Abstract
Fuzzy evidence theory, or fuzzy Dempster-Shafer Theory captures all three types of uncertainty, i.e. fuzziness, non-specificity, and conflict, which are usually contained in a piece of information within one framework. Therefore, it is known as one of the most promising approaches for practical applications. Quantifying the difference between two fuzzy bodies of evidence becomes important when this framework is used in applications. This work is motivated by the fact that while dissimilarity measures have been surveyed in the fields of evidence theory and fuzzy set theory, no comprehensive survey is yet available for fuzzy evidence theory. We proposed a modification to a set of the most discriminative dissimilarity measures (smDDM)-as the minimum set of dissimilarity with the maximal power of discrimination in evidence theory- to handle all types of uncertainty in fuzzy evidence theory. The generalized smDDM (FsmDDM) together with the one previously introduced as fuzzy measures make up a set of measures that is comprehensive enough to collectively address all aspects of information conveyed by the fuzzy bodies of evidence. Experimental results are presented to validate the method and to show the efficiency of the proposed method.
Highlights
Dempster-Shafer theory (DST) or evidence theory is accepted as a flexible framework to model various processes of quantitative reasoning and decision making under uncertainty [1] [2] [3]
We proposed a modification to a set of the most discriminative dissimilarity measures-as the minimum set of dissimilarity with the maximal power of discrimination in evidence theory- to handle all types of uncertainty in fuzzy evidence theory
It is widely used in practical applications such as belief function approximation [4] [5], regression analysis [6] [7], sensor reliability evaluation [8] [9], risk analysis [10], sensor fusion [11], pattern classification [12] [13], and evidential clustering [14], where Dempster-Shafer Theory (DST) framework could handle different types of non-specificity, and conflict during modeling under uncertainty
Summary
Dempster-Shafer theory (DST) or evidence theory is accepted as a flexible framework to model various processes of quantitative reasoning and decision making under uncertainty [1] [2] [3]. In our previous study [22], we proposed a framework for comprehensive assessment of dissimilarity between two BoEs. The outcome was the set of most discriminative dissimilarity measures (smDDM) representing the minimal set of dissimilarity measures needed for an overall evaluation of the differences between two BoEs. dissimilarity measures in the field of both evidence theory and fuzzy set theory have been studied separately, no comprehensive survey is yet available for fuzzy evidence theory to handle all types of uncertainties. To validate the proposed approach, it is tested through experimentation which shows a good agreement with experimental data
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