APAV - Academy of Sciences, Letters, Arts and Technology (E-Journals)
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Bar and Theta Hyperoperations
Get PDFIn questionnaires the replacement of the scale of Likert by a bar was suggested in 2008 by Vougiouklis & Vougiouklis. The use of the bar was rapidly accepted in social sciences. The bar is closely related with fuzzy theory and has several advantages during both the filling-in questionnaires and mainly in the research processing. In this paper we relate hyperstructure theory with questionnaires and we study the obtained hyperstructures which are used as an organising device of the problem
History and new possible research directions of hyperstructures
Get PDFWe present a summary of the origins and current developments of the theory of algebraic hyperstructures. We also sketch some possible lines of research
Combination of survival probabilities of the components in a system. An application to long-term financial valuation
Get PDFThe Net Present Value (NPV) is a well-known method to value an investment project. Nevertheless, this methodology exhibits a serious problem when the used discounting function decreases very rapidly, especially in (very) long-term projects, because the future cash-flows are not significant in the expression of the NPV. For this reason, this paper introduces a methodology to correct the discounting function used for valuing. To do this, a new operation between discounting functions is defined by reducing the (cumulative) instantaneous discount rate corresponding of the valuing discounting function with another appropriate discounting function. The result is a new discounting function which can be more adequate to value this class of investment projects
On geometrical hyperstructures of finite order
Get PDFIt is known that a concrete representation of a finite k-dimensional Projective Geometry can be given by means of marks of a Galois Field GF [p^n], denoted by PG(k, p^n).In this geometry, we define hyperoperations, which create hyperstructures of finite order and we present results, propositions and examples on this topic. Additionally, we connect these hyperstructures to Join Spaces
THE TRANSPOSITION AXIOM IN HYPERCOMPOSITIONAL STRUCTURES
Get PDFThe hypergroup (as defined by F. Marty), being a very general algebraic structure, was subsequently quickly enriched with additional axioms. One of these is the transposition axiom, the utilization of which led to the creation of join spaces (join hypergroups) and of transposition hypergroups. These hypergroups have numerous applications in geometry, formal languages, thetheory of automata and graph theory. This paper deals with transposition hypergroups. It also introduces the transposition axiom to weaker structures, which result from the hypergroup by the removal of certain axioms, thus defining the transposition hypergroupoid, the transposition semi-hypergroup and the transposition quasi-hypergroup. Finally, it presents hypercompositional structures with internal or external compositions and hypercompositions, in which the transposition axiom is valid. Such structures emerged during the study of formal languages and the theory of automata through the use of hypercompositional algebra
Homomorphism and quotient of fuzzy k-hyperideals
Get PDFIn [15], we introduced the notion of weak (resp. strong) fuzzy k- hyperideal. In this note we investigate the behavior of them under homomorphisms of semihyperrings. Also we define the quotient of fuzzy weak (resp. strong) k-hyperideals by a regular relation of semihyperring and obtain some results
Blockwise Repeated Burst Error Correcting Linear Codes
Get PDFThis paper presents a lower and an upper bound on the number of parity check digits required for a linear code that corrects a single sub-block containing errors which are in the form of 2-repeated bursts of length b or less. An illustration of such kind of codes has been provided. Further, the codes that correct m-repeated bursts of length b or less have also been studied
Error Locating Codes Dealing with Repeated Low-Density Burst Errors
Get PDFThis paper presents a study of linear codes which are capable to detect and locate errors which are repeated low-density bursts of length b(fixed) with weight w or less. An illustration for such a kind of code has also been provided
Repeated Burst Error Detecting Linear Codes
Get PDFThis paper presents lower bounds on the number of parity-check digits required for a linear code that is capable of detecting errors which are ‘m-repeated burst errors’. Further, codes capable of detecting and simultaneously correcting such errors have also been studied
On 2-Repeated Burst Codes
Get PDFThere are several kinds of burst errors for which error detecting and error correcting codes have been constructed. In this paper, we consider a new kind of burst error which will be termed as ‘2-repeated burst error of length b(fixed)’. Linear codes capable of detecting such errors have been studied. Further, codes capable of detecting and simultaneously correcting such errors have also been dealt with. The paper obtains lower and upper bounds on the number of parity-check digits required for such codes. An example of such a code has also been provided