Basil K. Papadopoulos

• Professor
• Emeritus Professor at Democritus University of Thrace

The research aims to investigate the linear relationship between meteorological drought and groundwater levels of shallow wells, as well as the key role of geology in drought propagation, in terms of time, to groundwater. To achieve the study's objective, a modification of Tanaka's fuzzy linear regression model is suggested. In the evaluation proce...

In this work, a novel fuzzy FEM (Finite Elements Method) numerical solution describing the recession flow in unconfined aquifers is proposed. In general, recession flow and drainage problems can be described by the nonlinear Boussinesq equation, while the introduced hydraulic parameters (Conductivity K and Porosity S) present significant uncertaint...

In this paper, we present two new classes of fuzzy negations. They are an extension of a well-known class of fuzzy negations, the Sugeno Class. We use it as a base for our work for the first two construction methods. The first method generates rational fuzzy negations, where we use a second-degree polynomial with two parameters. We investigate whic...

In this research paper, a generator of fuzzy methods based on theorems and axioms of fuzzy logic is derived, analyzed and applied. The family presented generates fuzzy implications according to the value of a selected parameter. The obtained fuzzy implications should satisfy a number of axioms, and the conditions of satisfying the maximum number of...

In this research paper an algorithm for the derivation of methods based on theorems and axioms of fuzzy logic is presented, analyzed and applied. This new proposed procedure generates fuzzy methods and evaluates the value of fuzzy propositions through fuzzy implication. The new implications of the family should satisfy a number of axioms. Also, we...

Fuzzy logic is becoming one of the most-influential fields of modern mathematics with applications that impact not only other sciences, but society in general. This newly found interest in fuzzy logic is in part due to the crucial role it plays in the development of artificial intelligence. As a result, new tools and practices for the development o...

In this paper, we revisit the generalized Dishkant implications and provide analytical proof that they are a new fuzzy implications’ class that contains the known class of Dishkant implications. Both classes are not always fuzzy implications. For this reason we use the term operations instead of implications in general. Nonetheless, it will be demo...

The assessment of rocking response is a challenging task due to its high nonlinearity. The present study investigates two methodologies to evaluate finite rocking rotations and overturn of three typical rocking systems. In particular, fuzzy linear regression (FLR) with triangular fuzzy numbers and a hybrid model combining logistic regression and fu...

In this research, fuzzy linear regression (FLR) method combined with three well-known fuzzy implications was implemented for evaluating the relation among the amount of fly ash in concrete mixture and the compressive strength of concrete. More specifically, 267 experimental data 40 of which were used for testing the validation of the process were s...

This paper proposes an approach for generating operational preparedness drill scenarios accompanied by a safety competency evaluation process. The approach combines the “Engineering for Humans” extension of the STPA (Systems Theoretic Process Analysis) hazard analysis introduced by France (2017) to identify causal scenarios incorporating human beha...

Determination of criteria's weights both based on the intuitionistic fuzzy sets approach, and in particular the intuitionistic fuzzy weighted averaging operator (IFWA), and on the graph theory approach using the DEMATEL method.

In this paper, generalized R'-implications are introduced and studied. Although they are not always fuzzy implications, the sufficient and necessary condition such that a generalized R'-operation is a fuzzy implication is discovered and proved. The satisfaction or violation of some basic properties of fuzzy implications, such as the left neutrality...

In this study is presented the influence of classical mathematical logic on the fuzzy logic and in the foundation of its basic operations. This effect is documented through the extensive presentation of generalizations of tautologies from classical logic to fuzzy logic that have been published until recently.

The process of how soil moisture profiles evolve into the soil and reach the root zone could be estimated by solving the appropriate strong nonlinear Richards’ equation. The nonlinearity of the equation occurs because diffusivity D is generally an exponential function of water content. In this work, the boundary conditions of the physical problem a...

Image conversion of malicious binaries, or binary visualisation, is a relevant approach in the security community. Recently, it has exceeded the role of a single-file malware analysis tool and has become a part of Intrusion Detection Systems (IDSs) thanks to the adoption of Convolutional Neural Networks (CNNs). However, there has been little effort...

In this paper, the solution of the one-dimensional second-order unsteady nonlinear fuzzy partial differential Boussinesq equation is examined. The physical problem concerns unsteady flow in a semi-infinite unconfined aquifer bordering a lake. In the examined problem, there is a sudden rise and subsequent stabilization of the lake's water level, thu...

In this paper we introduce the GD- operations, and we prove that they are a hyper class of the known D- operations, but not always fuzzy implications. Nevertheless, a necessary, but not sufficient condition for a GD- operation to be a fuzzy implication, will be proved. Moreover, we prove a theorem for Φ- conjugation in GD- operations.

In this paper, we introduce and study the GQL′-operations. We prove that this class is a hyper class of the known class of QL′-operations. Similar to QL′-operations, GQL′-operations are not always fuzzy implications. On the other hand, we present and prove a necessary but not sufficient condition that leads to the generation of a GQL′-implication....

The first person to introduce possibility theory was Lotfi A. Zadeh, in 1977. It was, of course, of no coincidence that he directly combined it with the theory of fuzzy sets. Later, several researchers dealt with the mathematical foundations of the theory of possibilities. They introduced possibility distribution as a concept, and they directly com...

Α new hybrid fuzzy probabilistic approach for the analysis and classification of meteorological and hydrological drought

The RealTSL methodology is based on STAMP and aims at determining the safety level of complex systems in real-time. RealTSL utilizes accident scenarios derived from STPA, together with: (a) The time durations required between system state transitions, (b) Managerial decisions regarding the sensitivity of the mathematical model, and (c) Real-time sy...

Fuzzy logic, during recent decades, has evolved into one of the most influential scientific fields. To an extent, this is due to its applications which have a profound impact on the daily life of people worldwide. The goal of this paper is to focus on the applications of fuzzy logic to the study of our climate, and especially if fuzzy implications...

In this article, we develop new constructed methods with specific conditions. The first method is a generalization of convex combination using n fuzzy implications. The second method is a parameterization of Lukasiewicz implication in an Ordering Property (OP) fuzzy implication form. The innovation in this work is the presentation of three new cons...

Image conversion of byte-level data, or binary visualisation, is a relevant approach to security applications interested in malicious activity detection. However, in practice, binary visualisation has always been seen to have great limitations when dealing with large volumes of data, and would be a reluctant candidate as the core building block of...

This paper is centered around the creation of new fuzzy connectives using automorphism functions. The fuzzy connectives theory has been implemented in many problems and fields. In particular, the N-negations, t-norms, S-conorms and I-implications concepts played crucial roles in forming the theory and applications of the fuzzy sets. Thus far, there...

Lightweight foamed concrete is defined as one of the most broadly implemented sustainable material in the construction of buildings. Due to its properties, it has been commonly applied in structural design providing energy conservation and excellent durability and functional properties. This paper describes the characteristics of lightweight foamed...

This study proposes a hybrid fuzzy multi-criteria methodology for the selection of the most preferable site for applying managed aquifer recharge (MAR) systems by utilizing floodwaters. The use of MAR can increase water resources for later water utilization in case of drought. In this multi-criteria problem, seven recharge sites are under considera...

The paper introduces a method for the construction of bivariate copulas with the usage of specific values of the parameters α and β (α,β transformation) and the parameters κ and λ in their domain. The produced bivariate copulas are defined in four subrectangles of the unit square. The bounds of the produced copulas are investigated, while a novel c...

The book starts with the assumption that vagueness is a fundamental property of this world. From a philosophical account of vagueness via the presentation of alternative mathematics of vagueness, the subsequent chapters explore how vagueness manifests itself in the various exact sciences: physics, chemistry, medicine, computer science, and engineer...

The fuzzy hypotheses testing is based on critical values and fuzzy test statistics produced by fuzzy estimators. This approach is particularly useful in critical situations, where subtle comparisons between almost equal statistical quantities have to be made. In such cases the fuzzy hypotheses tests give better results than the crisp ones, since th...

Data centres are experiencing significant growth in their scale, especially, with the ever-increasing demand for cloud and IoT services. However, this rapid growth has raised numerous security issues and vulnerabilities; new types of strategic cyber-attacks are aimed at specific physical components of data centres that keep them operating. Attacks...

In this paper, we introduce and study the GD'-operations, which are a hyper class of the known D'-operations. GD'-operations are in fact D'-operations, that are generated not only from the same fuzzy negation. Similar with D'-operations, they are not always fuzzy implications. Nevertheless, some sufficient, but not necessary conditions for a GD'-op...

This paper studies, through the principles of fuzzy set theory, groundwater response to meteorological drought in the case of an aquifer system located in the plains at the southeast of Xanthi, NE Greece. Meteorological drought is expressed through standardized Reconnaissance Drought Index (RDISt) and Standardized Precipitation Index (SPI), which a...

Vehicle automation holds significant opportunities in the efforts for safer road traffic. Even lower levels of automation like adaptive cruise control (ACC) systems have great potential. Apart from safety benefits, ACC systems could improve the efficiency of traffic networks. However, contemporary ACC systems are designed to be comfortable, but not...

In this paper, we revisit and study the basic properties of two families of fuzzy implications, the so-called (T,N)− and (N′,T,N)− implications. More specific, we study when these fuzzy implications satisfy, or not, the neutrality property (NP), the exchange principle (EP), the identity principle (IP) and the ordering property (OP). Moreover, a stu...

In this paper, we develop fuzzy, possibilistic hypothesis tests for testing crisp hypotheses for a distribution parameter from crisp data. In these tests, fuzzy statistics are used, which are produced by the possibility distribution of the estimated parameter, constructed by the known from crisp statistics confidence intervals. The results of these...

Dataset including over 40,000 generated images of malicious binaries for malware classification in machine learning as outlined in NARAD - A Novel Auto-learn Real-time Fuzzy Machine Learning Anomaly Detection and Classification System.

The trophic state of an aquatic body is influenced by many biotic and abiotic factors. When lots of parameters affect a phenomenon, such as eutrophication, it is difficult to distinguish which are the ones that affect the ecosystem the most. In this paper, we propose an alternative way for data analysis, in order to avoid complex systems with many...

In this paper, we present a new Fuzzy Implication Generator via Fuzzy Negations which was generated via conical sections, in combination with the well-known Fuzzy Conjunction. The new Fuzzy Implication Generator takes its final forms after being configured by the fuzzy strong negations and combined with the most well-known fuzzy conjunctions TM, TP...

Data centres are experiencing significant growth in their scale, especially, with the ever-increasing demand for cloud and IoT services. However, this rapid growth has raised numerous security issues and vulnerabilities; new types of strategic cyber-attacks are aimed at specific physical components of data centres that keep them operating. Attacks...

This study aims to assess the short-term response of groundwater to the main hydro-meteorological variables of drought in a coastal unconfined aquifer. For this purpose, a multiple fuzzy linear regression-based methodology is implemented in order to relate rainfall, streamflow and the potential evapotranspiration to groundwater. Fuzzy regression an...

The major drawback of the classic approaches for project appraisal is the lack of the possibility to handle change requests during the project’s life cycle. This fact incorporates the concept of uncertainty in the estimation of this investment’s worth. To resolve this issue, the authors use fuzzy numbers, possibilistic moments of fuzzy numbers and...

The crucial role that fuzzy implications play in many applicable areas was our motivation to revisit the topic of them. In this paper, we apply classical logic’s laws such as De Morgan’s laws and the classical law of double negation in known formulas of fuzzy implications. These applications lead to new families of fuzzy implications. Although a du...

The present paper discusses two fuzzy Surrogate Safety Metrics (SSMs) for rear-end collision, the Proactive Fuzzy SSM (PFS) and Critical Fuzzy SSM (CFS). The objective is to investigate their applicability for evaluating the real-time rear-end risk of collision of vehicles to support the operations of advanced driver assistance and automated vehicl...

In this paper we present five construction machines of generating fuzzy implications. In these formulas we present some examples by using known fuzzy implications and fuzzy negation as well and increasing function. Through these new formulas, we study the natural propagation of basic properties of given fuzzy implications from the initial ones to t...

Fuzzy implications are widely used in applications where propositional logic is applicable. In cases where a variety of fuzzy implications can be used for a specific application, it is important that the optimal candidate to be chosen in order valuable inference to be drawn for a given set of data. This study introduces a method for detecting the m...

In this article, an adjustment of the extreme theoretical probability distributions upon the sample is proposed, based on the conventional fuzzy linear regression model of Tanaka [1], where all the data must be included within the produced fuzzy band. This is achieved by using the quintile approach, which relates the observed return period with the...

In this paper, the prediction of compressive cement strength using the fuzzy linear regression (FLR) and adaptive neuro-fuzzy inference system (ANFIS) methods was studied. Specifically, an accurate prediction method is needed as the modeling of cement strength is a difficult task, which is based on its composite nature. However, many approaches are...

The aim of this research is to apply mathematical models for the solution of the one-dimensional convective–dispersive solute transport equation. For the derivation of the advection–dispersion equation it is assumed that the flow in the medium is unidirectional and that the average velocity is constant throughout the length of the flow field. Moreo...

In this paper, we develop a novel computation model of Intuitionistic Fuzzy Values with the usage of fuzzy negations and Archimedean copulas. This novel computation model’s structure is based on the extension of the existing operations of intuitionistic fuzzy values with some classes of fuzzy negations. Many properties of the proposed operations ar...

In this article, an adjustment of the extreme theoretical probability distributions upon the sample is proposed based on the conventional fuzzy linear regression model of Tanaka [1] where all the data must be included within the produced fuzzy band. This is achieved by using the quintile approach which relates the observed return period with the th...

In this article, an adjustment of the extreme theoretical probability distributions upon the sample is proposed based on the conventional fuzzy linear regression model of Tanaka [1] where all the data must be included within the produced fuzzy band. This is achieved by using the quintile approach which relates the observed return period with the th...

Most prediction outputs from regression models are either point estimates or interval estimates. Point estimates from a model are useful for making conclusions about model accuracy. Interval estimates on the other-hand are used to evaluate the uncertainty in the model predictions. These two approaches only produce either point or a single interval...

An advantage of the probabilistic approach is the exploitation of the observed probability values in order to test the goodness-of-fit for the examined theoretical probability distribution function (pdf). Since, in fact, the interest of the engineers is to achieve a relation between the hydrological variable and the corresponding probability which...

In this paper, we introduce a new construction method of a fuzzy implication from n increasing functions gi:0,1⟶0,∞, (g0=0) (i=1,2,…,n, n ∈N) and n+1 fuzzy negations Ni (i=1,2,…,n+1, n ∈N). Imagine that there are plenty of combinations between n increasing functions gi and n+1 fuzzy negations Ni in order to produce new fuzzy implications. This meth...

In fuzzy hypothesis testing we use fuzzy test statistics produced by fuzzy estimators and fuzzy critical values. In this paper we use the non-asymptotic fuzzy estimators in fuzzy hypothesis testing. These are triangular shaped fuzzy numbers that generalize the fuzzy estimators based on confidence intervals in such a way that eliminates discontinuit...

In this paper, we investigate a special case of an open problem that is related to the exchange principle, a property of fuzzy implications. We focus on the cases of (S,N)– implications and the preservation of the exchange principle via lattice operations. We present and prove some sufficient conditions such that the exchange principle is preserved...

In this paper we present a new Fuzzy Implication Generator via Fuzzy Negations which was generated via conical sections, in combination with the well-known Fuzzy Conjunction T-norm = min. Among these implications we choose the most appropriate one, after comparing them with the empiristic implication, which was created with the help of real tempera...

Fuzzy logic is an innovative scientific field with several successful applications. Genetic algorithms and fuzzy logic systems fusion provide real-world problems modeling through the development of intelligent and adaptive systems. Moreover, the statistical analysis of the epidemiology of infectious diseases, which combines fuzzy logic aspects, is...

The fusion of artificial neural networks and fuzzy logic systems allows researchers to model real-world problems through the development of intelligent and adaptive systems. Artificial neural networks are able to adapt and learn by adjusting the interconnections between layers, while fuzzy logic inference systems provide a computing framework based...

The effect of eutrophication is characterized by dense algal and plant growth due to the enrichment of nutrients for photosynthesis. As a result, it often plays an important role to the formation of plants that float in the surface of a water body. When nutrients are increasing in aquatic ecosystems, the photosynthetic plants grow rapidly. As a res...

In this paper we introduce a new method of generating fuzzy implications via known fuzzy implications. We focus on the case of generating fuzzy implications via a fuzzy connective and at least one known fuzzy implication. We present some basic desirable properties of fuzzy implications that are invariant via this method. Furthermore, we suggest som...

In this paper, we propose a fuzzy logic–based mathematical model of a sequence of earthquakes using fuzzy reasoning tools. We formed a set of fuzzy implications in order to study them, and we computed their deviation, so that we could compare them and conclude about the most accurate one. The compositional rule of inference was considered, which is...

This paper proposes a novel approach to dynamic safety level calculation for safety-critical systems based on the STAMP accident model and the implementation of a mathematical model. The proposed approach utilises (1) an STPA hazard analysis applied to the system in question, (2) system operational data from domain experts regarding process duratio...

This paper proposes a fuzzy version of the Streamflow Drought Indices (SDI) for the overlapping periods of 3, 6, 9 and 12 months within an examined hydrological year. SDI is based on the cumulative streamflow volume and is analogous to Standardized Precipitation Index (SPI). According tothe methodology of fuzzy estimators, standard deviation and me...

There are applications in which the content of a scanned document needs to be recognized or improved. We often achieve this by converting our input into a binary image and this is in fact the first step in many document analysis systems or optical character recognition (OCR) processes. In cases where our input is degraded or has a non-uniform illum...

Ο σκοπός της παρούσας έρευνας είναι η ανάπτυξη μαθηματικών εργαλείων για την εκτίμηση της αντοχής σε ποικιλία εδαφών ενισχυμένων με ίνες κυκλικής διατομής. Σε αυτή την προσπάθεια, δημιουργήθηκε μια βάση δεδομένων με χρήση της διεθνούς βιβλιογραφίας, στην οποία περιλήφθηκαν τα πειραματικά δεδομένα από δοκιμές άμεσης διάτμησης και τριαξονικής φόρτιση...

The combination of Artificial Neural Networks and Fuzzy Logic Systems enables the representation of real-world problems via the creation of intelligent and adaptive systems. By adapting the interconnections between layers, Artificial Neural networks are able to learn. A computing framework based on the concept of fuzzy set and rules as well as fuzz...

In this work, a hybrid fuzzy-probabilistic approach is proposed in order to classify the hydrological drought. The analysis focuses on the annual cumulative discharge which is considered to be a random variable. Based on a fuzzified version of the frequency factor method, the fitting between the empirical probabilities and the theoretical probabili...

As a variable system, the Lake of Kastoria is a good example regarding the pattern of the Mediterranean shallow lakes. The focus of this study is on the investigation of this lake’s eutrophication, analyzing the relation of the basic factors that affect this phenomenon using fuzzy logic. In the method we suggest, while there are many fuzzy implicat...

Drought is a complicated natural extreme event associated with the decline of water availability below the normal conditions of a hydrological system, both from a temporal and from a spatial point of view. This work aims to assess the drought impacts on groundwater fluctuation in a shallow coastal unconfined aquifer via a fuzzy approach. Meteorolog...

In this paper we propose a method for choosing the most appropriate fuzzy implication from a set of implications, using a set of data. To achieve this choice we use the compositional rule of inference which is based on the generalized modus pones (G.M.P) logical scheme.

In this work we revisit the subject of a seismic sequence but we use new innovative tools and so the conclusions extracted are more precise and more close to reality. Assuming that the major earthquake in a specified region has a certain intensity level, we study all the earthquakes, which follow, according to their magnitude and to the time differ...

In this paper we suggest a method of generating new implications from a given one. This can be achieved using an arbitrary negation with a simple way. Those implications which are generated in this way satisfy many important properties. A guide in the above process is the ability of fuzzy negation to preserve the basic qualities of fuzzy implicatio...

The rise of automation and connectivity crates new challenges for road safety. Vehicles equipped with a sophisticated network of sensors and controllers that can take over a part of the driving function are already available in the market. Furthermore, it is projected that in the future the majority of the vehicle fleet will be fully automated vehi...

The determination of the optimal path is a mathematical combinatorial optimization problem for which several deterministic and heuristic methods have been developed in recent years, applicable to route organization issues, passenger transport, storage and distribution of goods, waste collection, supply and control terminals, etc. Scope of the prese...

Fuzzy linear regression and crisp linear regression are different models which have different assumptions. Crisp linear regression makes statistical assumptions about model or data due to randomness while fuzzy linear regression on the other hand is a method which considers the vagueness or imprecision in data or model specification of a linear reg...

Drought is a natural phenomenon characterised by a significant decrease of water availability during a significant period of time and over a large area (Nalbantis and Tsakiris 2009). Drought is in fact, a relative, rather than absolute, condition. It occurs either in areas with significant rainfall, or in areas with low rainfall and virtually under...

In this study, we propose the Real-Time Safety Level (RealTSL) mathematical model for safety critical systems’ safety level determination during their operation, and its dynamic calculation, based on the STAMP accident model. The proposed model utilizes the outcome of an STPA hazard analysis to construct acyclic diagrams composed of nodes and lines...

In this note we support that the $5$-dimensional ``ambient cosmology'' does not appear to be necessary, neither is required to the scope of avoiding spacetime singularities. This scope can be reached with other, purely topological instruments, without postulating extra dimensions.

Maintaining safety into acceptable levels is among the major managerial concerns in many industries. To address this concern several safety indicators are used to monitor safety drifts about major hazards. Numerous categories of safety indicators have been proposed in the literature such as event indicators, barrier indicators, activity indicators,...

A list of all possible causal relations in the $2$-dimensional Minkowski space $M$ is exhausted, based on the duality between timelike and spacelike in this particular case, and thirty topologies are introduced, all of them encapsulating the causal structure of $M$. Generalisations of these results are discussed, as well as their significance in a...

We give a topological condition for a generic sliced space to be globally hyperbolic without any hypothesis on lapse function, shift function, and spatial metric.

Thresholding algorithms segment an image into two parts (foreground and background) by producing a binary version of our initial input. It is a complex procedure (due to the distinctive characteristics of each image) which often constitutes the initial step of other image processing or computer vision applications. Global techniques calculate a sin...

In this article we first observe that the Path topology of Hawking, King and MacCarthy is an analogue, in curved spacetimes, of a topology that was suggested by Zeeman as an alternative topology to his so-called Fine topology in Minkowski spacetime. We then review a result of a recent paper on spaces of paths and the Path topology, and see that the...

The value of travel time savings (VOTTS) is one of the most important variables for calculating the benefits of transportation projects. However, the way it is currently calculated (usually via discrete choice models) is complex, tedious and subject to a reasonable level of uncertainty. Furthermore, the method is not easily understood by government...

We give a topological condition for a generic sliced space to be globally hyperbolic, without any hypothesis on the lapse function, shift function and spatial metric.

The poem Helen of the Nobel laureate George Seferis was inspired by the anti war play Helen of Euripides. In his poem, Seferis empathizes with the hero of the tragedy, Teucer, who opposed the involvement of The Gods in the lives of the humans, posing unanswered and contradictory questions. With the verse What is god; What is not a god; what is ther...

The group of homothetic symmetries in the conformal infinity (the $4$-dimensional "ambient boundary") of a $5$-dimensional spacetime restricts the choice of topology to a topology under which the group of homeomorphisms of a spacetime manifold is the group of homothetic transformations. Since there are such spacetime topologies in the class of Zeem...

In this article, the solution to the fuzzy second order unsteady partial differential equation (Boussinesq equation) is examined, for the case of an aquifer recharging from a lake. In the examined problem, there is a sudden rise and subsequent stabilization of the lake’s water level, thus the aquifer is recharging from the lake. The aquifer boundar...

In this presentation, we continue and expand our previous work on fuzzy subsethood and entropy measures. After a minor alteration to the axioms of fuzzy inclusion, we are able to produce new possible fuzzy inclusion and entropy indicators. We believe that these measures could be used in applications which require or properly exploit fuzzy inclusion...