

In this paper we present a novel algorithm to synthesize an optimal decision tree from OR-decision tables, an extension of standard decision tables, complete with the formal proof of optimality and computational cost analysis. As many problems which require to recognize particular patterns can be modeled with this formalism, we select two common binary image processing algorithms, namely connected components labeling and thinning, to show how these can be represented with decision tables, and the benets of their implementation as optimal decision trees in terms of reduced memory accesses. Experiments are reported, to show the computational time improvements over state of the art implementations

Privet: A Privacy-Preserving Vertical Federated Learning Service for Gradient Boosted Decision Tables

Vertical federated learning (VFL) has recently emerged as an appealing distributed paradigm empowering multi-party collaboration for training high-quality models over vertically partitioned datasets. Gradient boosting has been popularly adopted in VFL, which builds an ensemble of weak learners (typically decision trees) to achieve promising prediction performance. Recently there have been growing interests in using decision table as an intriguing alternative weak learner in gradient boosting, due to its simpler structure, good interpretability, and promising performance. In the literature, there have been works on privacy-preserving VFL for gradient boosted decision trees, but no prior work has been devoted to the emerging case of decision tables. Training and inference on decision tables are different from that the case of generic decision trees, not to mention gradient boosting with decision tables in VFL. In light of this, we design, implement, and evaluate Privet, the first system framework enabling privacy-preserving VFL service for gradient boosted decision tables. Privet delicately builds on lightweight cryptography and allows an arbitrary number of participants holding vertically partitioned datasets to securely train gradient boosted decision tables. Extensive experiments over several real-world datasets and synthetic datasets demonstrate that Privet achieves promising performance, with utility comparable to plaintext centralized learning.Comment: Accepted in IEEE Transactions on Services Computing (TSC

Verification and Simplification of DMN Decision Tables

Decision Model and Notation (DMN) on standardne notatsioon, mida kasutatakse ärirakendustes otsuste loogika kirjeldamiseks. Otsustabelid on DMNi üks peamisi osi. DMNi otsustabelite suurenev kasutatavus igapäevaste äriotsuste ülesmärkimiseks ja automatiseerimiseks on tõstatanud vajadust analüüsida otsustabeleid. See lõputöö annab ülevaate DMN otsustabelist ja kirjeldab kolme skaleeruvat algoritmi, mis on mõeldud leidmaks kattuvaid reegleid ja puuduvaid reegleid ning lihtsustada otsustabeleid kasutades reeglite ühendamist. Kõik välja pakutud algoritmid on implementeeritud avatud lähtekoodiga DMN redaktorisse ja katsetatud suurte otsustabelite peal, mis pärinevad krediidiandmise andmebaasist.The Decision Model and Notation (DMN) is a standard notation to specify decision logic in business applications. A central construct in DMN is a decision table. The rising use of DMN decision tables to capture and to automate everyday business decisions raises the need to support analysis tasks on decision tables. This thesis provides scalable algorithms to tackle three analysis tasks: detection of overlapping rules, detection of missing rules and simplification of decision tables via rule merging. All proposed algorithms have been implemented in an open-source DMN editor and are tested on large decision tables derived from a credit lending data-set