• Proposes efficient genetic algorithms for reducing inconsistency in pairwise comparison matrices. • Introduces one algorithm for quantitative and two for qualitative multiplicative comparisons. • Employs a distance-based inconsistency index for quantitative analysis. • Adapts suitable evaluation functions for qualitative (non-numeric) comparisons. • Illustrates the effectiveness of genetic algorithms, particularly in qualitative cases. This paper discusses inconsistency reduction in qualitative and quantitative multiplicative pairwise comparison matrices by applying efficient genetic algorithms in detail. Three new algorithms are presented and discussed. One for the classical quantitative multiplicative pairwise comparisons, and two for a formal version of qualitative pairwise comparisons. For the quantitative case, a distance-based inconsistency index (Koczkodaj’s index) is used. Moreover the effects of different factors on its efficiency and the quality of results are analyzed. For the qualitative case, no numbers are used, so evaluation functions are tailored to use qualitative relations. For both quantitative and qualitative cases, the genetic algorithms perform reliably, and in the qualitative case they show strong performance compared to the existing method we evaluated

Recent studies have uncovered security issues with most of the federated learning models. One common false assumption in the federated learning model is that participants are the attacker and would not use polluted data. This vulnerability enables attackers to train their models using polluted data and then send the polluted updates to the training server for aggregation, potentially poisoning the overall model. In such a setting, it is challenging for an edge server to thoroughly inspect the data used for model training and supervise any edge device. This study evaluates the vulnerabilities present in federated learning and explores various types of attacks that can occur. This paper presents a robust prevention scheme to address these vulnerabilities. The proposed prevention scheme enables federated learning servers to monitor participants actively in real time and identify infected individuals by introducing an encrypted verification scheme. The paper outlines the protocol design of this prevention scheme and presents experimental results that demonstrate its effectiveness.

A relationship between the classical multiplicative pairwise comparisons that are based on aijaji = 1, the additive model based on b i j +b j i = 1, and qualitative pairwise comparisons that uses the relations j, ¯, ¢, < and z, is discussed in detail.A special attention is paid to the concept of consistency and weights calculations.An on-line tool is also discussed.

This special issue presents selected papers from the 41st International Conference on Application and Theory of Petri Nets and Concurrency (Petri Nets 2020), which was organized by the LoVe (Logics and Verification) team of the computer science laboratory LIPN (Laboratoire dInformatique de Paris Nord), University Sorbonne Paris Nord, and CNRS, jointly with the members of the Paris region MeFoSy-LoMa group (Méthodes Formelles pour les Systemes Logiciels et Matériels) in June 2020.The conference took place online due to the covid pandemics.The Program Committee selected 23 out of 56 papers submitted to Petri Nets 2020 by authors from 21 different countries.Each paper was reviewed by three reviewers.After the conference, five papers were distinguished by the Program Committee members, whose authors were invited to revise and extend their conference papers for this special issue.The extended submissions have been reviewed in a separate reviewing process to meet the standards of Fundamenta Informaticae.

Relational structures based on acyclic relations can successfully model fundamental aspects of concurrent systems behaviour. Examples include Elementary Net systems and Mazurkiewicz traces. There are however cases where more general relational structures are needed. In this paper, we present a general model of relational structures which can be used for a broad class of concurrent behaviours. We demonstrate how this general set-up works for combined order structures which are based on two relations, viz. an acyclic ‘before’ relation and a possibly cyclic ‘not later than’ relation.

Traces and their extensions as comtraces, step traces and interval traces are quotient monoids over sequences or step sequences that play an important role in the formal analysis and verification of concurrent systems. Step traces are generalizations of comtraces and classical traces while interval traces are specialized traces that can deal with interval order semantics. The algebraic structures and their properties as projections, hidings, canonical forms and other invariants are very well established for traces and fairly well established for comtraces. For step traces and interval traces they are the main subject of this paper.

A representation of interval orders by sequences of antichains is discussed, and its relationship to the Fishburn’s representation by sequences of the beginnings and endings of domain elements is analysed in detail. Moreover, an operational semantics based on sequences of maximal antichains is prop osed and investigated for a general class of safe Petri nets with context arcs.

In the study of behaviours of concurrent systems, traces are sets of behaviourally equivalent action sequences. Traces can be represented by causal partial orders. Step traces, on the other hand, are sets of behaviourally equivalent step sequences, each step being a set of simultaneous actions. Step traces can be represented by relational structures comprising non-simultaneity and weak causality. In this paper, we propose a classification of step alphabets as well as the corresponding step traces and relational structures representing them. We also explain how the original trace model fits into the overall framework.

Organizations use data to support different business processes. Data may become unclean because of corruptions in the central quality aspects due to factors such as duplicate records, outdated data, inconsistent values, incomplete information, or inaccurate values. Real datasets are usually not available for reasons such as privacy constraints. In the existing systems that generate or corrupt synthetic data, the intrinsic characteristics of data may not satisfy the quality aspects, and the injected types of errors do not corrupt multiple data quality aspects. Also, a lack of common datasets is a primary reason that representative comparisons between algorithms of different data quality management approaches are not possible. To address these issues, we present datumPIPE, a system that allows for the generation of data that satisfies a set of integrity constraints, including functional dependencies (FDs), conditional functional dependencies (CFDs), and inclusion dependencies (INDs). Also, datumPIPE provides the functionality to generate other types of attribute values such as sensors and personal data. It also allows for the corruption of the generated data through the introduction of quality issues in the central data quality aspects.

A step trace is an equivalence class of step sequences, where the equivalence is determined by dependencies between pairs of actions expressed as potential simultaneity and sequentialisability. Step traces can be represented by invariant structures with two relations: mutual exclusion and (possibly cyclic) weak causality. An important issue concerning invariant structures is to decide whether an invariant structure represents a step trace over a given step alphabet. For the general case this problem has been solved and an effective decision procedure has been proposed. In this paper, we restrict the class of order structures being considered with the aim of achieving a better characterisation. Requiring that the weak causality relation is acyclic, makes it possible to solve the problem in a purely local way, by considering pairs of events, rather than whole structures.

A step trace is an equivalence class of step sequences which can be thought of as different observations of the same underlying concurrent history. Equivalence is determined on basis of a step alphabet that describes the relations between events in terms of potential simultaneity and sequentialisab ility. Step traces cannot be represented by standard partial orders, but require so-called invariant structures, extended order structures that capture the phenomena of mutual exclusion and weak causality. In this paper, we present an effective way of deciding whether an invariant structure represents a step trace over a given step alphabet. We also describe a method by which one can check whether a given invariant structure can represent a step trace over any step alphabet. Moreover, if the answer is positive, the method provides a suitable step alphabet.

Weights or weighted attributes are a part of most measurement, indexing and classification techniques.However, when judgments are subjective; weight assignment, and especially weight consistency, is almost always problematic.A ranking or preference is usually defined as a weakly ordered relationship between a set of items such that, for any two items, the first is either "less preferred", "more preferred" or "indifferent" to the second one.While most existing methods involve numbers, in many cases using only qualitative assessments might be more trustworthy.Formulas and rules involving numbers are considered more scientific and credible than those that involve qualitative values only.This is obviously true when the notions of interest can be measured directly or indirectly, as for instance velocity, height, voltage, pressure etc.However, when it comes to subjective notions as love, importance, taste, beauty, etc., we have to be very careful when numbers are used.One of the ways to deal with such intangible concepts is the pairwise comparisons method.This method is based on the observation that it is much easier to judge the mutual relationship (preference, importance, intensity, etc.) of two objects than to do this for several objects at once.This special issue of Fundamenta Informaticae is devoted to different aspects of the pairwise comparisons method.It is comprised of fourteen excellent articles that present the phenomenon of pairwise comparisons from various perspectives.The work, "Continuous Pairwise Comparisons" written by Thomas Saaty definitely goes far beyond currently ongoing discussions and opens up new horizons for researchers.In the article he proposes changing perspective from a discrete to a continuous one.The suggested solution is to determine the rankings for continuous pairwise comparisons based on solving Fredholm's integral equation of the second kind.In "Complex Ranking Procedures" the authors Barbara Sandrasagra and Michael Soltys investigate pairwise ranking problems where relatively few items are to be ranked with a complex procedure and according to a large number of criteria.They discuss their solutions in the context of tender procedures.Andrew Schumann and Jan Woleński enrich the discussion on pairwise comparisons methods by presenting their logical approach enclosed in the article "Two Squares of Oppositions and Their Applications in Pairwise Comparisons Analysis".

Most existing classification algorithms either consider all features as equally important (equal weights), or do not analyze the consistency of weights assigned to features. When features are not equally important, assigning consistent weights is not an obvious task. In general, we have two cases. The first case assumes that a given sample of data does not contain any clues about the importance of features, so the weights are provided by a pool of experts and they are usually inconsistent. The second case assumes that the given sample contains some information about feature importance, hence we can derive the weights directly from the sample. In this paper, we deal with both cases. Pairwise comparisons and weighted support vector machines (SVMs) are used for the first case. For the second case, a new approach based on the observation that the feature importance could be determined by the discrimination power of features has been proposed. For the first case, we start with pairwise comparisons to rank the importance of features, then we use distance-based inconsistency reduction to refine the weight assessment and make the comparisons more precise. Next, we calculate the weights through the fully consistent or almost consistent pairwise comparison tables. For the second case, a novel concept of feature domain overlappings has been introduced. It can measure the feature discrimination power. This model is based on the assumption that less overlapping means more discriminatory ability, and this can be used to calculate weights characterizing the importance of particular features. For both cases, weighted SVMs are used to classify the data. Both methods have been tested using two benchmark datasets, Iris and Vertebral. The results were especially superior to those obtained without weights.

Non-interleaving semantics of concurrent systems is often expressed using posets, where causally related events are ordered and concurrent events are unordered. Each causal poset describes a unique concurrent history, i.e., a set of executions, expressed as sequences or step sequences, that are consistent with it. Moreover, a poset captures all precedence-based invariant relationships between the events in the executions belonging to its concurrent history. However, concurrent histories in general may be too intricate to be described solely in terms of causal posets. In this paper, we introduce and investigate generalised mutex order structures which can capture the invariant causal relationships in any concurrent history consisting of step sequence executions. Each such structure comprises two relations, viz. interleaving/mutex and weak causality. As our main result we prove that each generalised mutex order structure is the intersection of the step sequence executions which are consistent with it.

The ninth International Conference on the Application of Concurrency to System Design (ACSD) was held in July 2009 in Augsburg, Germany.Following a tradition, Fundamenta Informaticae publishes a special issue with revised and extended versions of a selection of the best papers from ACSD.The current issue is the eighth special issue devoted to ACSD.ACSD serves as a forum for disseminating theoretical results with application potential and advanced methods and tools for the design of complex concurrent systems.The conference aims at cross-fertilizing both theoretical and applied research on the following topics:• design methods, tools and techniques based on models of computation and concurrency (dataflow models, communicating automata, Petri nets, process algebras, state charts, MSCs, etc.), (performance) analysis, verification, testing and synthesis;• hardware / software co-design, platform-based design, component-based design, refinement techniques, hardware / software abstractions, co-simulation and verification;

A systematic procedure for deriving weakly ordered non-numerical rankings from given sets of data is proposed and analysed. The data are assumed to be collected using the Pairwise Comparisons paradigm. The concept of a partially ordered approximation of an arbitrary binary relation is formally defined and some solutions are proposed. The problem of testing and the importance of indifference and the power of weak order extensions are also discussed.

The trace assertion method is a formal state machine based method for specifying module interfaces. A module interface specification treats the module as a black-box, identifying all the module's access programs (i.e., programs that can be invoked from outside of the module) and describing their externally visible effects. In the method, both the module states and the behaviors observed are fully described by traces built from access program invocations and their visible effects. A formal model for the trace assertion method is proposed. The concept of step-traces is introduced and applied. The stepwise refinement of trace assertion specifications is considered. The role of nondeterminism, normal and exceptional behavior, value functions, and multiobject modules are discussed. The relationship with algebraic specifications is analyzed. A tabular notation for writing trace specifications to ensure readability is adapted.

In the formal treatment of concurrent computing systems, causality and weak causality can be used to provide abstract specifications of the temporal ‘earlier than’ and ‘not later than’ orderings. In this paper we consider relational structures comprising causality and weak causality — called stratified order structures — which can be used to provide a non-sequential semantics of Petri nets with inhibitor arcs. We show that this approach can be extended to nets augmented with priority specifications. In particular, we demonstrate how to derive stratified order structures for such nets by generalising the standard construction of causal partial orders based on occurrence nets.

In [8, 11, 12] Parnas at al. advocate the use of relational model for documenting the intended behaviour of programs.In this method, tabular expressions (or tables) are used to improve readability so that formal documentation can replace conventional documentation.Parnas [9] describes several classes of tables and provides their formal syntax and semantics.In this paper, an alternative, more general and more homogeneous semantics is proposed.1