We study the following fault tolerant variant of the interval group testing model: Given three positive integers n, p, e, determine the minimum number of questions needed to identify a (possibly empty) set P ⊆ {1, 2, . . . , n} (|P | ≤ p), under the following constraints. Questions have the form “Is I∩P 6= ∅?”, where I can be any interval in {1, 2 . . . , n}. Up to e of the answers can be erron...

Planning resources for a supply chain is a major factor determining its success or failure. In this paper we introduce an Interval Type-2 Fuzzy Logic model of a distribution network. It is believed that the additional degree of uncertainty provided by Interval Type-2 Fuzzy Logic will allow for better representation of the uncertainty and vagueness present in resource planning models. First, the...

Type-2 fuzzy sets are growing in popularity as, for certain applications they model uncertainty and imprecision better than type1 fuzzy sets. However, type-2 fuzzy sets can be difficult to understand and explain. Recent work has introduced embedded type-2 fuzzy sets and the Representation Theorem which enable us to discuss type-2 fuzzy sets in a different way. In particular they allow for alter...

The class of 2-interval graphs has been introduced for modelling scheduling and allocation problems, and more recently for specific bioinformatic problems. Some of those applications imply restrictions on the 2-interval graphs, and justify the introduction of a hierarchy of subclasses of 2-interval graphs that generalize line graphs: balanced 2-interval graphs, unit 2-interval graphs, and (x,x)...

This paper presents the development and design of a graphical user interface and a command line programming toolbox for construction, edition and observation of Interval Type-2 Fuzzy Inference Systems. The Interval Type-2 Fuzzy Logic System Toolbox (IT2FLS), is an environment for interval type-2 fuzzy logic inference system development. Tools that cover the different phases of the fuzzy system ...

This paper proposes a new approach based on Bonferroni mean operator and possibility degree to solve fuzzy multi-attribute decision making (FMADM) problems in which the attribute value takes the form of interval type-2 fuzzy numbers. We introduce the concepts of interval possibility mean value and present a new method for calculating the possibility degree of two interval trapezoidal type-2 fuz...

Is it true that for all integer n > 1 and k ≤ n there exists a prime number in the interval [kn, (k + 1)n]? The case k = 1 is the Bertrand’s postulate which was proved for the first time by P. L. Chebyshev in 1850, and simplified later by P. Erdős in 1932, see [2]. The present paper deals with the case k = 2. A positive answer to the problem for any k ≤ n implies a positive answer to the old pr...

Knowledge about recruitment in a population can be critical when making conservation decisions, particularly for harvested species. Harvest can affect population demography in complex ways and this may be particularly true for cooperatively breeding species whose successful reproduction is often linked with complex social dynamics. We currently have a poor understanding of how harvest affects r...