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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 which of these two conditions must be satisfied to be a fuzzy negation. In the second method, we use an increasing function instead of the parameter δ of the Sugeno class. In this method, using an arbitrary increasing function with specific conditions, fuzzy negations are produced, not just rational ones. Moreover, we compare the equilibrium points of the produced fuzzy negation of the first method and the Sugeno class. We use the equilibrium point to present a novel method which produces strong fuzzy negations by using two decreasing functions which satisfy specific conditions. We also investigate the convexity of the new fuzzy negation. We give some conditions that coefficients of fuzzy negation of the first method must satisfy in order to be convex. We present some examples of the new fuzzy negations, and we use them to generate new non-symmetric fuzzy implications by using well-known production methods of non-symmetric fuzzy implications. We use convex fuzzy negations as decreasing functions to construct an Archimedean copula. Finally, we investigate the quadratic form of the copula and the conditions that the coefficients of the first method and the increasing function of the second method must satisfy in order to generate new copulas of this form. [ABSTRACT FROM AUTHOR]

The class of Zeeman topologies on spacetimes in the frame of relativity theory is considered to be of powerful intuitive justification, satisfying a sequence of properties with physical meaning, such as the group of homeomorphisms under such a topology is isomorphic to the Lorentz group and dilatations, in Minkowski spacetime, and to the group of homothetic symmetries in any curved spacetime. In this article, we focus on two distinct topologies that were suggested by Zeeman as alternatives to his fine topology, showing their connection with two orders, ie, a timelike and a (noncausal) spacelike one. For the (noncausal) spacelike order, we introduce a partition of the null cone, which gives the desired topology invariantly from the choice of the hyperplane of partition. In particular, we observe that these two orders induce topologies within the class of Zeeman topologies, while the two suggested topologies by Zeeman himself are intersection topologies of these two order topologies (respectively) with the manifold topology. We end up with a list of open questions and a discussion, comparing the topologies with bounded against those with unbounded open sets and their possible physical interpretation. [ABSTRACT FROM AUTHOR]

Program (or project) evaluation review technique (PERT) has remained a modern method in project scheduling for decades. Since its invention, numerous authors have tried modifications to its basic method in an attempt to overcome its intrinsic drawbacks. In this paper, the authors research improvements to the Fuzzy version of PERT. The initial motivation is the avoidance of the backward recursion problem in Fuzzy PERT, with fuzzy input data for the task durations through an alternative approach. Furthermore, the authors propose various membership functions for the representation of the fuzzy task duration in accordance with the nature of each task. This approach is intended to give more realistic results. The tools for this operation are the possibilistic mean and the possibilistic variance of fuzzy numbers. The possibilistic method acts as a defuzzification method that results in a crisp value as an outcome both for the task times (earliest/latest start - earliest/latest finish) and for the floats (total/free/safety). The authors also base this study on estimates of experts in project scheduling who are experienced in time management. A practical application is also provided for a better comprehension of the proposed method. [ABSTRACT FROM AUTHOR]

Taking into account the intrinsic drawbacks of both classic and fuzzy PERT, the authors present a new approach in an attempt to deal with them. The tools for this approach are fuzzy statistics and fuzzy probabilities. A necessary condition for this approach is the existence of statistical data for the project activity duration. The final findings are the fuzzy activity times (earliest/latest start - earliest/latest finish), the fuzzy float, the Criticality Degree both for each activity and for each path, a fuzzy probability for the activity duration to be in a certain time interval and a fuzzy probability for the project completion time to be in certain time interval. A numerical example is provided for thorough comprehension. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we present an application of a new method of constructing fuzzy estimators for the parameters of a given probability distribution function, using statistical data. This application belongs to the financial field and especially to the section of financial engineering. In financial markets there are great fluctuations, thus the element of vagueness and uncertainty is frequent. This application concerns Theoretical Pricing of Options and in particular the Black and Scholes Options Pricing formula. We make use of fuzzy estimators for the volatility of stock returns and we consider the stock price as a symmetric triangular fuzzy number. Furthermore we apply the Black and Scholes formula by using adaptive fuzzy numbers introduced by Thiagarajah et al. [K. Thiagarajah, S.S. Appadoo, A. Thavaneswaran, Option valuation model with adaptive fuzzy numbers, Computers and Mathematics with Applications 53 (2007) 831–841] for the stock price and the volatility and we replace the fuzzy volatility and the fuzzy stock price by possibilistic mean value. We refer to both cases of call and put option prices according to the Black & Scholes model and also analyze the results to Greek parameters. Finally, a numerical example is presented for both methods and a comparison is realized based on the results. [Copyright &y& Elsevier]

Abstract: In this paper our intention is to demonstrate the applicability of fuzzy difference equations in the field of finance. In order to achieve that, we follow the work done by Deeba et al. and Papashinopoulos et al. and we study the existence of positive solutions to fuzzy financial difference equations. Initially, we appose a method realized by Buckley that deals with fuzzy analogues of the elementary compound interest problem. Afterwards we approach this case via the fuzzy difference equations method. After making a comparison between the two methods we notice that they end up to the same general formula. The main contribution of this paper is the simplicity of the method presented, which gives us the opportunity to create formulas for cases, which are specialized and also more realistic than the very basic one of the compound interest. Moreover, by using difference equations we can study the “factors”, which cause the change in the value of money, in different time periods. As a source for these cases of finance we use the work of Kwapisz and we study a well-known problem of financial mathematics. This problem deals with the time value of money and as a direct application of it we study the balance of bank deposits. Finally, a numerical example is presented for better understanding. [Copyright &y& Elsevier]

In this paper we introduce a specific method, which is based on generalized modus ponens and generalized modus tollens, for introducing an ordering relation on the set of fuzzy implications. The existence of an ordering relation between fuzzy implications helps us to order fuzzy implications in a more powerful and/or more functional classes. We believe that, apart from the theoretical interest, this method appears to have interesting applications. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we propose a computational method to evaluate the arithmetic operations on fuzzy numbers with nonlinear membership functions. The simplicity and the overall effectiveness in the implementation are the attractions of the method and this is shown by some numerical examples. [Copyright &y& Elsevier]

The relationships between “two-sided” categorical models of linear logic and Goguen sets is investigated. In particular, we show that only certain Goguen sets can be represented as Chu spaces, while it is possible to represent any Goguen set as a Dialectica space. In addition, we discuss the benefits of these representations. [Copyright &y& Elsevier]

In this paper we study the existence the boundedness and the asymptotic behavior of the positive solutions of the fuzzy equation xn+1=A+xn/xn−m, n=0,1,… where xn is a sequence of fuzzy numbers, A is a fuzzy number and m∈{1,2,…}. [Copyright &y& Elsevier]

Chu spaces, which derive from the Chu construct of *-autonomous categories, can be used to represent most mathematical structures. Moreover, the logic of Chu spaces is linear logic. Most efforts to incorporate fuzzy set theory into the realm of linear logic are based on the assumption that fuzzy and linear negation are identical operations. We propose an incorporation based on the opposite assumption and we provide an interpretation of some linear connectives. Furthermore, we show that it is possible to represent any fuzzy relational structure as a Chu space by means of the functor G. [ABSTRACT FROM AUTHOR]

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 hybrid (fuzzy statistic) fuzzy estimators' method in order to introduce a fuzzy possibilistic version of the expanded net present value method (FPeNPV). This approach consists of two factors: the fuzzy possibilistic NPV and the fuzzy option premium. For the estimation of the fuzzy NPV, some basic assumptions are taken into consideration: (1) the opportunity cost of capital, used as the present value interest factor calculated through the weighted average cost of capital (WACC), (2) the equity cost, determined through the possibilistic set-up of the capital asset pricing model CAPM, and (3) the inflation factor, also included in the estimation of the NPV. The fuzzy estimators' method is used for the computation of the fuzzy option premium. An algorithm of nine major steps leads to the computation of the FPeNPV. This gives the administration the opportunity to adapt to potential changes in the company's internal and external environments. In this way, the symmetry between the planning and execution phase of a project can be reinstated. The results validate the statement that fuzzy and intelligent methods remain valuable tools to express uncertainty in various scientific areas. Finally, an illustrative example aims at a thorough comprehension of this new approach of the expanded NPV method. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new construction method of a fuzzy implication from n increasing functions g i : [ 0 , 1 ] → [ 0 , ∞) ,   (g (0) = 0) ( i = 1 , 2 , ... , n ,   n   ∈ ℕ ) and n + 1 fuzzy negations N i ( i = 1 , 2 , ... , n + 1 ,   n   ∈ ℕ ). Imagine that there are plenty of combinations between n increasing functions g i and n + 1 fuzzy negations N i in order to produce new fuzzy implications. This method allows us to use at least two fuzzy negations N i and one increasing function g in order to generate a new fuzzy implication. Choosing the appropriate negations, we can prove that some basic properties such as the exchange principle (EP), the ordering property (OP), and the law of contraposition with respect to N are satisfied. The worth of generating new implications is valuable in the sciences such as artificial intelligence and robotics. In this paper, we have found a novel method of generating families of implications. Therefore, we would like to believe that we have added to the literature one more source from which we could choose the most appropriate implication concerning a specific application. It should be emphasized that this production is based on a generalization of an important form of Yager's implications. [ABSTRACT FROM AUTHOR]

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 some ways of preservation or violation of these properties, based in this method. We show how we can generate not greater or not weaker fuzzy implications with specific properties. Finally, two subclasses of any fuzzy implication arise, the so called T and S subclasses. [ABSTRACT FROM AUTHOR]

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 variables. For the examined Mediterranean shallow lake, the studied parameters are water temperature (°C), ammonia (NH4‐N) (mg/L), dissolved oxygen (mg/L), turbidity (NTU), pH, conductivity (mS/cm), and chlorophyll‐a (μg/L). We formed groups with the variables above based on fuzzy equivalence relations and from each group we chose the parameter influence the studied phenomenon the most. Numerical results of fuzzy linear regression showed strong agreement with the proposed method above and pH, NH4‐N, and dissolved oxygen are the variables influence this ecosystem more than the others. Practitioner points: When having many parameters in a studied ecosystem, we propose a way we can distinguish the most representative ones, the parameters that influence more the phenomenon we study each time.Formation of groups in variables can be applied to many case studies in order to have a clear idea of our data and the relevance of each of them in our dependent one.Fuzzy linear regression can be used in order to check the final results and ensure that the equivalence relations are a such a good method used in the data analysis while the researchers save time in long procedures of analyzing parameters not very close involved to the phenomenon investigated every time. [ABSTRACT FROM AUTHOR]

In this paper, we first correct a recent misconception about a topology that was suggested by Zeeman as a possible alternative to his fine topology. This misconception appeared while trying to establish the causality in the ambient boundary-ambient space cosmological model. We then show that this topology is actually the intersection topology (in the sense of Reed [The intersection topology w.r.t. the real line and the countable ordinals, Trans. Am. Math. Soc. 297(2) (1986) 509-520]) between the Euclidean topology on and the order topology whose order, namely horismos, is defined on the light cone and we show that the order topology from horismos belongs to the class of Zeeman topologies. These results accelerate the need for a deeper and more systematic study of the global topological properties of spacetime manifolds. [ABSTRACT FROM AUTHOR]

In this note, we support that the five-dimensional "ambient cosmology" does not appear to be necessary, neither is required for the scope of avoiding spacetime singularities. This scope can be reached with other, purely topological instruments, without postulating extra dimensions. [ABSTRACT FROM AUTHOR]

• Calculating the Safety Level of a system using a mathematical model. • Implementing the severity of accidents to the calculations of the Safety Level. • Assisting decision makers in maintaining safety in acceptable levels. • Utilizing a new accident causation model based on systems theory. 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 system data. This manuscript proposes an extension of the RealTSL mathematical model that allows analysts to distinguish system-level accidents according to their severity, and introduces a new expression of the safety level. In addition, this paper shows how the information contained in the graphical form of the acyclic diagram can be used as an interface so that managers can: (a) Comprehend the current systems state against possible accidents, (b) Interpret the results of the mathematical model, and (c) Help them decide whether mitigation actions are needed. The safety level of a system in time t, therefore, is defined as SL = p → w A i > p → w A j > ⋯ > p → w A m ordering, where m is the number of system accidents and p → w A i are the most detrimental to safety sequences of safety constraint violations for every accident and ordered according to the severity of their corresponding accidents. The extended mathematical model is demonstrated using a fictitious system, providing a graphic rendition of how unsafe situations progress to accidents through time. This paper aims to open a new perspective in the STAMP literature, on discussions on the problem of measuring what the actual safety level of a system is at a certain moment in time and in a certain context. [ABSTRACT FROM AUTHOR]

One-dimensional injection tests were conducted on sand columns with a height of 134 cm for the penetrability evaluation of microfine cement grouts. Three ordinary cement types were pulverized to obtain microfine cements having nominal maximum grain sizes of 20 and 10 μm, and these cements were used in the present investigation. Suspensions with water to cement ( W/ C) ratios of 1, 2, and 3, by weight, were injected into 13 clean sands with d15 ranging from 0.17 to 2.25 mm and Cu ranging from 1.19 to 6.67. Pulverization of the ordinary cements to produce microfine cements extends the range of groutable sands to 'medium-to-fine'. Cement fineness; suspension W/ C ratio and apparent viscosity; and sand grain size, gradation, and relative density are very important parameters, as they substantially affect both grout penetration and maximum injection pressure. The penetration length of cement grouts was correlated to parameters pertinent to the suspension, sand, and injection process by performing fuzzy and ordinary linear regression analyses of the injection test results. The resultant fuzzy regression models provided successful penetration length predictions for the majority of the cases analyzed, while the best ordinary regression model exhibited a correlation coefficient not higher than 0.363. [ABSTRACT FROM AUTHOR]

Workflow management becomes increasingly important in today's information-oriented society. An important research area of workflow management is performance analysis that is driven by the need for improved efficiency of business processes. The study of the performance of a workflow process, as the focus of this paper, requires the estimation of the duration of tasks, which is often unpredictable and nondeterministic. Current research in this field has focused on workflow stochastic Petri nets (PNs)—which are a class of workflow nets with exponential distributed execution times assigned to transitions. In this paper, in order to deal with this uncertainty, we use fuzzy estimators constructed from statistical data to describe time, and we present an analytical method to proceed with the performance evaluation of workflow stochastic PNs based on block reduction. A comparison example is provided to show the benefits of the proposed method. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]