Questionnaires with the ‘bar’ in social sciences

Vougiouklis & Vougiouklis have proposed the replacement of Likert scales, usually used in questionnaires, with a bar. With this proposal a discrete situation is replaced by a fuzzy one. There are identified certain advantages concerning the use of the bar as compared to that of a scale during both the stages of filling-in as well as processing a questionnaire. The main advantage is the fact that it is much quicker to fill in and much easier to explain to participants. The bar provides the potential for different types of processing Likert scales cannot offer. Therefore the researchers are allowed to ascertain that the given answers follow the Gauss or a parabola distribution, and they have the opportunity to ‘correct’ this tendency. In this research it is offered a possibility of choosing amongst a number of alternatives by utilizing fuzzy logic in the same way as it has already been done in industry and combining mathematical models with multivalued operations. Finally, the suggested method is applied in a Course and Teaching Evaluation process by the students of Democritus University of Thrace

Helix-Hopes on Finite Hyperfields

Hyperstructure theory can overcome restrictions which ordinary algebraic structures have. A hyperproduct on non-square ordinary matrices can be defined by using the so called helix-hyperoperations. We study the helix-hyperstructures on the representations using ordinary fields. The related theory can be faced by defining the hyperproduct on the set of non square matrices. The main tools of the Hyperstructure Theory are the fundamental relations which connect the largest class of hyperstructures, the Hv-structures, with the corresponding classical ones. We focus on finite dimensional helix-hyperstructures and on small Hv-fields, as well.

Minimal Hv-Fields

Hyperstructures have applications in mathematics and in other sciences, which range from biology, hadronic physics, leptons, linguistics, sociology, to mention but a few. For this, the largest class of the hyperstructures, the Hv-structures, is used. They satisfy the weak axioms where the non-empty intersection replaces equality. The fundamental relations connect, by quotients, the Hv-structures with the classical ones. Hv-numbers are elements of Hv-field, and they are used in representation theory. We focus on minimal Hv-fields

Bar and Theta Hyperoperations

In 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

A HYPEROPERATION DEFINED ON A GROUPOID EQUIPPED WITH A MAP

The Hv-structures are hyperstructures where the equality is replaced by the non-empty intersection. The fact that this class of the hyperstructures is very large, one can use it in order to define several objects that they are not possible to be defined in the classical hypergroup theory. In the present paper we introduce a kind of hyperoperations which are defined on a set equipped with an operation or a hyperoperation and a map on itself

From Continuous to Discrete via V&V Bar

The ‘continuous’ and the ‘discrete’ in nature and in science live and fight forever. The questionnaires and the Lickert scales are indispensable and widely used tools in social sciences research. Vougiouklis & Vougiouklis bar is a new tool introduced as an alternative to Lickert scales. We believe that such an alternative might offer some solutions to problems that crop up during the fight between continuous and discrete. Nevertheless, the greatest contribution of the V&V bar is that it offers the researchers freedom in all stages of the research procedure using a questionnaire

Philosophical suggestions by the single elements

The largest class of hyperstructures is the one which satisfy the weak properties. These are called Hv-structures introduced in 1990 and they proved to have a lot of applications on several applied sciences. Special classes of elements appeared to have new interesting properties applicable in other sciences. We present some results on hyperstructures containing ‘single’ elements, and some new constructions.Keywords: hyperstructures; Hv-structures; single elements

Finite H_v-Fields with Strong-Inverses

The largest class of hyperstructures is the class of H v -structures. This is the class of hyperstructures where the equality is replaced by the non-empty intersection. This extremely large class can used to define several objects that they are not possible to be defined in the classical hypergroup theory. It is convenient, in applications, to use more axioms and conditions to restrict the research in smaller classes. In this direction, in the present paper we continue our study on H v -structures which have strong-inverse elements. More precisely we study the small finite cases

The Lie-Santilli admissible hyperalgebras of type An

The largest class of hyperstructures is the one which satisfy the weak properties. These are called H v -structures introduced in 1990 and they proved to have a lot of applications on several applied sciences. In this paper we present a construction of the hyperstructures used in the Lie-Santilli admissible theory on square matrices

Hv-semigroups as noise pollution models in urban areas

Poor urban planning may give rise to noise pollution, since side by side industrial and residential buildings can result in noise pollution in the residential area. In this paper we represent the noise pollution with an Hv-semigroup. More specic, we introduce the concept of right reproductive Hv-semigroup which seems to be a useful tool to study the noise pollution problem in urban areas