In this paper, we prove that any BL-general fuzzy automaton (BL-GFA) and its quotient have the same behavior. In addition, we obtain the minimal quotient BL-GFA and minimal quotient transformation of the BL-GFA, considering the notion of maximal admissible partition. Furthermore, we show that the number of input symbols and time complexity of the minimal quotient transformation of a BL-GFA are ...

It is known that any self-dual Boolean function can be decomposed into compositions of 3-bit majority functions. In this paper, we define a notion of a ternary majority formula, which is a ternary tree composed of nodes labeled by 3-bit majority functions and leaves labeled by literals. We study their complexity in terms of formula size. In particular, we prove upper and lower bounds for ternar...

We define the Lukasiewicz Transform as a residuated map and a homomorphism between semimodules over the semiring reducts of an MV-algebra. Then we describe the “ Lukasiewicz Transform Based” ( LTB) algorithm for image processing. We also propose a strong extension of such concepts and results in the framework of quantales and quantale modules. 1 The Lukasiewicz transform and its applications Th...

prolonged excessive intake of fluoride during child's growth and development stages has been associated with mental and physical problems. the aim of this study was to investigate the effect of excessive fluoride intake on the intelligence quotient (iq) of children living in five rural areas in makoo/iran.in this cross-sectional study, 293 children aged 6-11 years were selected from five villag...

The range and midrange are widely used, particularly in statistical quality control as an estimator of the dispersion tendency. In fact, the range itself is a very simple measure of dispersion, gives a quick and easy to estimate indication about the spread of data. The extremal quotient is used in climatic study, industrial quality control, life testing, small-area variation analysis and the cl...

For Gorenstein quotient spaces C/G, a direct generalization of the classical McKay correspondence in dimensions d ≥ 4 would primarily demand the existence of projective, crepant desingularizations. Since this turned out to be not always possible, Reid asked about special classes of such quotient spaces which would satisfy the above property. We prove that the underlying spaces of all Gorenstein...