Datatypes for Real Numbers in Type Theory Mart́ın Hötzel Escardó and Alex Simpson 1 School of Computer Science, University of Birmingham 2 LFCS, School of Informatics, University of Edinburgh Abstract. We propose an abstract datatype for a closed interval of real numbers to type theory, providing a representation-independent approach to programming with real numbers. The abstract datatype requir...

A manufacturing inventory model with shortages with carrying cost, shortage cost, setup cost and demand quantity as imprecise numbers, instead of real numbers, namely interval number is considered here. First, a brief survey of the existing works on comparing and ranking any two interval numbers on the real line is presented. A common algorithm for the optimum production quantity (Economic lot-...

Interval-valued intuitionistic fuzzy number uses membership degree and non-member ship degree to express a decision-maker’s hesitation, which make decision-maker express his/her opinion in uncertainty decision-making environment easily. The comparison between some intervalvalued intuitionistic fuzzy numbers can not be undertaken because of its limitation. In application such as weak consistency...

Noninvertible circle maps may have a rotation interval instead of a unique rotation number. One may ask which of the numbers or sets of numbers within this rotation interval may be observed with positive probability in term of Lebesgue measure on the circle. We study this question numerically for families of circle maps. Both the interval and “observed” rotation numbers are computed for large n...

An interval vector is a (0, 1)-vector in Rn for which all the 1’s appear consecutively, and an interval-vector polytope is the convex hull of a set of interval vectors in Rn. We study three particular classes of interval vector polytopes which exhibit interesting geometric-combinatorial structures; e.g., one class has volumes equal to the Catalan numbers, whereas another class has face numbers ...

* Correspondence author. Abstract The fuzzy multi-attribute decision making problems are investigated, in which the attribute values are given as intervalvalued intuitionistic fuzzy numbers and the attribute weight information is incomplete. Some operational laws of interval-valued intuitionistic fuzzy numbers, score function and accuracy function of interval-valued intuitionistic fuzzy numbers...

Capital cost, resale value and running cost including maintenance costs, repairing costs, and operation costs of equipment are considered as crisp numbers in ordinary replacement problem. Nevertheless, in a special situation such as operating military equipments during wartime, the working efficiency of the machine and its related costs are no longer crisp but uncertain. This uncertainty can be...

The purpose of this paper is to determine when and under which conditions the solution game value infinite interval matrix games will exist. Firstly, concept a reasonable defined in was extended games. Then, were characterized by using sequences numbers (defined Chiao, 2002) their convergence numbers. Considering that each row or column payoff sequence numbers, we assume converges same number α...

Abstract A new family of p -Bernoulli numbers and polynomials was introduced by Rahmani (J. Number Theory 157:350–366, 2015) with the help Gauss hypergeometric function. Motivated that paper in light recent interests finding degenerate versions, we construct generalized Bernoulli means In addition, type Eulerian as a version numbers. For numbers, express them terms Stirling second kind, -Stirli...