Some important concepts about algebraic hyperstructures, especially from a geometric point of vie... more Some important concepts about algebraic hyperstructures, especially from a geometric point of view, are recalled. Many applications of the Hv structures, introduced by Vougiouklis in 1990, to the de Finetti subjective probability theory are considered. We show how the wealth of probabilistic meanings of Hv-structures confirms the importance of the theoretical results obtained by Vougiouklis. Such results can be very meaningful also in many application fields, such as decision theory, highly dependent on subjective probability.
In this paper we have considered a mathematical model to appraise the real feasibility of the las... more In this paper we have considered a mathematical model to appraise the real feasibility of the last type of urban project. In particular we have tried to find some previsions about the effects produced by that kind of project in the urban contest. This model is founded on: -some categories of feasibility; these classes represent the various aspects of social welfare pursued by an urban project; -some weighed objects that represent the different needs of the community whom the project is intended to; -a verification about the attainment of aforesaid objects by the tested project. We have noticed that the statement of this model has common something with the theory of fuzzy sets.
The applications of fuzzy numbers to Social Sciences, Economy, and Natural Sciences request, in v... more The applications of fuzzy numbers to Social Sciences, Economy, and Natural Sciences request, in various cases that the spreads, i.e. the region of indeterminateness, of the results of the operations between fuzzy numbers be less than the ones expected by the Zadeh’s extension principle. Moreover, it appears to be necessary to consider operations that save the shapes of fuzzy numbers. To this aim fuzzy operations are dealt with, alternatives to the operations induced by the extension principle. Critical analyses of logical principles which support the various operations are carried out. Some application to Social Sciences and Economy are considered
Ranking alternatives is a central issue in multi-criteria and multi-person decision making. Each ... more Ranking alternatives is a central issue in multi-criteria and multi-person decision making. Each member of a committee of experts has his own knowledge-base and a current information in order to make decisions. We assume the committee adopt the AHP as the tool that each expert uses to construct the personal ranking of alternatives. As described and formalized in (Carlsson et al., 1992; Eklund et al., 2007; Maturo, and Ventre, 2008) each decision maker is represented by a point of the Euclidean space R m, where the coordinates are the scores of the alternatives. Enhancing consensus in the group reduces to implementing a procedure that makes these points closer, so that they can be included in a suitably small neighborhood. In order to obtain consensus the more peripheral decision makers are invited by an impartial chairman, called the Demiurge, to modify their assessments. What seems to us worth to be considered is a further convergence procedure related to the weights of the criteri...
Often in a group of decision makers there is a considerable variability in the scores that decisi... more Often in a group of decision makers there is a considerable variability in the scores that decision makers assign to the alternatives. In this paper we represent this variability with fuzzy numbers. Moreover we present an algorithm for the achievement of consensus based on suitable fuzzy numbers, on preorder and order relations in sets of fuzzy numbers, and on a procedure to decrease the spreads.
In Social Sciences propositions and descriptions of interpersonal relationships are given by mean... more In Social Sciences propositions and descriptions of interpersonal relationships are given by means of linguistic expressions, which cannot be formalized with the classic binary logic. Then a necessary tool are fuzzy sets that give the possibility to measure the degree of belonging of an element to a set described by a linguistic property or the degree of a relation between individuals. Moreover many times there is uncertainty on the result of an aggregation operation and we can have the necessity to consider together many possible results of the interaction of any ordered pair of elements, e.g. individuals. We propose the algebraic hyperoperations as very useful instruments to manage these types of uncertainty. We show as fuzzy relations and hypergroupoids permit to have an efficient representations of many aspects of social phenomena.
Sunto Uno strumento efficace per comprendere realmente la geometria euclidea è lo studio di model... more Sunto Uno strumento efficace per comprendere realmente la geometria euclidea è lo studio di modelli alternativi e delle loro applicazioni. Infatti essi permettono di capire la reale portata di vari assiomi che visti dall'interno della geometria euclidea sembrerebbero scontati o addirittura inutili. Il lavoro parte da una rivisitazione dell'assiomatica di Hilbert a partire dal punto di vista più generale adottato da Albrecht Beutelspacher e Ute Rosenbaum nel loro libro del 1998 sui fondamenti della geometria proiettiva generale, definita attraverso un sistema di assiomi di incidenza. Parole chiave: Critica dei fondamenti. Geometrie finite. Assiomi di Hilbert. Applicazioni.
In this paper we consider some definitions and results about fuzzy operations and fuzzy relations... more In this paper we consider some definitions and results about fuzzy operations and fuzzy relations. In particular we consider the similitude relations and the fuzzy partition. We show some applications of these concepts to some problems of Social Sciences and Town-Planning.
The work starts from an analysis of the critical problems of the prison system in Italy. It aims ... more The work starts from an analysis of the critical problems of the prison system in Italy. It aims to develop a decision-making model to address the issue of sustainable protection of human rights in prisons. It shows how, using the Saaty AHP procedure, it is possible to have an analytical reasoning guideline for the understanding of the validity of the various alternative choices, in order to facilitate the situation of the prisoners and their reintegration into society.
Some important concepts about algebraic hyperstructures, especially from a geometric point of vie... more Some important concepts about algebraic hyperstructures, especially from a geometric point of view, are recalled. Many applications of the Hv structures, introduced by Vougiouklis in 1990, to the de Finetti subjective probability theory are considered. We show how the wealth of probabilistic meanings of Hv-structures confirms the importance of the theoretical results obtained by Vougiouklis. Such results can be very meaningful also in many application fields, such as decision theory, highly dependent on subjective probability.
In this paper we have considered a mathematical model to appraise the real feasibility of the las... more In this paper we have considered a mathematical model to appraise the real feasibility of the last type of urban project. In particular we have tried to find some previsions about the effects produced by that kind of project in the urban contest. This model is founded on: -some categories of feasibility; these classes represent the various aspects of social welfare pursued by an urban project; -some weighed objects that represent the different needs of the community whom the project is intended to; -a verification about the attainment of aforesaid objects by the tested project. We have noticed that the statement of this model has common something with the theory of fuzzy sets.
The applications of fuzzy numbers to Social Sciences, Economy, and Natural Sciences request, in v... more The applications of fuzzy numbers to Social Sciences, Economy, and Natural Sciences request, in various cases that the spreads, i.e. the region of indeterminateness, of the results of the operations between fuzzy numbers be less than the ones expected by the Zadeh’s extension principle. Moreover, it appears to be necessary to consider operations that save the shapes of fuzzy numbers. To this aim fuzzy operations are dealt with, alternatives to the operations induced by the extension principle. Critical analyses of logical principles which support the various operations are carried out. Some application to Social Sciences and Economy are considered
Ranking alternatives is a central issue in multi-criteria and multi-person decision making. Each ... more Ranking alternatives is a central issue in multi-criteria and multi-person decision making. Each member of a committee of experts has his own knowledge-base and a current information in order to make decisions. We assume the committee adopt the AHP as the tool that each expert uses to construct the personal ranking of alternatives. As described and formalized in (Carlsson et al., 1992; Eklund et al., 2007; Maturo, and Ventre, 2008) each decision maker is represented by a point of the Euclidean space R m, where the coordinates are the scores of the alternatives. Enhancing consensus in the group reduces to implementing a procedure that makes these points closer, so that they can be included in a suitably small neighborhood. In order to obtain consensus the more peripheral decision makers are invited by an impartial chairman, called the Demiurge, to modify their assessments. What seems to us worth to be considered is a further convergence procedure related to the weights of the criteri...
Often in a group of decision makers there is a considerable variability in the scores that decisi... more Often in a group of decision makers there is a considerable variability in the scores that decision makers assign to the alternatives. In this paper we represent this variability with fuzzy numbers. Moreover we present an algorithm for the achievement of consensus based on suitable fuzzy numbers, on preorder and order relations in sets of fuzzy numbers, and on a procedure to decrease the spreads.
In Social Sciences propositions and descriptions of interpersonal relationships are given by mean... more In Social Sciences propositions and descriptions of interpersonal relationships are given by means of linguistic expressions, which cannot be formalized with the classic binary logic. Then a necessary tool are fuzzy sets that give the possibility to measure the degree of belonging of an element to a set described by a linguistic property or the degree of a relation between individuals. Moreover many times there is uncertainty on the result of an aggregation operation and we can have the necessity to consider together many possible results of the interaction of any ordered pair of elements, e.g. individuals. We propose the algebraic hyperoperations as very useful instruments to manage these types of uncertainty. We show as fuzzy relations and hypergroupoids permit to have an efficient representations of many aspects of social phenomena.
Sunto Uno strumento efficace per comprendere realmente la geometria euclidea è lo studio di model... more Sunto Uno strumento efficace per comprendere realmente la geometria euclidea è lo studio di modelli alternativi e delle loro applicazioni. Infatti essi permettono di capire la reale portata di vari assiomi che visti dall'interno della geometria euclidea sembrerebbero scontati o addirittura inutili. Il lavoro parte da una rivisitazione dell'assiomatica di Hilbert a partire dal punto di vista più generale adottato da Albrecht Beutelspacher e Ute Rosenbaum nel loro libro del 1998 sui fondamenti della geometria proiettiva generale, definita attraverso un sistema di assiomi di incidenza. Parole chiave: Critica dei fondamenti. Geometrie finite. Assiomi di Hilbert. Applicazioni.
In this paper we consider some definitions and results about fuzzy operations and fuzzy relations... more In this paper we consider some definitions and results about fuzzy operations and fuzzy relations. In particular we consider the similitude relations and the fuzzy partition. We show some applications of these concepts to some problems of Social Sciences and Town-Planning.
The work starts from an analysis of the critical problems of the prison system in Italy. It aims ... more The work starts from an analysis of the critical problems of the prison system in Italy. It aims to develop a decision-making model to address the issue of sustainable protection of human rights in prisons. It shows how, using the Saaty AHP procedure, it is possible to have an analytical reasoning guideline for the understanding of the validity of the various alternative choices, in order to facilitate the situation of the prisoners and their reintegration into society.
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Papers by Antonio Maturo