Conjoint Analysis (CA) is a very popular class of methods for measuring consumer preferences, bot... more Conjoint Analysis (CA) is a very popular class of methods for measuring consumer preferences, both in research and practice. However, since a couple of years, the Analytic Hierarchy Process (AHP) is being discussed in this field as well. Several empirical studies have shown the general potential of AHP, particularly in complex product evaluation tasks consisting of many attributes. But, in spite of its promising results, marketing practice seems to ignore AHP so far. This is somewhat astonishing if one considers the closeness of both approaches. Already almost thirty years ago Wind and Saaty (1980, p. 657) stated: "In some cases both the AHP and Conjoint Analysis can be used, and it is desirable to compare the results of the two approaches …". This paper contributes to fill this gap. In order to increase the practical relevance of such a comparison for marketing practitioners, we run AHP against the commercially successful Choice-Based Conjoint Analysis (CBC) in an online survey. We outline how both the hierarchy and the scale used in AHP can be adapted to preference measurement and how Harker's (1987) technique for incomplete pairwise comparison matrices can be applied in a beneficial way. Our results indicate that, indeed, both methods are equivalent with regard to convergent validity and the individual prediction of holdout tasks, but AHP significantly outperforms CBC in market share predictions.
Colombian higher education institutions have an interest in obtaining recognized high quality sta... more Colombian higher education institutions have an interest in obtaining recognized high quality standards. This recognition is obtained by an accreditation granted by the Colombian Government. The Consejo Nacional de Acreditación (CNA) is the academic body responsible for coordinating such process. This paper is based on the re-accreditation process of the industrial engineering undergraduate program at the Universidad de los Andes in Bogotá. The paper focuses on the process for weighing the components (factors) and criteria (characteristics) established by the CNA. For this process, the Industrial Engineering Department organized a workshop where academics deliberated about the weights they had to assign to each component and criteria. Due to the fact that many of the criteria are related to each other, we proposed to use the ANP for establishing the weights. The ANP model we built was complex because the network was dense and also because it was necessary to consider a high number of criteria for its construction. The results obtained were significantly different from those obtained at the workshop. The ANP model results indicate that the source components of the network had the higher weights, whereas the sink components had the lowest weights. In the source components the proportion of criteria within the component that influences on other criteria is greater than the influences they receive; the same argument works for the sink components. The construction of the ANP model was essential because the weights obtained were used to make the self-assessment of the program.
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.
The new challenges for European cities are competitiveness, social inclusion, sustainability, mul... more The new challenges for European cities are competitiveness, social inclusion, sustainability, multilevel governance, smartness. In order to overcome these challenges, the environmental education which is based on knowledge of past experiences is an essential tool to present and prevent future environmental problems, outlining strategies to choose among various alternative s for the organization of the city. Significant experiences of Strategic Planning for a middle-long term regeneration of cities have been implemented in some European areas in achieving the EU sustainability goals. In this paper the outcomes of the first studies for a Strategic Plan in Pescara are presented and some questions are taken into consideration. The recent processes of urban regeneration taking place in the city show the importance to examine closely the urban landscape in order to enhance the loca l natural resources and to implement projects which could affect the overall urban structure, reconnecting parts of the city remained incomplete or disjoined. We also highlight the need for a strengthening of transparency and communication of public choices to the community. In particular we outline the question of the port areas regeneration in Pescara; we formulate a decision making model for the functional re-use of these areas which have a particular environmental value and which are considered as 2012 Published by Elsevier Ltd.
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.
New results on remotality in Banach spaces M. Sababheh, R. Khalil pp. 59-66 The hyperbolic Menela... more New results on remotality in Banach spaces M. Sababheh, R. Khalil pp. 59-66 The hyperbolic Menelaus theorem in the Poincaré disc model of hyperbolic geometry Florentin Smarandache, Cătălin Barbu pp. 67-72 On the finite groups with average length 3 of conjugacy classes Xianglin Du pp. 73-78 On (λ,μ)-fuzzy subhyperlattices Yuming Feng, Qingsong Zeng, Huiling Duan pp. 79-86 Blockwise repeated low-density burst error correcting linear codes Dass Bal Kishan, Madan Surbhi pp. 87-100 Multidimensional generating relations suggested by a generating relation for hyper-bessel functions M.A. Pathan And M.G. Bin-Saad pp. 101-108 Rarely b-continuous functions Saeid Jafari, Ugur Sengul pp. 109-116 A study on augmented graded rings Mashhoor Refai pp. 117-124 Weak lattices Ivan Chajda, Helmut Länger pp. 125-140 Characterization of hyper BCI-algebra of order 3 R. Ameri, A. Radfar, A. Borzooei pp.
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.
in 1970. In 1973, he was elected Professor, Chair of Advanced Mathematics, Faculty of Engineering... more in 1970. In 1973, he was elected Professor, Chair of Advanced Mathematics, Faculty of Engineering Aristotle University of Thessaloniki, where he served till his retirement in 1985, occupying important posts including that of the Dean of the Faculty; straight after his retirement he was awarded the title of Professor Emeritus. He was a member of a numerous societies and member of the editorial committee of several journals. He was awarded The National Resistance 1941-1944 Medal for his participation in the resistance during the German Occupation of Greece. Professors Mittas's contribution to hyperstructure theory was pioneering as he published numerous papers in several journals and proceedings among which his most famous paper Hypergroupes canoniques, Math. Balkanica, V.2, (1972). He continued working and publishing results and research papers and his ex PhD students and co-researchers go on publishing results
Measuring strength or degree of statistical dependence between two random variables is a common p... more Measuring strength or degree of statistical dependence between two random variables is a common problem in many domains. Pearson's correlation coefficient ρ is an accurate measure of linear dependence. We show that ρ is a normalized, Euclidean type distance between joint probability distribution of the two random variables and that when their independence is assumed while keeping their marginal distributions. And the normalizing constant is the geometric mean of two maximal distances; each between the joint probability distribution when the full linear dependence is assumed while preserving respective marginal distribution and that when the independence is assumed. Usage of it is restricted to linear dependence because it is based on Euclidean type distances that are generally not metrics and considered full dependence is linear. Therefore, we argue that if a suitable distance metric is used while considering all possible maximal dependences then it can measure any non-linear dependence. But then, one must define all the full dependences. Hellinger distance that is a metric can be used as the distance measure between probability distributions and obtain a generalization of ρ for the discrete case.
Steady three-dimensional hydromagnetic stagnation point flow towards a stretching sheet with heat... more Steady three-dimensional hydromagnetic stagnation point flow towards a stretching sheet with heat generation Hazem Ali Attia pp. 9-18 Tranzient MHD Couette flow of a Casson fluid between parallel plates with heat transfer Hazem Ali Attia, Mohamed Eissa Sayed-Ahmed pp. 19-38 Two-dimensional wavelets for nonlinear autoregressive models with an application in dynamical system H. Doosti, M.S. Islam, Y.P. Chaubey, P. Góra pp. 39-62 On periodic solutions for nested polygon planar 2N+1-body problems with arbitrary masses Liu Xuefei, Zhang Shiqing, Luo Jianmei pp. 63-80 On generalized pre-closure spaces and separation for some special types of functions Miguel Caldas, Erdal Ekici, Saeid Jafari pp. 81-90 Certain subclasses of analytic functions involving Sălăgean operator J.K. Prajapat, R.K. Raina pp. 91-98 Fuyyz stability of quartic mappings Alireza Kamel Mirmostafaee pp. 99-106 Some results on non-commuting graph of a finite group M.R. Darafsheh, H. Bigdely, A. Bahrami, M. Davoudi Monfared pp. 107-118 Hyper K-algebras induced by a deterministic finite automaton M. Golmohamadian, M.M. Zahedi pp. 119-140 Common fixed point for Lipschitzian mappings satisfying rational contractive conditions Mujahid Abbas pp. 141-146 Fuzzy minimal structures and fuzzy minimal subspaces Mohammad Javad Nematollahi, Mehdi Roohi pp. 147-156 Interval-valued intuiotionistic fuzzy subsemimodules with (S,T)-norms H. Hedayati pp. 157-166 α-Generalized-convergence theory of L-fuzzy nets and its applications Bin Chen pp. 167-178 Certain transformation and summation formulae for q-series Remy Y. Denis, S.N. Singh, S.P. Singh pp. 179-190 A note on continues fractions and 3 ψ 3 series Maheshwar Pathak, Pankaj Srivastava pp. 191-200 A connection between categories of (fuzzy) multialgebras and (fuzzy) algebras R. Ameri, T. Nozari pp. 201-208 Lipschitz estimates for multilinear commutator of Littlewood-Paley operator Ying Shen, Lanzhe Liu pp. 209-224 A functional associated with bounded linear operators in Hilbert spaces and related inequalities S.S. Dragomir pp. 225-240 Generalization of Golbach's conjecture and some special cases Ioannis Mittas pp. 241-254 Strong colourings of hypergraphs Sandro Rajola, Maria Scafati Tallini pp. 255-272 p-Fuzzy hypergroups and p-fuzzy join spaces obtained from p-fuzzy hypergraphs Yuming Feng pp. 273-280 Fuzzy Lie ideals over a fuzzy field M. Akram, K.P. Shum pp. 281-292 On a finer topological space than τ θ and some maps E. Ekici, S. Jafari, R.M. Latif pp. 293-304 Homomorphisms and epimorphisms of some hypergroups W. Phanthawimol, Y. Kemprasit pp. 305-312 On homomorphisms of some multiplicative hyperring M. Kaewneam, Y. Kemprasit pp. 313-320 Upper topological generalized groups F.H. Ghane, Z. Hamed pp. 321-332 Analysis of a two-step method for numerical solution of fuzzy ordinary differential equations M. Sh. Dahaghin, M. Mohseni Moghadam pp. 333-340
Conjoint Analysis (CA) is a very popular class of methods for measuring consumer preferences, bot... more Conjoint Analysis (CA) is a very popular class of methods for measuring consumer preferences, both in research and practice. However, since a couple of years, the Analytic Hierarchy Process (AHP) is being discussed in this field as well. Several empirical studies have shown the general potential of AHP, particularly in complex product evaluation tasks consisting of many attributes. But, in spite of its promising results, marketing practice seems to ignore AHP so far. This is somewhat astonishing if one considers the closeness of both approaches. Already almost thirty years ago Wind and Saaty (1980, p. 657) stated: "In some cases both the AHP and Conjoint Analysis can be used, and it is desirable to compare the results of the two approaches …". This paper contributes to fill this gap. In order to increase the practical relevance of such a comparison for marketing practitioners, we run AHP against the commercially successful Choice-Based Conjoint Analysis (CBC) in an online survey. We outline how both the hierarchy and the scale used in AHP can be adapted to preference measurement and how Harker's (1987) technique for incomplete pairwise comparison matrices can be applied in a beneficial way. Our results indicate that, indeed, both methods are equivalent with regard to convergent validity and the individual prediction of holdout tasks, but AHP significantly outperforms CBC in market share predictions.
Colombian higher education institutions have an interest in obtaining recognized high quality sta... more Colombian higher education institutions have an interest in obtaining recognized high quality standards. This recognition is obtained by an accreditation granted by the Colombian Government. The Consejo Nacional de Acreditación (CNA) is the academic body responsible for coordinating such process. This paper is based on the re-accreditation process of the industrial engineering undergraduate program at the Universidad de los Andes in Bogotá. The paper focuses on the process for weighing the components (factors) and criteria (characteristics) established by the CNA. For this process, the Industrial Engineering Department organized a workshop where academics deliberated about the weights they had to assign to each component and criteria. Due to the fact that many of the criteria are related to each other, we proposed to use the ANP for establishing the weights. The ANP model we built was complex because the network was dense and also because it was necessary to consider a high number of criteria for its construction. The results obtained were significantly different from those obtained at the workshop. The ANP model results indicate that the source components of the network had the higher weights, whereas the sink components had the lowest weights. In the source components the proportion of criteria within the component that influences on other criteria is greater than the influences they receive; the same argument works for the sink components. The construction of the ANP model was essential because the weights obtained were used to make the self-assessment of the program.
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.
The new challenges for European cities are competitiveness, social inclusion, sustainability, mul... more The new challenges for European cities are competitiveness, social inclusion, sustainability, multilevel governance, smartness. In order to overcome these challenges, the environmental education which is based on knowledge of past experiences is an essential tool to present and prevent future environmental problems, outlining strategies to choose among various alternative s for the organization of the city. Significant experiences of Strategic Planning for a middle-long term regeneration of cities have been implemented in some European areas in achieving the EU sustainability goals. In this paper the outcomes of the first studies for a Strategic Plan in Pescara are presented and some questions are taken into consideration. The recent processes of urban regeneration taking place in the city show the importance to examine closely the urban landscape in order to enhance the loca l natural resources and to implement projects which could affect the overall urban structure, reconnecting parts of the city remained incomplete or disjoined. We also highlight the need for a strengthening of transparency and communication of public choices to the community. In particular we outline the question of the port areas regeneration in Pescara; we formulate a decision making model for the functional re-use of these areas which have a particular environmental value and which are considered as 2012 Published by Elsevier Ltd.
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.
New results on remotality in Banach spaces M. Sababheh, R. Khalil pp. 59-66 The hyperbolic Menela... more New results on remotality in Banach spaces M. Sababheh, R. Khalil pp. 59-66 The hyperbolic Menelaus theorem in the Poincaré disc model of hyperbolic geometry Florentin Smarandache, Cătălin Barbu pp. 67-72 On the finite groups with average length 3 of conjugacy classes Xianglin Du pp. 73-78 On (λ,μ)-fuzzy subhyperlattices Yuming Feng, Qingsong Zeng, Huiling Duan pp. 79-86 Blockwise repeated low-density burst error correcting linear codes Dass Bal Kishan, Madan Surbhi pp. 87-100 Multidimensional generating relations suggested by a generating relation for hyper-bessel functions M.A. Pathan And M.G. Bin-Saad pp. 101-108 Rarely b-continuous functions Saeid Jafari, Ugur Sengul pp. 109-116 A study on augmented graded rings Mashhoor Refai pp. 117-124 Weak lattices Ivan Chajda, Helmut Länger pp. 125-140 Characterization of hyper BCI-algebra of order 3 R. Ameri, A. Radfar, A. Borzooei pp.
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.
in 1970. In 1973, he was elected Professor, Chair of Advanced Mathematics, Faculty of Engineering... more in 1970. In 1973, he was elected Professor, Chair of Advanced Mathematics, Faculty of Engineering Aristotle University of Thessaloniki, where he served till his retirement in 1985, occupying important posts including that of the Dean of the Faculty; straight after his retirement he was awarded the title of Professor Emeritus. He was a member of a numerous societies and member of the editorial committee of several journals. He was awarded The National Resistance 1941-1944 Medal for his participation in the resistance during the German Occupation of Greece. Professors Mittas's contribution to hyperstructure theory was pioneering as he published numerous papers in several journals and proceedings among which his most famous paper Hypergroupes canoniques, Math. Balkanica, V.2, (1972). He continued working and publishing results and research papers and his ex PhD students and co-researchers go on publishing results
Measuring strength or degree of statistical dependence between two random variables is a common p... more Measuring strength or degree of statistical dependence between two random variables is a common problem in many domains. Pearson's correlation coefficient ρ is an accurate measure of linear dependence. We show that ρ is a normalized, Euclidean type distance between joint probability distribution of the two random variables and that when their independence is assumed while keeping their marginal distributions. And the normalizing constant is the geometric mean of two maximal distances; each between the joint probability distribution when the full linear dependence is assumed while preserving respective marginal distribution and that when the independence is assumed. Usage of it is restricted to linear dependence because it is based on Euclidean type distances that are generally not metrics and considered full dependence is linear. Therefore, we argue that if a suitable distance metric is used while considering all possible maximal dependences then it can measure any non-linear dependence. But then, one must define all the full dependences. Hellinger distance that is a metric can be used as the distance measure between probability distributions and obtain a generalization of ρ for the discrete case.
Steady three-dimensional hydromagnetic stagnation point flow towards a stretching sheet with heat... more Steady three-dimensional hydromagnetic stagnation point flow towards a stretching sheet with heat generation Hazem Ali Attia pp. 9-18 Tranzient MHD Couette flow of a Casson fluid between parallel plates with heat transfer Hazem Ali Attia, Mohamed Eissa Sayed-Ahmed pp. 19-38 Two-dimensional wavelets for nonlinear autoregressive models with an application in dynamical system H. Doosti, M.S. Islam, Y.P. Chaubey, P. Góra pp. 39-62 On periodic solutions for nested polygon planar 2N+1-body problems with arbitrary masses Liu Xuefei, Zhang Shiqing, Luo Jianmei pp. 63-80 On generalized pre-closure spaces and separation for some special types of functions Miguel Caldas, Erdal Ekici, Saeid Jafari pp. 81-90 Certain subclasses of analytic functions involving Sălăgean operator J.K. Prajapat, R.K. Raina pp. 91-98 Fuyyz stability of quartic mappings Alireza Kamel Mirmostafaee pp. 99-106 Some results on non-commuting graph of a finite group M.R. Darafsheh, H. Bigdely, A. Bahrami, M. Davoudi Monfared pp. 107-118 Hyper K-algebras induced by a deterministic finite automaton M. Golmohamadian, M.M. Zahedi pp. 119-140 Common fixed point for Lipschitzian mappings satisfying rational contractive conditions Mujahid Abbas pp. 141-146 Fuzzy minimal structures and fuzzy minimal subspaces Mohammad Javad Nematollahi, Mehdi Roohi pp. 147-156 Interval-valued intuiotionistic fuzzy subsemimodules with (S,T)-norms H. Hedayati pp. 157-166 α-Generalized-convergence theory of L-fuzzy nets and its applications Bin Chen pp. 167-178 Certain transformation and summation formulae for q-series Remy Y. Denis, S.N. Singh, S.P. Singh pp. 179-190 A note on continues fractions and 3 ψ 3 series Maheshwar Pathak, Pankaj Srivastava pp. 191-200 A connection between categories of (fuzzy) multialgebras and (fuzzy) algebras R. Ameri, T. Nozari pp. 201-208 Lipschitz estimates for multilinear commutator of Littlewood-Paley operator Ying Shen, Lanzhe Liu pp. 209-224 A functional associated with bounded linear operators in Hilbert spaces and related inequalities S.S. Dragomir pp. 225-240 Generalization of Golbach's conjecture and some special cases Ioannis Mittas pp. 241-254 Strong colourings of hypergraphs Sandro Rajola, Maria Scafati Tallini pp. 255-272 p-Fuzzy hypergroups and p-fuzzy join spaces obtained from p-fuzzy hypergraphs Yuming Feng pp. 273-280 Fuzzy Lie ideals over a fuzzy field M. Akram, K.P. Shum pp. 281-292 On a finer topological space than τ θ and some maps E. Ekici, S. Jafari, R.M. Latif pp. 293-304 Homomorphisms and epimorphisms of some hypergroups W. Phanthawimol, Y. Kemprasit pp. 305-312 On homomorphisms of some multiplicative hyperring M. Kaewneam, Y. Kemprasit pp. 313-320 Upper topological generalized groups F.H. Ghane, Z. Hamed pp. 321-332 Analysis of a two-step method for numerical solution of fuzzy ordinary differential equations M. Sh. Dahaghin, M. Mohseni Moghadam pp. 333-340
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