The support of a set A is the crisp subset of A with nonzero membership grades. Similarly, the core of a set A is the crisp subset of A with membership grade equal to one. So, supp(A) = {x|μA(x) > 0} and core(A) = {x|μA(x) = 1}. (1.1.4) The α-cut Aα of a set A is the crisp subset of A with membership grades of at least α. So, Aα = α-cut(A) = {x|μA(x) ≥ α}. (1.1.5) Note that core(A) = 1-cut(A). ...

In this paper, we show a connection between a certain online low-congestion routing problem and an online prediction of graph labeling. More specifically, we prove that if there exists a routing scheme that guarantees a congestion of α on any edge, there exists an online prediction algorithm with mistake bound α times the cut size, which is the size of the cut induced by the label partitioning ...

investigation of reliability characteristics under fuzzy environments is proposed in this paper. fuzzy weibull distribution and lifetimes of components are using it described. formulas of a fuzzy reliability function, fuzzy hazard function and their α-cut set are presented. furthermore, the fuzzy functions of series systems and parallel systems are discussed, respectively. finally, some numeric...

The (α, β) cut of an Intuitionistic Fuzzy Set (IFS) was studied by P. K. Sharma [4]. In this paper we introduce a new type of cut strong (α, β) cut of IFS and study their properties. Also three decomposition theorems are discussed.

The proposed bi-objective fuzzy data envelopment analysis (BOFDEA) model is a new approach to assess the performance efficiency of decision-making units (DMUs) in uncertain environments using α-cuts. based on (FDEA) and considers two objectives, solution method ranking system are provided. Generally, score obtained for DMU α-cut an interval. Intervals partially ordered sets, due which intervals...

In this paper, a new Fuzzy Morphology (FM) based on the GeneralizedDempster-Shafer Theory (GDST) is proposed. At first, in order to clarify the similarity ofdefinitions between Mathematical Morphology (MM) and Dempster-Shafer Theory (DST),dilation and erosion morphological operations are studied from a different viewpoint. Then,based on this similarity, a FM based on the GDST is proposed. Unlik...

this research presents a dynamic mathematical system for modeling and simulating the quality management process in construction projects. through sets of cause and effect feedback loops, all factors that internally and externally affect the quality management process are addressed. the proposed system integrates fuzzy logic with system dynamics simulation scheme to consider the uncertainties as...

Control charts are widely used in industry as a tool to monitor process characteristics. Deviations from process targets can be detected based on the evidence of statistical significance. The control chart helps to take decisions such as the need for machine or technology replacement to monitor the process with categorical observations. Fuzzy logic is used to cram the uncertainty and vagueness ...

We describe a model-theoretic approach to ordinal analysis via the finite combinatorial notion of an α-large set of natural numbers. In contrast to syntactic approaches that use cut elimination, this approach involves constructing finite sets of numbers with combinatorial properties that, in nonstandard instances, give rise to models of the theory being analyzed. This method is applied to obtai...