A method based on similarity measures for interactive group decision-making with intuitionistic fuzzy preference relations

In this paper, we study the group decision-making problem in which the preference information given by experts takes the form of intuitionistic fuzzy preference relations, and the information about experts’ weights is completely unknown. We first utilize the intuitionistic fuzzy weighted averaging operator to aggregate all individual intuitionistic fuzzy preference relations into a collective intuitionistic fuzzy preference relation. Then, based on the degree of similarity between the individual intuitionistic fuzzy preference relations and the collective one, we develop an approach to determine the experts’ weights. Furthermore, based on intuitionistic fuzzy preference relations, a practical interactive procedure for group decision-making is proposed, in which the similarity measures between the collective preference relation and intuitionistic fuzzy ideal solution are used to rank the given alternatives. Finally, an illustrative numerical example is given to verify the developed approach.     

A collective choice method based on individual preferences relational systems (p.r.s.)

In group decision-making literature, several procedures are proposed in order to establish a collective preference from the different individual ones. The majority of these procedures, however, reveal that the individual preferences are always expressed in total pre-orders (or ranking). Indeed, until now very few have considered individual preferences which are expressed in partial pre-orders or, more generally, in preferences relational systems (p.r.s.). Moreover, many of these procedures generate collective preferences which are expressed in total pre-orders (ranking decision-making problematic). The efforts reported in the literature to develop procedures which treat other decision-making problematics—such as choice problematic—remain insufficient. In this paper, we propose a method which would determine from individual p.r.s. at least one collective subset containing the “best” alternatives. Each of these collective subsets results from the exploitation—according to the choice problematic—of a collective p.r.s. obtained from the aggregation of the individual p.r.s. Furthermore, each collective p.r.s. has two main characteristics: (i) it is at a minimum distance from all individual p.r.s. and (ii) it takes into account the members’ relative importance.     

A distributed social choice protocol for combinatorial domains

In this paper, we study the problem of collective decision-making over combinatorial domains, where the set of possible alternatives is a Cartesian product of (finite) domain values for each of a given set of variables, and these variables are not preferentially independent. Due to the large alternative space, most common rules for social choice cannot be directly applied to compute a winner. In this paper, we introduce a distributed protocol for collective decision-making in combinatorial domains, which enjoys the following desirable properties: (i) the final decision chosen is guaranteed to be a Smith member; (ii) it enables distributed decision-making and works under incomplete information settings, i.e., the agents are not required to reveal their preferences explicitly; (iii) it significantly reduces the amount of dominance testings (individual outcome comparisons) that each agent needs to conduct, as well as the number of pairwise comparisons; (iv) it is sufficiently general and does not restrict the choice of preference representation languages.     

管理者过度自信对并购绩效的影响——基于群体决策视角的分析和实证

我国公司决策更多的是群体而非个体决策,群体决策强化还是弱化了过度自信偏差?本文从群体决策的层面研究了管理者的过度自信对公司并购绩效的影响。摈弃传统公司并购理论中的管理者理性假设,从行为公司金融理论出发,以我国422家上市发行A股的并购公司为样本进行了实证分析和研究。结果表明:群体决策中的管理者普遍存在着过度自信;管理者过度自信与并购长期绩效显著负相关;与短期绩效也负相关,但在统计上不显著。最后,根据分析结果提出了克服或减少管理者决策偏差行为的若干可行的举措。     

The fluted fragment with transitive relations

The fluted fragment is a fragment of first-order logic (without equality) in which, roughly speaking, the order of quantification of variables coincides with the order in which those variables appear as arguments of predicates. It is known that this fragment has the finite model property. We consider extensions of the fluted fragment with various numbers of transitive relations, as well as the equality predicate. In the presence of one transitive relation (together with equality), the finite model property is lost; nevertheless, we show that the satisfiability and finite satisfiability problems for this extension remain decidable. We also show that the corresponding problems in the presence of two transitive relations (with equality) or three transitive relations (without equality) are undecidable, even for the two-variable sub-fragment.     

An ordinal sorting method for group decision-making

Several group decision-making methods were proposed with the aim to establish, from individual opinions, a collective one. However, the literature review of such methods show that, until now, few of them accept individual preferences expressed in partial pre-orders or, more generally, in preferences relational systems (p.r.s.). In addition, the majority of these methods produce a ranking on the alternative set, i.e. they concern the ranking decision-making problematic. In fact, the efforts provided to develop methods which treat, for example, the sorting problematic, remain insufficient. For these reasons, we propose in this paper an ordinal sorting method which determines, from individual p.r.s., at least one collective assignment which takes into account the relative importance of the members. If there is more than one collective assignment, an interactive procedure to reach a consensus assignment is proposed.     

Binary games in constitutional form and collective choice

In this paper, we define the notion of binary game in constitutional form. For this game, we define a core and give a necessary and sufficient condition for a game to be stable.We define a representation of a collective choice rule by a binary game in constitutional form and characterize those collective choice rules which are representable.We finally introduce the notion of c-social decision function and characterize, as an application of our theorem on stability of binary constitutional games, the collective choice rules which are c-social decision functions.Our representation of a collective choice rule by a binary game in constitutional form is an obvious improvement of the classical representation by a simple game.     

The impact of other-regarding tendencies on the spatial vaccination game

Using the evolutionary game framework to describe the vaccination behaviors of individuals, this work focuses on the impact of other-regarding tendencies on collective decision-making of vaccination. With extensive computational simulations, we find that when the vaccination cost is small or moderate, the variance of vaccination coverage as well as epidemic size is monotonically depending on the other-regarding effect. However, with a high price of vaccine, a moderate deviation from being entirely self-centered results in a poor communal vaccination benefit. In addition, we also find that the other-regarding effect may lead to an optimal total social cost.     

Collective work with resources: an essential dimension for teacher documentation

In this paper we study the collective dimensions of teachers’ work in their ordinary daily practice. We argue that teachers’ ordinary work comprises many collaborative aspects, and that the interactions with colleagues, often through resources, are crucial for teacher professional development. Using a theoretical framework based on teacher documentation work, we focused on interactions between teachers and resources to study two teachers’ work: one teacher in France and one teacher in Norway. For both teachers we identified collective dimensions in their work with resources. Contrasting these two cases enabled us to identify particular features, but also possible invariants, of teachers’ work with resources. Our results indicate that collective dimensions are always present in teachers’ work, but that true communities of practice, which could be considered as an achievement of collective teachers’ work, are scarce. We discuss the conditions for the emergence of such communities.     

Equality measures properties for location problems

The objectives underlying location decisions can be various. Among them, equity objectives have received an increasing attention in recent years, especially in the applications related to the public sector, where fair distributions of accessibility to the services should be guaranteed among users. In the literature a huge number of equality measures have been proposed; then, the problem of selecting the most appropriate one to be adopted in the decision-making processes is crucial. For this reason, many authors focused on the analysis of properties that equality measures should satisfy in order to be considered suitable. Most of the proposed properties are too general and related solely to the mathematical formulation of the measure itself (i.e., simpleness, impartiality, invariance). Hence, they do not give any indications about the behaviour of such measures in the optimization contexts. In this work, we propose some new properties to be associated to equality measures in order to describe characteristics which may be useful to drive optimization procedures in the search of optimal (or near-optimal) solutions. To this aim some empirical analyses have been performed in order to understand the typical behavior of remarkable measures in presence of a uniform distribution of demand points in a regular location spaces.     

Equality conditions for lower bounds on the smallest singular value of a bidiagonal matrix

Several lower bounds have been proposed for the smallest singular value of a square matrix, such as Johnson’s bound, Brauer-type bound, Li’s bound and Ostrowski-type bound. In this paper, we focus on a bidiagonal matrix and investigate the equality conditions for these bounds. We show that the former three bounds give strict lower bounds if all the bidiagonal elements are non-zero. For the Ostrowski-type bound, we present an easily verifiable necessary and sufficient condition for the equality to hold.     

基于可拓方法我国银行体系脆弱性的评价

在银行体系脆弱性评价中借助物元的概念,建立了银行体系脆弱性评价模型,并采用较为客观的评价方法——可拓方法对该模型进行评价,介绍了一种新的银行体系脆弱性评价方法.消除了其它主观评价方法带来的偏差,从而为我国银行体系脆弱性的监管决策提供有益参考.     

Non-cooperative implementation: A survey of recent results

Strategic decentralization of collective decision-making is considered when the agents' behaviour is non-cooperative. Specifically they use dominant, maximin risk-avert or sophisticated strategies. The existing results applying these equilibrium concepts are reviewed in three familiar economically meaningful contexts: ordinal (as in voting), random (as in bargaining) and quasilinear (as in public goods problems).     

Collective Mathematical Understanding as Improvisation

This article explores the phenomenon of mathematical understanding, and offers a response to the question raised by Martin (2001) at the Annual Meeting of the Psychology of Mathematics Education Group (North American Chapter) about the possibility for and nature of collective mathematical understanding. In referring to collective mathematical understanding, we point to the kinds of learning and understanding we may see occurring when a group of learners work together on a piece of mathematics. We characterize the growth of collective mathematical understanding as a creative and emergent improvisational process and illustrate how this can be observed in action. In doing this, we demonstrate how a collective perspective on mathematical understanding can more fully explain its growth. We also discuss how considering the growth of mathematical understanding as a collective process has implications for classroom practice and in particular for the setting of mathematical tasks.     

On pseudo-equality algebras

Recently, a new algebraic structure called pseudo-equality algebra has been defined by Jenei and Kóródi as a generalization of the equality algebra previously introduced by Jenei. As a main result, it was proved that the pseudo-equality algebras are term equivalent with pseudo-BCK meet-semilattices. We found a gap in the proof of this result and we present a counterexample and a correct version of the theorem. The correct version of the corresponding result for equality algebras is also given.     

Pseudo equality algebras

A new structure, called pseudo equality algebras, will be introduced. It has a constant and three connectives: a meet operation and two equivalences. A closure operator will be introduced in the class of pseudo equality algebras; we call the closed algebras equivalential. We show that equivalential pseudo equality algebras are term equivalent with pseudo BCK-meet-semilattices. As a by-product we obtain a general result, which is analogous to a result of Kabziński and Wroński: we provide an equational characterization for the equivalence operations of pseudo BCK-meet-semilattices. Our result treats a much more general algebraic structure, namely, pseudo BCK-meet-semilattice instead of Heyting algebras, on the other hand, we also need to use the meet operation. Finally, we prove that the variety of pseudo equality algebras is a subtractive, 1-regular, arithmetical variety.     

Bias of LS estimators in nonlinear regression models with constraints. Part I: General Case

We derive expressions for the asymptotic approximation of the bias of the least squares estimators in nonlinear regression models with parameters which are subject to nonlinear equality constraints.The approach suggested modifies the normal equations of the estimator, and approximates them up to o _p(N ^–1), where N is the number of observations. The bias equations so obtained are solved under different assumptions on constraints and on the model. For functions of the parameters the invariance of the approximate bias with respect to reparametrisations is demonstrated. Singular models are considered as well, in which case the constraints may serve either to identify the parameters, or eventually to restrict the parameter space.     

Autoregressive functions estimation in nonlinear bifurcating autoregressive models

Bifurcating autoregressive processes, which can be seen as an adaptation of autoregressive processes for a binary tree structure, have been extensively studied during the last decade in a parametric context. In this work we do not specify any a priori form for the two autoregressive functions and we use nonparametric techniques. We investigate both nonasymptotic and asymptotic behaviour of the Nadaraya–Watson type estimators of the autoregressive functions. We build our estimators observing the process on a finite subtree denoted by \(\mathbb {T}_n\), up to the depth n. Estimators achieve the classical rate \(|\mathbb {T}_n|^{-\beta /(2\beta +1)}\) in quadratic loss over Hölder classes of smoothness. We prove almost sure convergence, asymptotic normality giving the bias expression when choosing the optimal bandwidth. Finally, we address the question of asymmetry: we develop an asymptotic test for the equality of the two autoregressive functions which we implement both on simulated and real data.     

Equality Constraints in Multiobjective Robust Design Optimization: Decision Making Problem

Robust design optimization (RDO) problems can generally be formulated by incorporating uncertainty into the corresponding deterministic problems. In this context, a careful formulation of deterministic equality constraints into the robust domain is necessary to avoid infeasible designs under uncertain conditions. The challenge of formulating equality constraints is compounded in multiobjective RDO problems. Modeling the tradeoffs between the mean of the performance and the variation of the performance for each design objective in a multiobjective RDO problem is itself a complex task. A judicious formulation of equality constraints adds to this complexity because additional tradeoffs are introduced between constraint satisfaction under uncertainty and multiobjective performance. Equality constraints under uncertainty in multiobjective problems can therefore pose a complicated decision making problem. In this paper, we provide a new problem formulation that can be used as an effective multiobjective decision making tool, with emphasis on equality constraints. We present two numerical examples to illustrate our theoretical developments.