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The idea of fuzzy graphs is crucial for dealing with uncertainty in day-to-day living situations. In this work, we have a present a work fuzzy graph associates with robustness model that’s easy, flexible, and simple. With this model, we have a tendency to address the examination planning downside below uncertainty supported. Randomness and unclearness are two very separate types of uncertainty in knowledge. This study bridges resilient fuzzy graphs and addresses every type of uncertainty in higher cognitive processes. In this paper we introduce a type of fuzzy graph relating with robustness is called robust fuzzy graph and some of its properties. Robust fuzzy graph becomes a best tool in evidence theory for calculating belief functions, plausibility functions, spanning functions etc.

The motivation for our consideration comes from the fuzzy set theory in a potential relation to quantum theories and mathematical economics: Given a certain non-additive assignment on a Boolean algebra (a kind of "belief measure"), can this assignment be extended over a larger Boolean algebra? We answer this question in the affirmative. By examining the universality of the method used, we conclude that even when we let the assignment subject to an arbitrary collection of unsharp inequalities, we are always able to extend the measure so defined over a larger Boolean algebra. [ABSTRACT FROM AUTHOR]

Many relations in the real world can be described by mathematical language. Fuzzy set theory can transform human language into mathematical language and use membership degree function to describe relations between events. Dempster-Shafer evidence theory provides basic probability assignment (BPA), which can describe the occurrence rate of attributes in basic events. Based on the known membership degree function and BPA distribution, a new evaluation method is proposed in this paper to analyze decision making. Given the relations among relevant events, which are expressed by BPA distribution and membership degree function, the relations among basic events and top event can be obtained. The Dempster's combination rule and pignistic probability transformation are used to transform BPA distribution into probability distribution. The belief measure is applied to deal with these fuzzy relations. Some numerical examples are given in this paper to illustrate the proposed evaluation methodology. [ABSTRACT FROM AUTHOR]

Recently a new type of central limit theorem for belief functions was given in Epstein et al. [9] . In this paper, we generalize the central limit theorem in Epstein et al. [9] to accommodate general bounded random variables. These results are a natural extension of the classical central limit theory for additive probability measures. [ABSTRACT FROM AUTHOR]

De Finetti has introduced lower and upper probabilities as boundary set functions when extending a fixed probability from an atomic algebra to an atomic superalgebra. We discuss the relationship of de Finetti’s lower and upper probabilities with belief and plausibility measures, and also investigate the order of their additivity. Finally, two open problems are formulated.