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Rough membership functions: a tool for reasoning with uncertainty

100%

Pawlak Z. , Skowron A.

Banach Center Publications

1993

tom 28

nr 1

135-150

A variety of numerical approaches for reasoning with uncertainty have been investigated in the literature. We propose rough membership functions, rm-functions for short, as a basis for such reasoning. These functions have values in the interval [0,1] and are computable on the basis of the observable information about the objects rather than on the objects themselves. We investigate properties of the rm-functions. In particular, we show that our approach is intensional with respect to the class of all information systems [P91]. As a consequence we point out some differences between the rm-functions and the fuzzy membership functions [Z65], e.g. the rm-function values for X ∪ Y (X ∩ Y) cannot be computed in general by applying the operation max(min) to the rm-function values for X and Y.

Knowledge base development for assembly planning using evidence theory

100%

Kutschenreiter-Praszkiewicz I. , Matuszny M.

Journal of Machine Engineering

2022

tom Vol. 22, No. 2

125--137

This paper presents an approach to assembly planning in the early phase of product development. The product specification, workstation, environment, equipment and tools are not fully known in the early stage of product development. When comparing product variants at this stage there is a lack of data that affects the efficiency of the manufacturing process. It is therefore necessary to apply methods useful in processing incomplete and uncertain data. The main indicator which helps in comparing different product variants is manufacturing time standard. This papier is focused on assembly tool selection which is one of important data influenced assembly time. Based on the proposed algorithm and case study, a tool selection method using a decision tree induced from a training set with reduced uncertainty is presented.

Disset: a disjunctive sorting method based on evidence theory

100%

Boujelben M. A. , De Smet Y. , Frikha A. , Chabchoub H.

Foundations of Computing and Decision Sciences

2007

tom Vol. 32, No. 4

253-274

We consider sorting problems where information about categories is represented by a Learning Set (LS), i.e. a set of alternatives and their related labels. The distinctive feature of our approach relies on the fact that both precise and imprecise information about the LS can be handled. More precisely, we assume that each alternative of the LS may belong to a unique category or a disjunction of successive categories. Our method proceeds in four stages: the comparison, the definition of Basic Belief Assignments (BBA's), the combination and the assignment. Artificial data sets are used to test the method and to compare its results with those provided by an ELECTRE TRI like procedure.

Three-way learnability: A learning theoretic perspective on Three-way Decision

51%

Campagner A. , Ciucci D.

Annals of Computer Science and Information Systems

2022

tom Vol. 30

243--246

In this article we study the theoretical properties of Three-way Decision (TWD) based Machine Learning, from the perspective of Computational Learning Theory, as a first attempt to bridge the gap between Machine Learning theory and Uncertainty Representation theory. Drawing on the mathematical theory of orthopairs, we provide a generalization of the PAC learning framework to the TWD setting, and we use this framework to prove a generalization of the Fundamental Theorem of Statistical Learning. We then show, by means of our main result, a connection between TWD and selective prediction.