Since their introduction more than four decades ago, invariant assertions have, justifiably, dominated the analysis of while loops, and have been the focus of sustained research interest in the seventies and eighties, and renewed interest in the last decade. In this paper, we tentatively submit an alternative concept for the analysis of while loops, explore its attributes, and its relationship ...

In general fuzzy linear regression, the coefficients of the fuzzy regression model are symmetric triangular fuzzy numbers, while we try to replace them by more general ones, which are asymmetric trapezoidal fuzzy numbers. Possibility of equality between two asymmetric trapezoidal fuzzy numbers is explained by possibility distribution. Two different models are presented in this paper. Furthermor...

We examine a corpus of reflective tutorial dialogues between human tutor and student after the student completed introductory physics problems, to predict when the tutor abstracted from the student’s preceding turn or when the tutor specialized from the student’s preceding turn. Tutor abstraction occurs when the tutor repeats a segment of the student’s turn using more general terms. Tutor speci...

the classical control charts by using precise and specified data divide the production process into two groups: in-control or out of control, while the fuzzy sets with the definition continuous and cohesive membership functions and also using ambiguous and vague fuzzy numbers (triangular and trapezoid), it introduces different levels of decisions for the decision makers. in this paper, using th...

Data envelopment analysis (DEA) is a mathematical method to evaluate the performance of decision-making units (DMU). In the performance evaluation of an organization based on the classical theory of DEA, input and output data are assumed to be deterministic, while in the real world, the observed values of the inputs and outputs data are mainly fuzzy and random. A normal distribution is a contin...

In this paper we establish equivalence between a theory of fuzzy functional dependences and a fragment of fuzzy logic. We give a way to interpret fuzzy functional dependences as formulas in fuzzy logic. This goal is realized in four steps. Truth assignment of attributes is defined in terms of closeness between two tuples in a fuzzy relation. A corresponding fuzzy formula is associated to a fuzz...

In this paper we establish equivalence between a theory of fuzzy functional dependences and a fragment of fuzzy logic. We give a way to interpret fuzzy functional dependences as formulas in fuzzy logic. This goal is realized in a few steps. Truth assignment of attributes is defined in terms of closeness between two tuples in a fuzzy relation. A corresponding fuzzy formula is associated to a fuz...