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J C R Alcantud

University of Salamanca, Economía e Historia Económica, Faculty Member

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José Carlos R. Alcantud, Professor, received his M.Sc. in Mathematics in 1991 from the University of Valencia, Spain, and his Ph.D. in Mathematics in 1996 from the University of Santiago de Compostela, Spain. Since 2010 he is a Professor of Economic Analysis in the Department of Economics and Economic History at the University of Salamanca, Spain. He acts as Head of the Department of Economics and Economic History at the University of Salamanca, Spain, since 2012. Professor Alcantud is a founding member of the Multidisciplinary Institute of Enterprise of the University of Salamanca. He has published well over 50 papers in mathematical economics and mathematics. His current research interests include soft computing models, decision making and its applications, and social choice.
Address: Salamanca, Castilla y Leon, Spain

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Papers by J C R Alcantud

Uniform spaces based on a way below relation

Computational and Applied Mathematics

A Social Choice Approach to Graded Soft Sets: slides for FUZZ-IEEE 2017

A New Criterion for Soft Set Based Decision Making Problems under Incomplete Information

International Journal of Computational Intelligence Systems, 2017

We put forward a completely redesigned approach to soft set based decision making problems under ... more We put forward a completely redesigned approach to soft set based decision making problems under incomplete information. An algorithmic solution is proposed and compared with previous approaches in the literature. The computational performance of our algorithm is critically analyzed by an experimental study.

The relationship between Mathematical Utility Theory and the Integrability Problem: some arguments in favour

The resort to utility-theoretical issues will permit us to propose a constructive proce-dure for ... more The resort to utility-theoretical issues will permit us to propose a constructive proce-dure for deriving a homogeneous of degree one, continuous function that gives raise to a primitive demand function under suitably mild conditions. This constitutes the first elementary proof of a necessary and sufficient condition for an integrability problem to have a solution by continuous (subjective utility) functions. Such achievement reinforces the relevance of a technique that was succesfully formalized in Alcantud and Rodŕıguez-Palmero [3]. The analysis of these two works exposes deep relationships between two apparently separate fields: mathematical utility theory and the revealed preference approach to the integrability problem. JEL classification: D11

Topological Properties of Spaces Ordered by Preferences

In this paper, we analyze the main topological properties of a relevant class of topologies assoc... more In this paper, we analyze the main topological properties of a relevant class of topologies associated with spaces ordered by preferences (asymmetric, negatively transi-tive binary relations). This class consists of certain continuous topologies which include the order topology. The concept of saturated identification is introduced in order to provide a natural proof of the fact that all these spaces possess topological properties analogous to those of linearly ordered topological spaces, inter alia monotone and hereditary normality, and complete regularity.

New correlation coefficients for hesitant fuzzy sets

The previous correlation measures for hesitant fuzzy sets proposed in the literature only capture... more The previous correlation measures for hesitant fuzzy sets proposed in the literature only capture the strength of the correlations. We present a new approach based on the classical Pearson correlation coefficient for crisp values. In this way we can ex-press not only the strength of the relationship be-tween two hesitant fuzzy sets, but also whether they are positively or negatively associated.

CHoice-Nash-equilibria

We provide existence results for equilibria of games where players employ abstract (non-binary) c... more We provide existence results for equilibria of games where players employ abstract (non-binary) choice rules. Such results are shown to encompass as a relevant instance that of games where players have (nontransitive) SSB (Skew-Symmetric Bilinear) preferences, as well as other well-known transitive (e.g. Nash’s) and non-transitive (e.g. Shafer and Sonnenschein’s) models in the literature. Further, our general model contains games where players display procedural rationality.

Conditional extensions of fuzzy preorders

Fuzzy Sets and Systems

The problem of embedding incomplete into complete rela- tions has been an important topic of rese... more The problem of embedding incomplete into complete rela- tions has been an important topic of research in the context of crisp relations and their applications. Several variations of the acclaimed Szpilrajn’s theorem have been provided, inclusive of the case when some order conditions between elements are imposed on the extension. We extend the analysis of that topic by Alcantud to the fuzzy case. By appealing to generators to decompose (fuzzy) preference relations into strict preference and indifference relations, we give general extension results for the corresponding concept of compatible extension of a fuzzy reflexive relation. Then we investigate the conditions under which compatible order extensions exist such that certain elements are connected by the asymmetric part, resp., and certain other elements by the symmetric part, to respective elements with degree 1.

On the Existence of Certainty Equivalents of Various Relevant Types

We tackle the problem of associating certainty equivalents with preferences over stochastic situa... more We tackle the problem of associating certainty equivalents with preferences over stochastic situations, which arises in a number of different fields (e.g., the theory of risk attitudes or the analysis of stochastic cooperative games). We study the possibility of endowing such preferences with certainty equivalence functionals that satisfy relevant requirements (such as positive homogeneity, translation invariance, monotonicity with respect to first-order stochastic dominance, and subadditivity). Uniqueness of the functional is also addressed in fairly general conditions.

Approval consensus measures Jos é

In many realistic group decision making problems where a “representative” collective output must ... more In many realistic group decision making problems where a “representative” collective output must be produced, it is relevant to measure how much consensus this solution conveys to the group. Many aspects influence the final decision in group decision making problems. Two key issues are the experts’ individual opinions and the methodology followed to compute such a final decision (aggregation operators, voting systems, etc.). In this paper we consider situations where each member of a population decides upon approving or not approving each of a set of options. The experts express their opinions in a dichotomous way, e.g., because they intend to use approval voting. In order to measure the consensus or cohesiveness that the expression of the individual preferences conveys we propose the concept of approval consensus measure (ACM), which does not refer to any priors of the agents like preferences or other decision-making processes. Then we give axiomatic characterizations of two generi...

Pairwise Dichotomous Cohesiveness Measures

Group Decision and Negotiation, 2014

In a framework where experts or agents express their opinions in a dichotomous way, we analyze th... more In a framework where experts or agents express their opinions in a dichotomous way, we analyze the cohesiveness of their opinions on a fixed set of issues in a population. A parametric family of related measures are introduced and axiomatically characterized. They are ordinally equivalent when the population is fixed, and some further properties are proved. In order to argue that this restricted dichotomous situation is nevertheless versatile, the paper ends with several empirical illustrations based on real forecasts (for the 2012 American presidential election) and elections (with real data from referenda in two countries and from elections in several scientific societies).

Consensus and the Act of Voting

Studies in Microeconomics, 2013

In this paper we are concerned with assessing the cohesiveness of a society whose individual pref... more

Fuzzy preorders: conditional extensions, extensions and their representations

Fuzzy Optimization and Decision Making, 2016

Ordering infinite utility streams: Efficiency, continuity, and no impatience

Mathematical Social Sciences, 2014

• Study no-impatience postulates in the context of (possibly incomplete) intertemporal preference... more

Inequality averse criteria for evaluating infinite utility streams: The impossibility of Weak Pareto

Journal of Economic Theory, 2010

This paper investigates ethical aggregation of infinite utility streams by representable social w... more This paper investigates ethical aggregation of infinite utility streams by representable social welfare relations. We prove that the Hammond Equity postulate and other variations of it like the Pigou-Dalton transfer principle are incompatible with positive responsiveness to welfare improvements by every generation. The case of Hammond Equity for the Future is investigated too. JEL classification: D63; D71; D90.

A new methodology to measure consensus

In some group decision making problems of real life not only is significant to rank the alternati... more In some group decision making problems of real life not only is significant to rank the alternatives but it also is important to measure how much consensus this solution conveys to the group. Due to this fact, in this work we propose a new methodology to measure the degree of consensus obtained by a group decision making process. To develop that approach, we define a class of consensus measures based on particular social rules. Some of their basic properties are proved too.

Preference through indifference: a topological approach

Journal of Mathematical Economics, 1999

Topological separability and axioms of countability in GPO-spaces

Bulletin of The Australian Mathematical Society, 1997

In this paper we obtain characterisations of first and second countability and separability for G... more In this paper we obtain characterisations of first and second countability and separability for GPO-spaces, a class of topological spaces that include LOTS and GO-spaces. Some additional results concerning the transmission of these properties to weaker/finer topologies are derived in this framework.

Mixed choice structures, with applications to binary and non-binary optimization

Journal of Mathematical Economics, 2008

We introduce the concept of mixed choice structure in order to propose an alternative model of no... more We introduce the concept of mixed choice structure in order to propose an alternative model of non-binary choice behavior under certainty. Some general sufficient conditions for optimality on not-necessarily compact sets are proven. The main conclusion is that one single result incorporates as particular cases classical theorems that exemplify different approaches both to binary – [Bergstrom, T.C., 1975, Maximal elements of acyclic relations on compact sets, Journal of Economic Theory 10, 403–404; Mehta, G., 1989, Maximal elements in Banach spaces, Indian Journal of Pure and Applied Mathematics 20, 690–697; Sonnenschein, H., 1971, Demand theory without transitive preferences, with applications to the theory of competitive equilibrium. In: Chipman, J.S., Hurwicz, L., Richter, M.K., Sonnenschein, H. (Eds.), Preferences, Utility and Demand. Harcourt Brace Jovanovich, New York; Walker, M., 1977, On the existence of maximal elements, Journal of Economic Theory 16, 470–474] – and non-binary – [Nehring, K., 1996, Maximal elements of non-binary choice functions on compact sets, Economics Letters 50, 337–340; Alcantud, J.C.R., 2002a, Characterization of the existence of maximal elements of acyclic relations, Economic Theory 19, 407–416] – optimization.

Weak utilities from acyclicity

Theory and Decision, 1999

In this paper weak utilities are obtained for acyclic binary relations satisfying a condition wea... more In this paper weak utilities are obtained for acyclic binary relations satisfying a condition weaker than semicontinuity on second countable topological spaces. In fact, in any subset of such a space we obtain a weak utility that characterizes the maximal elements as maxima of the function. The addition of separability of the relation yields the existence of semicontinuous representations. This property of the utility provides a result of existence of maximal elements for a class of spaces that include compact spaces. However, we offer a negative result that continuity may not be reached under such hypotheses.

Uniform spaces based on a way below relation

Computational and Applied Mathematics

A Social Choice Approach to Graded Soft Sets: slides for FUZZ-IEEE 2017

A New Criterion for Soft Set Based Decision Making Problems under Incomplete Information

International Journal of Computational Intelligence Systems, 2017

We put forward a completely redesigned approach to soft set based decision making problems under ... more We put forward a completely redesigned approach to soft set based decision making problems under incomplete information. An algorithmic solution is proposed and compared with previous approaches in the literature. The computational performance of our algorithm is critically analyzed by an experimental study.

The relationship between Mathematical Utility Theory and the Integrability Problem: some arguments in favour

The resort to utility-theoretical issues will permit us to propose a constructive proce-dure for ... more The resort to utility-theoretical issues will permit us to propose a constructive proce-dure for deriving a homogeneous of degree one, continuous function that gives raise to a primitive demand function under suitably mild conditions. This constitutes the first elementary proof of a necessary and sufficient condition for an integrability problem to have a solution by continuous (subjective utility) functions. Such achievement reinforces the relevance of a technique that was succesfully formalized in Alcantud and Rodŕıguez-Palmero [3]. The analysis of these two works exposes deep relationships between two apparently separate fields: mathematical utility theory and the revealed preference approach to the integrability problem. JEL classification: D11

Topological Properties of Spaces Ordered by Preferences

In this paper, we analyze the main topological properties of a relevant class of topologies assoc... more In this paper, we analyze the main topological properties of a relevant class of topologies associated with spaces ordered by preferences (asymmetric, negatively transi-tive binary relations). This class consists of certain continuous topologies which include the order topology. The concept of saturated identification is introduced in order to provide a natural proof of the fact that all these spaces possess topological properties analogous to those of linearly ordered topological spaces, inter alia monotone and hereditary normality, and complete regularity.

New correlation coefficients for hesitant fuzzy sets

The previous correlation measures for hesitant fuzzy sets proposed in the literature only capture... more The previous correlation measures for hesitant fuzzy sets proposed in the literature only capture the strength of the correlations. We present a new approach based on the classical Pearson correlation coefficient for crisp values. In this way we can ex-press not only the strength of the relationship be-tween two hesitant fuzzy sets, but also whether they are positively or negatively associated.

CHoice-Nash-equilibria

We provide existence results for equilibria of games where players employ abstract (non-binary) c... more We provide existence results for equilibria of games where players employ abstract (non-binary) choice rules. Such results are shown to encompass as a relevant instance that of games where players have (nontransitive) SSB (Skew-Symmetric Bilinear) preferences, as well as other well-known transitive (e.g. Nash’s) and non-transitive (e.g. Shafer and Sonnenschein’s) models in the literature. Further, our general model contains games where players display procedural rationality.

Conditional extensions of fuzzy preorders

Fuzzy Sets and Systems

The problem of embedding incomplete into complete rela- tions has been an important topic of rese... more The problem of embedding incomplete into complete rela- tions has been an important topic of research in the context of crisp relations and their applications. Several variations of the acclaimed Szpilrajn’s theorem have been provided, inclusive of the case when some order conditions between elements are imposed on the extension. We extend the analysis of that topic by Alcantud to the fuzzy case. By appealing to generators to decompose (fuzzy) preference relations into strict preference and indifference relations, we give general extension results for the corresponding concept of compatible extension of a fuzzy reflexive relation. Then we investigate the conditions under which compatible order extensions exist such that certain elements are connected by the asymmetric part, resp., and certain other elements by the symmetric part, to respective elements with degree 1.

On the Existence of Certainty Equivalents of Various Relevant Types

We tackle the problem of associating certainty equivalents with preferences over stochastic situa... more We tackle the problem of associating certainty equivalents with preferences over stochastic situations, which arises in a number of different fields (e.g., the theory of risk attitudes or the analysis of stochastic cooperative games). We study the possibility of endowing such preferences with certainty equivalence functionals that satisfy relevant requirements (such as positive homogeneity, translation invariance, monotonicity with respect to first-order stochastic dominance, and subadditivity). Uniqueness of the functional is also addressed in fairly general conditions.

Approval consensus measures Jos é

In many realistic group decision making problems where a “representative” collective output must ... more In many realistic group decision making problems where a “representative” collective output must be produced, it is relevant to measure how much consensus this solution conveys to the group. Many aspects influence the final decision in group decision making problems. Two key issues are the experts’ individual opinions and the methodology followed to compute such a final decision (aggregation operators, voting systems, etc.). In this paper we consider situations where each member of a population decides upon approving or not approving each of a set of options. The experts express their opinions in a dichotomous way, e.g., because they intend to use approval voting. In order to measure the consensus or cohesiveness that the expression of the individual preferences conveys we propose the concept of approval consensus measure (ACM), which does not refer to any priors of the agents like preferences or other decision-making processes. Then we give axiomatic characterizations of two generi...

Pairwise Dichotomous Cohesiveness Measures

Group Decision and Negotiation, 2014

In a framework where experts or agents express their opinions in a dichotomous way, we analyze th... more In a framework where experts or agents express their opinions in a dichotomous way, we analyze the cohesiveness of their opinions on a fixed set of issues in a population. A parametric family of related measures are introduced and axiomatically characterized. They are ordinally equivalent when the population is fixed, and some further properties are proved. In order to argue that this restricted dichotomous situation is nevertheless versatile, the paper ends with several empirical illustrations based on real forecasts (for the 2012 American presidential election) and elections (with real data from referenda in two countries and from elections in several scientific societies).

Consensus and the Act of Voting

Studies in Microeconomics, 2013

In this paper we are concerned with assessing the cohesiveness of a society whose individual pref... more

Fuzzy preorders: conditional extensions, extensions and their representations

Fuzzy Optimization and Decision Making, 2016

Ordering infinite utility streams: Efficiency, continuity, and no impatience

Mathematical Social Sciences, 2014

• Study no-impatience postulates in the context of (possibly incomplete) intertemporal preference... more

Inequality averse criteria for evaluating infinite utility streams: The impossibility of Weak Pareto

Journal of Economic Theory, 2010

This paper investigates ethical aggregation of infinite utility streams by representable social w... more This paper investigates ethical aggregation of infinite utility streams by representable social welfare relations. We prove that the Hammond Equity postulate and other variations of it like the Pigou-Dalton transfer principle are incompatible with positive responsiveness to welfare improvements by every generation. The case of Hammond Equity for the Future is investigated too. JEL classification: D63; D71; D90.

A new methodology to measure consensus

In some group decision making problems of real life not only is significant to rank the alternati... more In some group decision making problems of real life not only is significant to rank the alternatives but it also is important to measure how much consensus this solution conveys to the group. Due to this fact, in this work we propose a new methodology to measure the degree of consensus obtained by a group decision making process. To develop that approach, we define a class of consensus measures based on particular social rules. Some of their basic properties are proved too.

Preference through indifference: a topological approach

Journal of Mathematical Economics, 1999

Topological separability and axioms of countability in GPO-spaces

Bulletin of The Australian Mathematical Society, 1997

In this paper we obtain characterisations of first and second countability and separability for G... more In this paper we obtain characterisations of first and second countability and separability for GPO-spaces, a class of topological spaces that include LOTS and GO-spaces. Some additional results concerning the transmission of these properties to weaker/finer topologies are derived in this framework.

Mixed choice structures, with applications to binary and non-binary optimization

Journal of Mathematical Economics, 2008

We introduce the concept of mixed choice structure in order to propose an alternative model of no... more We introduce the concept of mixed choice structure in order to propose an alternative model of non-binary choice behavior under certainty. Some general sufficient conditions for optimality on not-necessarily compact sets are proven. The main conclusion is that one single result incorporates as particular cases classical theorems that exemplify different approaches both to binary – [Bergstrom, T.C., 1975, Maximal elements of acyclic relations on compact sets, Journal of Economic Theory 10, 403–404; Mehta, G., 1989, Maximal elements in Banach spaces, Indian Journal of Pure and Applied Mathematics 20, 690–697; Sonnenschein, H., 1971, Demand theory without transitive preferences, with applications to the theory of competitive equilibrium. In: Chipman, J.S., Hurwicz, L., Richter, M.K., Sonnenschein, H. (Eds.), Preferences, Utility and Demand. Harcourt Brace Jovanovich, New York; Walker, M., 1977, On the existence of maximal elements, Journal of Economic Theory 16, 470–474] – and non-binary – [Nehring, K., 1996, Maximal elements of non-binary choice functions on compact sets, Economics Letters 50, 337–340; Alcantud, J.C.R., 2002a, Characterization of the existence of maximal elements of acyclic relations, Economic Theory 19, 407–416] – optimization.

Weak utilities from acyclicity

Theory and Decision, 1999

In this paper weak utilities are obtained for acyclic binary relations satisfying a condition wea... more In this paper weak utilities are obtained for acyclic binary relations satisfying a condition weaker than semicontinuity on second countable topological spaces. In fact, in any subset of such a space we obtain a weak utility that characterizes the maximal elements as maxima of the function. The addition of separability of the relation yields the existence of semicontinuous representations. This property of the utility provides a result of existence of maximal elements for a class of spaces that include compact spaces. However, we offer a negative result that continuity may not be reached under such hypotheses.

A New Criterion for Soft Set Based Decision Making Problems under Incomplete Information

by Gustavo Santos-García and J C R Alcantud

We put forward a completely redesigned approach to soft set based decision making problems under ... more We put forward a completely redesigned approach to soft set based decision making problems under incomplete information. An algorithmic solution is proposed and compared with previous approaches in the literature. The computational performance of our algorithm is critically analyzed by an experimental study.