ordinal regression revisited multiple criteria ranking using a set of additive value functions abstract we present a new method called utagms for multiple criteria ranking of alternatives from set a using a set of additive value functions which result from an ordinal regression the preference information provided by the decision maker is a set of pairwise comparisons on a subset of alternatives ar a called reference alternatives the preference model built via ordinal regression is the set of all additive value functions compatible with the preference information using this model one can define two relations in the set a the necessary weak preference relation which holds for any two alternatives a b from set a if and only if for all compatible value functions a is preferred to b and the possible weak preference relation which holds for this pair if and only if for at least one compatible value function a is preferred to b these relations establish a necessary and a possible ranking of alternatives from a being respectively a partial preorder and a strongly complete relation the utagms method is intended to be used interactively with an increasing subset ar and a progressive statement of pairwise comparisons when no preference information is provided the necessary weak preference relation is a weak dominance relation and the possible weak preference relation is a complete relation every new pairwise comparison of reference alternatives for which the dominance relation does not hold is enriching the necessary relation and it is impoverishing the possible relation so that they converge with the growth of the preference information distinguishing necessary and possible consequences of preference information on the complete set of actions utagms answers questions of robustness analysis moreover the method can support the decision maker when his her preference statements cannot be represented in terms of an additive value function the method is illustrated by an example solved using the utagms software some extensions of the method are also presented

preference inference with general additive value models and holistic pair wise statements additive multi attribute value models and additive utility models with discrete outcome sets are widely applied in both descriptive and normative decision analysis their non parametric application allows preference inference by analyzing sets of general additive value functions compatible with the observed or elicited holistic pair wise preference statements in this paper we provide necessary and sufficient conditions for the preference inference based on a single preference statement and sufficient conditions for the inference based on multiple preference statements in our computational experiments all inferences could be made with these conditions moreover our analysis suggests that the non parametric analyses of general additive value models are unlikely to be useful by themselves for decision support in contexts where the decision maker preferences are elicited in the form of holistic pair wise statements

formalizing and solving the problem of clustering in mcda the topic of clustering has been widely studied in the field of data analysis where it is defined as an unsupervised process of grouping objects together based on notions of similarity clustering in the field of multi criteria decision aid mcda has seen a few adaptations of methods from data analysis most of them however using concepts native to that field such as the notions of similarity and distance measures as in mcda we model the preferences of a decision maker over a set of decision alternatives we can find more diverse ways of comparing them than in data analysis as a result these alternatives may also be arranged into different potential structures in this paper we wish to formally define the problem of clustering in mcda using notions that are native to this field alone and highlight the different structures which we may try to uncover through this process following this we propose a method for finding these structures as in any clustering problem finding the optimal result in an exact manner is impractical and so we propose a stochastic heuristic approach which we validate through tests on a large set of artificially generated benchmarks

jie ke versus alphago a ranking approach using decision making method for large scale data with incomplete information abstract ranking historical players in sports is challenging since some players have never played against each other it is even more complex in go because of alphago a project based on artificial intelligence who became the world s number 1 after it defeated the 528th and the 4th human go players alphago is ranked high in the current go ranking system because it is undefeated the objective of this paper is to propose a new ranking method for large scale go players by means of incomplete fuzzy pair wise comparison matrix whose priority vector is derived using a cosine similarity measure using match results provided by go4go net experiments are designed to rank top go players in the past 45 years and examine the change in ranking after alphago faced off against jie ke furthermore the proposed method was applied to rank all 1544 go players available at go4go net to illustrate its efficiency in handling large scale data

de bakker zucker processes revisited the sets of compact and of closed subsets of a metric space endowed with the hausdorff metric are studied both give rise to a functor on the category of 1 bounded metric spaces and nonexpansive functions it is shown that the former functor has a terminal coalgebra and that the latter does not

robustness analysis for decision under uncertainty with rule based preference model we introduce robust ordinal regression to decision under uncertainty we propose an integrated framework for robustness analysis with the rule based preference model we formulate the procedures for deriving a univocal classification of acts we account for different types of indirect preference information we consider group decision under uncertainty with dominance based rough set approach we consider decision under uncertainty as a multi attribute classification problem where a set of acts is described by outcomes gained with given probabilities the decision maker dm provides desired classification for a small subset of reference acts such preference information is structured using dominance based rough set approach drsa and the resulting lower approximations of the quality class unions are used as an input for construction of an aggregate preference model we induce all minimal cover sets of rules being compatible with the non ambiguous assignment examples and satisfying some additional requirements that may be imposed by the dm applying such compatible instances of the preference model on a set of all acts we draw conclusions about the certainty of recommendation assured by different minimal cover sets of rules in particular we analyze the diversity of class assignments assignment based preference relations and class cardinalities then we solve an optimization problem to get a univocal precise classification for all acts taking into account the robustness concern this optimization problem admits incorporation of additional indirect and imprecise preferences in form of desired class cardinalities and assignment based pairwise comparisons finally we extend the proposed approach to group decision under uncertainty we present a set of indicators and outcomes giving an insight into the spaces of consensus and disagreement between the dms

robust ordinal regression for dominance based rough set approach to multiple criteria sorting we present a new multiple criteria sorting method deriving from dominance based rough set approach drsa the preference information supplied by the decision maker dm is a set of possibly imprecise and inconsistent assignment examples on a subset of reference alternatives relatively well known to the dm to structure the data we use drsa and subsequently represent the assignment examples by all minimal sets of rules covering all alternatives from the lower approximations of class unions such a set of rules is called minimal cover set it is one of the instances of the preference model compatible with dm s preference information in this way we implement the principle of robust ordinal regression ror to decision rule preference model for each alternative we derive the necessary and possible assignments specifying the range of classes to which the alternative is assigned by all or at least one compatible set of rules respectively as well as class acceptability indices we also introduce the notion of a representative compatible minimal cover set of rules whose selection builds on the results of ror addressing the robustness concern application of the approach is demonstrated by classifying 69 land zones in 4 classes representing different risk levels

testing equivalences for processes abstract given a set of processes and a set of tests on these processes we show how to define in a natural way three different equivalences on processes these equivalences are applied to a particular language ccs we give associated complete proof systems and fully abstract models these models have a simple representation in terms of trees

theory of interaction abstract theory of interaction aims to provide a foundational framework for computation and interaction it proposes four fundamental principles that characterize the common features of all models of computation and interaction these principles suffice to support a model independent treatment of the two most important relationships in computer science the equality between processes and the relative expressiveness between models based on the two relationships the theory of equality the theory of expressiveness and the theory of completeness are developed

a fixed point theorem in a category of compact metric spaces various results appear in the literature for deriving existence and uniqueness of fixed points for endofunctors on categories of complete metric spaces all these results are proved for contracting functors which satisfy some further requirements depending on the category in question following a new kind of approach based on the notion of isometry we show that the sole hypothesis of contractivity is enough for proving existence and uniqueness of fixed points for endofunctors on the category of compact metric spaces and embedding projection pairs

when are prime formulae characteristic abstract in the setting of the modal logic that characterizes modal refinement over modal transition systems boudol and larsen showed that the formulae for which model checking can be reduced to preorder checking that is the characteristic formulae are exactly the consistent and prime ones this paper presents general sufficient conditions guaranteeing that characteristic formulae are exactly the consistent and prime ones it is shown that the given conditions apply to various behavioural relations in the literature in particular characteristic formulae are exactly the prime and consistent ones for all the semantics in van glabbeek s linear time branching time spectrum

cpo models for compact gsos languages in this paper we present a general way of giving denotational semantics to a class of languages equipped with an operational semantics that fits the gsos format of bloom istrail and meyer the canonical model used for this purpose will be abramsky s domain of synchronization trees and the denotational semantics automatically generated by our methods will be guaranteed to be fully abstract with respect to the finitely observable part of the bisimulation preorder in the process of establishing the full abstraction result we also obtain several general results on the bisimulation preorder including a complete axiomatization for it and give a novel operational interpretation of gsos languages

axiomatising finite concurrent processes we re examine the well known observational equivalence between processes with a view to modifying it so as to distinguish between concurrent and purely nondeterministic processes observational equivalence is based on atomic actions or observations in the first part of this paper we generalise these atomic observations so that arbitrary processes may act as observers we show for a particular language based on finite ccs terms that the generalised equivalence coincides with observational equivalence the more powerful observers do not lead to a finer equivalence in the second part of the paper we consider observers which can distinguish the beginning and ending of atomic actions the resulting equivalence distinguishes a concurrent process from the purely nondeterministic process obtained by interleaving its possible actions we give a complete axiomatisation for the congruence generated by the new equivalence

observation equivalence as a testing equivalence a notion of testing is developed for transition systems with divergence the forms of testing include traces refusals copying and global testing both denotational and operational formulations of testing are given the equivalence based on this notion of testing is shown to coincide with observation equivalence

modal logics for communicating systems abstract simple modal logics for milner s sccs and ccs are presented we offer sound and complete axiomatizations of validity relative to these calculi as models also we present compositional proof systems for when a program satisfies a formula these involve proof rules which are like gentzen introduction rules except that there are also introduction rules for the program combinators of sccs and ccs the compositional rules for restriction or hiding and parallel combinators arise out of a simple semantic strategy

the comparison of a cpo based semantics with cms based semantics for csp we study two semantics for csp both semantics are compositional and interleaving the first uses the concept of complete partial orders cpo for the handling of repetitive constructs and for the creation of suitable semantic domains the second uses the concept of complete metric spaces cms for the same purposes our results show that the cms semantics gives more detailed information about a program and that we can obtain the cpo semantics from it from this investigation we can draw conclusions concerning the influence of the mathematical discipline on the kind of semantics obtained

a group decision making approach based on evidential reasoning for multiple criteria sorting problem with uncertainty a new group decision making approach is developed to address a multiple criteria sorting problem with uncertainty the uncertainty in this paper refers to imprecise evaluations of alternatives with respect to the considered criteria the belief structure and the evidential reasoning approach are employed to represent and aggregate the uncertain evaluations in our approach the preference information elicited from a group of decision makers is composed of the assignment examples of some reference alternatives the disaggregation aggregation paradigm is utilized to infer compatible preference models from these assignment examples to help the group reach an agreement on the assignment of alternatives we propose a consensus reaching process in this process a consensus degree is defined to measure the agreement among the decision makers opinions when the decision makers are not satisfied with the consensus degree possible solutions are explored to help them adjust assignment examples in order to improve the consensus level if the consensus degree arrives at a satisfactory level a linear program is built to determine the collective assignment of alternatives the application of the proposed approach to a customer satisfaction analysis is presented at the end of the paper

recursively defined metric spaces without contraction in this paper we use the theory of accessible categories to find fixed points of endofunctors on the category of 1 bounded complete metric spaces and nonexpansive functions in contrast to previous approaches we do not assume that the endofunctors are locally contractive and our results do not depend on banach s fixed point theorem our approach is particularly suitable for constructing models of systems that feature quantitative data for instance using the kantorovich metric on probability measures we construct a quantitative model for probabilistic transition systems the metric in our model can reasonably be seen as measuring the behavioural distance between states of the system it depends exclusively on the transition probabilities and not on an arbitrary discount factor

some inequalities about the kaplan meier estimator in this paper we consider the product limit estimator of the survival distribution function in the context of independent but nonidentically distributed censoring times an upper bound on the mean square increment of the stopped kaplan meier process is obtained also a representation is given for the ratio of the survival distribution function to the product limit estimator as the product of a bounded process and a martingale from this representation bounds on the mean square of the ratio and on the tail probability of the sup norm of the ratio are derived

the category theoretic solution of recursive domain equations recursive specifications of domains plays a crucial role in denotational semantics as developed by scott and strachey and their followers the purpose of the present paper is to set up a categorical framework in which the known techniques for solving these equations find a natural place the idea is to follow the well known analogy between partial orders and categories generalizing from least fixed points of continuous functions over cpos to initial ones of continuous functors over omega categories to apply these general ideas we introduce wand s bf o categories where the morphism sets have a partial order structure and which include almost all the categories occurring in semantics the idea is to find solutions in a derived category of embeddings and we give order theoretic conditions which are easy to verify and which imply the needed categorical ones the main tool is a very general form of the limit colimit coincidence remarked by scott in the concluding section we outline how compatibilit

bisimulation and divergence abstract behavioural preorders based on the idea of bisimulation but refining the notion of bisimulation equivalence and providing explicit treatments of the phenomenon of divergence in communicating systems are investigated particular study is made of these preorders in the context of milner s calculus of communicating systems the precongruence relations generated by the preorders are characterized and axiomatized on the classes of finite closed terms and sequential terms a verification technique based on the theory of the preorders is introduced and illustrated

terminal coalgebras in well founded set theory abstract this paper shows that in order to obtain the theorem of aczel and mendler on the existence of terminal coalgebras for an endofunctor on the category of sets it is entirely unnecessary to delve into such exotica as non well founded set theory in addition we discuss the canonical map from the initial algebra for an endofunctor on sets to the terminal coalgebra and show that in many cases it embeds the former as a dense subset of the latter in a certain natural topology by way of example we calculate the terminal coalgebra for various simple endofunctors

trees and semantics abstract several types of trees are proposed in the literature to model the behaviour of nondeterministic processes the purpose of this paper is to clarify the distinction between the various types of trees and to discuss their use as semantic domains trees in the sense of milner s derivation trees and bisimulation equivalence classes of trees are considered in three different settings in the category of sets in the metric setting and in the partial order setting each type of tree is characterized by a domain equation special attention is given to the use of trees as models for processes which allow for unbounded nondeterminism as for instance milners ccs processes in this case one has to deal with infinitely branching trees which cause problems to give denotational semantics that are fully abstract w r t a transition system based operational semantics

elicitation of multiattribute value functions through high dimensional model representations monotonicity and interactions abstract this work addresses the early phases of the elicitation of multiattribute value functions proposing a practical method for assessing interactions and monotonicity we exploit the link between multiattribute value functions and the theory of high dimensional model representations the resulting elicitation method does not state any a priori assumption on an individual s preference structure we test the approach via an experiment in a riskless context in which subjects are asked to evaluate mobile phone packages that differ on three attributes

acuta a novel method for eliciting additive value functions on the basis of holistic preference statements in multiple criteria decision aiding it is common to use methods that are capable of automatically extracting a decision or evaluation model from partial information provided by the decision maker about a preference structure in general there is more than one possible model leading to an indetermination which is dealt with sometimes arbitrarily in existing methods this paper aims at filling this theoretical gap we present a novel method based on the computation of the analytic center of a polyhedron for the selection of additive value functions that are compatible with holistic assessments of preferences we demonstrate the most important characteristics of this technique with an experimental and comparative study of several existing methods belonging to the uta family

a characterization of distance between 1 bounded compact ultrametric spaces through a universal space abstract the category of 1 bounded compact ultrametric spaces kums and non distance increasing functions has been extensively used in the semantics of concurrent programming languages in this paper a universal space u for kums is introduced such that each kum can be isometrically embedded in it the space u consists of a suitable subset of the space of functions from 0 1 to n endowed with a prefix based ultrametric u allows to characterize the distance between kums introduced in alessi et al 1995 in terms of the hausdorff distance between its compact subsets as applications it is proved how to derive the existence of limits for cauchy towers of spaces without using the classical categorical construction and how to find solutions of recursive domain equations inside nco u

a new decision making approach for multiple criteria sorting with an imbalanced set of assignment examples abstract we propose a novel approach to address a multiple criteria sorting mcs problem with an imbalanced set of assignment examples the approach employs a piecewise linear additive value function as the preference model and adopts the disaggregation aggregation paradigm to infer a sorting model from provided assignment examples on a set of reference alternatives we utilize a hierarchical clustering algorithm and several linear programming models to identify reference alternatives that are active to develop the sorting model so that inactive ones are eliminated from the whole set of reference alternatives then in order to construct a balanced set of assignment examples a balancing algorithm is proposed to balance active reference alternatives across categories finally the sorting model is obtained by minimizing the sum of violations between values of active reference alternatives and corresponding category thresholds furthermore the performance of the proposed approach is investigated on a hypothetical problem and several real data sets the experimental results show that our approach is efficient to address the mcs problem with an imbalanced set of assignment examples

algebraic laws for nondeterminism and concurrency since a nondeterministic and concurrent program may in general communicate repeatedly with its environment its meaning cannot be presented naturally as an input output function as is often done in the denotational approach to semantics in this paper an alternative is put forth first a definition is given of what it is for two programs or program parts to be equivalent for all observers then two program parts are said to be observation congruent if they are in all program contexts equivalent the behavior of a program part that is its meaning is defined to be its observation congruence class the paper demonstrates for a sequence of simple languages expressing finite terminating behaviors that in each case observation congruence can be axiomatized algebraically moreover with the addition of recursion and another simple extension the algebraic language described here becomes a calculus for writing and specifying concurrent programs and for proving their properties

modeling assignment based pairwise comparisons within integrated framework for value driven multiple criteria sorting abstract we introduce a new preference disaggregation modeling formulations for multiple criteria sorting with a set of additive value functions the preference information supplied by the decision maker dm is composed of 1 possibly imprecise assignment examples 2 desired class cardinalities and 3 assignment based pairwise comparisons the latter have the form of imprecise statements referring to the desired assignments for pairs of alternatives but without specifying any concrete class additionally we account for preferences concerning the shape of the marginal value functions and desired comprehensive values of alternatives assigned to a given class or class range the exploitation of all value functions compatible with these preferences results in three types of results 1 necessary and possible assignments 2 extreme class cardinalities and 3 necessary and possible assignment based preference relations these outputs correspond to different types of admitted preference information by exhibiting different outcomes we encourage the dm in various ways to enrich her his preference information interactively the applicability of the framework is demonstrated on data involving the classification of cities into liveability classes

multiple criteria sorting with a set of additive value functions we present a new multiple criteria sorting method that aims at assigning actions evaluated on multiple criteria to p pre defined and ordered classes the preference information supplied by the decision maker dm is a set of assignment examples on a subset of actions relatively well known to the dm these actions are called reference actions each assignment example specifies a desired assignment of a corresponding reference action to one or several contiguous classes the set of assignment examples is used to build a preference model of the dm represented by a set of general additive value functions compatible with the assignment examples for each action a the method computes two kinds of assignments to classes concordant with the dm s preference model the necessary assignment and the possible assignment the necessary assignment specifies the range of classes to which the action can be assigned considering all compatible value functions simultaneously the possible assignment specifies in turn the range of classes to which the action can be assigned considering any compatible value function individually the compatible value functions and the necessary and possible assignments are computed through the resolution of linear programs

preference programming with incomplete ordinal information abstract this paper extends possibilities for analyzing incomplete ordinal information about the parameters of an additive value function such information is modeled through preference statements which associate sets of alternatives or attributes with corresponding sets of rankings these preference statements can be particularly helpful in developing a joint preference representation for a group of decision makers who may find difficulties in agreeing on numerical parameter values because these statements can lead to a non convex set of feasible parameters a mixed integer linear formulation is developed to establish a linear model for the computation of decision recommendations this makes it possible to complete incomplete ordinal information with other forms of incomplete information

calculi for synchrony and asynchrony abstract a calculus for distributed computation is studied based upon four combinators a central idea is an abelian group of actions which models the interfaces between components of a distributed computing agent using a notion of bisimulation congruence relations are defined over computing agents and thence an algebraic theory is derived the calculus models both synchronous and asynchronous computation in particular it is shown that the author s calculus of communicating systems 1980 which is an asynchronous model is derivable from the calculus presented here

connections between two theories of concurrency metric spaces and synchronization trees a connection is established between the semantic theories of concurrency and communication in the works of de bakker and zucker who develop a denotational semantics of concurrency using metric spaces instead of complete partial orders and milner who develops an algebraic semantics of communication based upon observational equivalence between processes his rigid synchronization trees rsts are endowed with a simple pseudometric distance induced by milner s weak equivalence relation and the quotient space is shown to be complete an isometry between this space and the solution to a domain equation of de bakker and zucker is established presenting their solution in a conceptually simpler framework under an additional assumption the equivalence between the weak equivalence relation over rsts and the elementary equivalence relation induced by the sentences of a modal logic due to hennessy and milner is established

termination deadlock and divergence in this paper a process algebra that incorporates explicit representations of successful termination deadlock and divergence is introduced and its semantic theory is analyzed both an operational and a denotational semantics for the language is given and it is shown that they agree the operational theory is based upon a suitable adaptation of the notion of bisimulation preorder the denotational semantics for the language is given in terms of the initial continuous algebra that satisfies a set of equations e ci e it is shown that ci e is fully abstract with respect to our choice of behavioral preorder several results of independent interest are obtained namely the finite approximability of the behavioral preorder and a partial completeness result for the set of equations e with respect to the preorder

integrated framework for preference modeling and robustness analysis for outranking based multiple criteria sorting with electre and promethee a novel framework for preference modeling and robustness analysis is proposed we apply a sorting rule deriving from the semantic meaning of an outranking relation we ensure input output correspondence with respect to three sorting perspectives the generality of our framework is illustrated with its two specific implementations preference modeling can be simplified when using model instances providing precise assignments we introduce an integrated framework for preference modeling and robustness analysis in outranking based multiple criteria sorting the preference information supplied by the decision maker dm is composed of parts of desired recommendation and imprecise requirements that the delivered outcomes should satisfy its allowed forms are imprecise assignment examples desired class cardinalities and assignment based pairwise comparisons the exploitation of all instances of the outranking model compatible with these preferences results in three types of outcomes these raise robustness concerns in terms of the stability of a suggested assignment for each alternative an observed size of each class and a comparison between recommendation delivered for pairs of alternatives the correspondence between different types of inputs and outputs facilitates the dialogue with the dm and enhances her his confidence in the suggested recommendation while referring only to a semantic meaning of an outranking relation we present the procedures for translating the preference information into parameters of compatible outranking model instances and for deriving various kinds of sorting results then we implement this general framework in the context of outranking models specific for electre and promethee finally we show how preference modeling and robustness analysis can be performed and greatly simplified with a set of preference model instances providing precise assignments for the alternatives the framework proposed for this case is based on mixed integer linear programming milp being independent of the underlying model and method application of the approaches is demonstrated on the case of classifying polish research units into four quality classes