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2011 Workshop-School on Theoretical Computer Science, 2011
Interval fuzzy sets allow us to deal not only with vagueness (lack of sharp class boundaries), but also with uncertainty (lack of information). The aim of this tutorial is to present some basic concepts about interval fuzzy numbers. Several concepts related to fuzzy sets are extended to the interval approach.
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Interval fuzzy sets allow us to deal not only with vagueness (lack of sharp class boundaries), but also with uncertainty (lack of information). The aim of this tutorial is to present some basic concepts about interval fuzzy numbers. Several concepts related to fuzzy sets are extended to the interval approach.
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Archiv der Mathematik, 1988
Let \({\mathcal B}\) denote the set of natural numbers which are a sum of two squares, and let \[ B_ 2(x,k,\ell)=| \{n\leq x: n, n+1\in {\mathcal B},\quad n\equiv \ell (mod k)\}| \quad. \] \textit{G. Bantle} [Math. Z. 189, 561-570 (1985; Zbl 0545.10029)] obtained an upper bound for \(B_ 2(x,k,\ell)-B_ 2(x-x^{\delta},k,\ell)\) for \(k\ll \log^ Ax\) and \
Indlekofer, Karl-Heinz, Kátai, Imre
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Let \({\mathcal B}\) denote the set of natural numbers which are a sum of two squares, and let \[ B_ 2(x,k,\ell)=| \{n\leq x: n, n+1\in {\mathcal B},\quad n\equiv \ell (mod k)\}| \quad. \] \textit{G. Bantle} [Math. Z. 189, 561-570 (1985; Zbl 0545.10029)] obtained an upper bound for \(B_ 2(x,k,\ell)-B_ 2(x-x^{\delta},k,\ell)\) for \(k\ll \log^ Ax\) and \
Indlekofer, Karl-Heinz, Kátai, Imre
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Fuzzy granulation of interval numbers
2011 Eighth International Conference on Fuzzy Systems and Knowledge Discovery (FSKD), 2011Investigation on fuzzy granulation method for interval numbers is of great importance. This paper aims to propose some methods of granulating interval numbers. Although there exit a few methods, some of them still have imperfections in granulating process or granulation results.
Mingxin Zhang, Keqiang Dong, Fusheng Yu
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The interval logarithmic number system
16th IEEE Symposium on Computer Arithmetic, 2003. Proceedings., 2004We introduce the interval logarithmic number system (ILNS), in which the logarithmic number system (LNS) is used as the underlying number system for interval arithmetic. The basic operations in ILNS are introduced and an efficient method for performing ILNS addition and subtraction is presented.
M.G. Arnold, J. Garcia, M.J. Schulte
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Goldbach numbers in short intervals
ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, 2022Elaborating on the works of \textit{G. Harman} [Prime-detecting sieves. Princeton, NJ: Princeton University Press (2007; Zbl 1220.11118), Chapter 10] and of \textit{K. Matomäki} et al. [Proc. Lond. Math. Soc. (3) 115, No. 2, 323--347 (2017; Zbl 1400.11132)], the author of this very well-written paper shows that almost every even integer in the interval
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Interval number and fuzzy number linear programmings
Fuzzy Sets and Systems, 1994Abstract In this paper, we focus on two kinds of linear programmings with fuzzy numbers. They are called interval number and fuzzy number linear programmings, respectively. The problems of linear programmings with interval number coefficients are approached by taking maximum value range and minimum value range inequalities as constraint conditions ...
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Intervals' Numbers (INs) interpolation/extrapolation
2013 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), 2013An Intervals' Number (IN) is a mathematical object known to represent either a probability distribution or a possibility distribution. The space of INs has been studied during the last years. After summarizing some instrumental mathematical results, this work demonstrates comparatively novel schemes for tunable fuzzy rule interpolation and ...
V. G. Kaburlasos +3 more
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Powered numbers in short intervals
Let \(\kappa(n) = \prod_{p \mid n} p\) be the squarefree kernel of \(n\). For given real \(\ell \ge 1\), a positive integer \(n\) is \(\ell\)-powered if \(\kappa(n) \le n^{1/\ell}\). In the paper under review, the author performs a conditional study of powered numbers over short intervals. For, he lets \(S_\theta(x)=\#\{n\leq x : \kappa(n)\leq n^\theta\openaire +2 more sources
1999
This paper gives an overview of single-number interval I/O which provides a convenient method for inputting and outputting intervals. With this technique, each interval is normally represented externally as a single decimal number. Single-number interval I/O has been implemented in interval-enhanced versions of GNU’s and Sun’s Fortran compilers, an ...
Michael Schulte +3 more
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This paper gives an overview of single-number interval I/O which provides a convenient method for inputting and outputting intervals. With this technique, each interval is normally represented externally as a single decimal number. Single-number interval I/O has been implemented in interval-enhanced versions of GNU’s and Sun’s Fortran compilers, an ...
Michael Schulte +3 more
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Preference for mixed-interval versus fixed-interval schedules: number of component intervals.
Journal of the experimental analysis of behavior, 2010Six pigeons were trained under a concurrent chains procedure so that preference for fixed-interval versus mixed-interval schedules with varying numbers of component intervals could be examined. The smallest and largest intervals in the terminal links were the same value as those used by Davison (1969).
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