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Articles 1 - 4 of 4
Full-Text Articles in Set Theory
Multi-Criteria Decision Making Based On Dsmt-Ahp, Jean Dezert, Jean Marc Tacnet, Mireille Batton-Hubert, Florentin Smarandache
Multi-Criteria Decision Making Based On Dsmt-Ahp, Jean Dezert, Jean Marc Tacnet, Mireille Batton-Hubert, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
In this paper, we present an extension of the multicriteria decision making based on the Analytic Hierarchy Process (AHP) which incorporates uncertain knowledge matrices for generating basic belief assignments (bba’s). The combination of priority vectors corresponding to bba’s related to each (sub)- criterion is performed using the Proportional Conflict Redistribution rule no. 5 proposed in Dezert-Smarandache Theory (DSmT) of plausible and paradoxical reasoning. The method presented here, called DSmT-AHP, is illustrated on very simple examples.
Non Bayesian Conditioning And Deconditioning, Jean Dezert, Florentin Smarandache
Non Bayesian Conditioning And Deconditioning, Jean Dezert, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
In this paper, we present a Non-Bayesian conditioning rule for belief revision. This rule is truly Non-Bayesian in the sense that it doesn’t satisfy the common adopted principle that when a prior belief is Bayesian, after conditioning by X, Bel(X|X) must be equal to one. Our new conditioning rule for belief revision is based on the proportional conflict redistribution rule of combination developed in DSmT (Dezert-Smarandache Theory) which abandons Bayes’ conditioning principle. Such Non-Bayesian conditioning allows to take into account judiciously the level of conflict between the prior belief available and the conditional evidence. We also introduce the deconditioning problem …
Fusion Of Sources Of Evidence With Different Importances And Reliabilities, Florentin Smarandache, Jean Dezert, J.M. Tacnet
Fusion Of Sources Of Evidence With Different Importances And Reliabilities, Florentin Smarandache, Jean Dezert, J.M. Tacnet
Branch Mathematics and Statistics Faculty and Staff Publications
This paper presents a new approach for combining sources of evidences with different importances and reliabilities. Usually, the combination of sources of evidences with different reliabilities is done by the classical Shafer’s discounting approach. Therefore, to consider unequal importances of sources, if any, a similar reliability discounting process is generally used, making no difference between the notion of importance and reliability. In fact, in multicriteria decision context, these notions should be clearly distinguished. This paper shows how this can be done and we provide simple examples to show the differences between both solutions for managing importances and reliabilities of sources. …
An Introduction To Dsmt, Florentin Smarandache, Jean Dezert
An Introduction To Dsmt, Florentin Smarandache, Jean Dezert
Branch Mathematics and Statistics Faculty and Staff Publications
The management and combination of uncertain, imprecise, fuzzy and even paradoxical or highly conflicting sources of information has always been, and still remains today, of primal importance for the development of reliable modern information systems involving artificial reasoning. In this introduction, we present a survey of our recent theory of plausible and paradoxical reasoning, known as Dezert-Smarandache Theory (DSmT), developed for dealing with imprecise, uncertain and conflicting sources of information. We focus our presentation on the foundations of DSmT and on its most important rules of combination, rather than on browsing specific applications of DSmT available in literature. Several simple …