Use Of Fuzzy Sets Research Articles

QRAM a Qualitative Occupational Safety Risk Assessment Model for the construction industry that incorporate uncertainties by the use of fuzzy sets

Occupational safety risk assessment is the core of safety practices. Is a complex process that requires the consideration of sundry parameters, which are often difficult to quantify.This paper presents the new developed fuzzy QRAM model, which intends to support construction companies in carrying out their responsibilities to reduce occupational safety risks. The innovative aspects of QRAM model is to embody assess of the safety climate and the safety barriers effectiveness as assessment dimensions and the use of fuzzy sets theory to enhance the use of imprecise and incomplete information, elicited by linguistic variables.The QRAM model was designed based on the best academic and empirical knowledge about safety risks on construction industry, biomechanical data and laws of physics, chemistry and engineering.The lack of credible and accurate data, resulting from the in-depth investigation of work accidents in construction industry was the greatest difficulty in carry-out this work.QRAM was, firstly evaluated by “peer” review, with 12 safety experts from Brazil (2), Bulgaria (1), Greece (3), Turkey (3) and Portugal (3) and, then, appraised by comparing QRAM with 2 other occupational safety risk assessment techniques.The safety experts evaluators concluded that: (a) QRAM is a versatile tool to assess occupational safety risk assessment on construction sites; (b) the specific checklists for knowledge elicitation are a good aid and enhance the process objectivity, and (c) the use of linguistic variables is a better way to rate the risk factors thus to render the risk assessment process more objective and reliable.

Evaluation of Graduates’ Performance Using Fuzzy Approach

This study offers an argument on the use of ordinal values in Likert scale that represents the linguistic terms of the level of satisfaction perceived by employers on the graduates’ performance. Generally, ordinal data are regarded as nonparametric and cannot be added. This paper recommends the use of fuzzy sets to represent linguistic terms in Likert scale. The evaluation of employers’ satisfaction level for the graduates’ performance applied the technique using fuzzy conjoint method. The investigation findings show that the analysis using fuzzy conjoint method yields consistent outcome compared to the analysis using the statistics mean and percentage. In addition, the fuzzy membership values obtained from fuzzy conjoint method ranks the attributes that used to measure employers’ satisfaction level. Therefore, this finding provides useful information for decision-making in finding the attributes that need to be enhanced in engineering graduates.

Fuzzy stochastic elements method. Spectral approach

We study a complex dynamic problem, which concerns a structure with uncertain parameters subjected to a stochastic excitation. Formulation of such a problem introduces fuzzy random variables for parameters of the structure and fuzzy stochastic processes for the load process. The uncertainty has two sources, namely the randomness of structural parameters such as geometry characteristics, material and damping properties, load process and imprecision of the theoretical model and incomplete information or uncertain data. All of these have a great influence on the response of the structure. By analyzing such problems we describe the random variability using the probability theory and the imprecision by use of fuzzy sets. Due to the fact that it is difficult to find an analytic expression for the inversion of the stochastic operator in the stochastic differential equation, a number of approximate methods have been proposed in the literature which can be connected to the finite element method. To evaluate the effects of excitation in the frequency domain we use the spectral density function. The spectral analysis is widely used in stochastic dynamics field of linear systems for stationary random excitation. The concept of the evolutionary spectral density is used in the case of non-stationary random excitation.We solve the considered problem using fuzzy stochastic finite element method. The solution is based on the idea of a fuzzy random frequency response vector for stationary input excitation and a transient fuzzy random frequency response vector for the fuzzy non-stationary one. We use the fuzzy random frequency response vector and the transient fuzzy random frequency response vector in the context of spectral analysis in order to determine the influence of structural uncertainty on the fuzzy random response of the structure.We study a linear system with random parameters subjected to two particular cases of stochastic excitation in a frequency domain. The first one when the excitation is a weakly stationary stochastic process with a given spectral density function and the second one which is constituted by a non stationary process with evolutionary spectral density function. We derive the formulas for both cases. The presented computational algorithm has a quite general scope and may be used in the vibration analysis of different kinds of structures.

A fuzzy multi-objective multi-follower linear Bi-level programming problem to supply chain optimization

Article history: Received June 10, 2013 Received in revised format 25 August 2013 Accepted September 15 2013 Available online September 17 2013 In today's world, many planning problems include a hierarchical decision structure with independent and often conflicting objectives. Therefore, the optimization of supply chains with hierarchical structure is essential. In this paper, we investigate a fuzzy multi-objective multi-products supply chain optimization problem in a bi-level structure with one level corresponding to a manufacturer planning problem, while the other to K distribution centers problem. In our model, customer demand and supply chain costs are considered uncertain and will be modeled with use of fuzzy sets. We first describe how different kinds of problems can be modeled as bi-level programming problems. Then, this fuzzy model is first converted into an equivalent crisp model by using α-cut method in each level, and then by applying extended Kuhn–Tucker approach, we have a linear multi-objective programming problem. Fuzzy goal programming technique is applied to solve the multi-objective linear programming problem to obtain a set of Pareto-optimal solutions. Finally, a numerical example is illustrated to demonstrate the feasibility of the proposed approach. © 2013 Growing Science Ltd. All rights reserved.

Fuzzy Set Based Models and Methods of Decision Making and Power Engineering Problems

The results of research into the use of fuzzy set based models and methods of multicriteria decision making for solving power engineering problems are presented. Two general classes of models related to multiobjective (X，M> models) and multiattribute (X，R> models) problems are considered. The analysisX，M> of models is based on the use of the Bellman-Zadeh approach to decision making in a fuzzy environment. Its application conforms to the principle of guaranteed result and provides constructive lines in obtaining harmonious solutions on the basis of analyzing associated maxmin problems. Several techniques based on fuzzy preference modeling are considered for the analysis of X，R> models. A review of the authors’ results associated with the application of these models and methods for solving diverse types of problems of power system and subsystems planning and operation is presented. The recent results on the use ofX，M> andX，R> models and methods of their analysis for the allocation of reactive power sources in distribution systems and for the prioritization in maintenance planning in distribution systems, respectively, are considered.

Computing fuzzy trajectories for nonlinear dynamic systems

One approach for representing uncertainty is the use of fuzzy sets or fuzzy numbers. A new approach is described for the solution of nonlinear dynamic systems with parameters and/or initial states that are uncertain and represented by fuzzy sets or fuzzy numbers. Unlike current methods, which address this problem through the use of sampling techniques and do not account rigorously for the effect of the uncertain quantities, the new approach is not based on sampling and provides mathematically and computationally rigorous results. This is achieved through the use of explicit analytic representations (Taylor models) of state variable bounds in terms of the uncertain quantities. Examples are given that demonstrate the use of this new approach and its computational performance.

Axiomatic of Fuzzy Complex Numbers

Fuzzy numbers are fuzzy subsets of the set of real numbers satisfying some additional conditions. Fuzzy numbers allow us to model very difficult uncertainties in a very easy way. Arithmetic operations on fuzzy numbers have also been developed, and are based mainly on the crucial Extension Principle. When operating with fuzzy numbers, the results of our calculations strongly depend on the shape of the membership functions of these numbers. Logically, less regular membership functions may lead to very complicated calculi. Moreover, fuzzy numbers with a simpler shape of membership functions often have more intuitive and more natural interpretations. But not only must we apply the concept and the use of fuzzy sets, and its particular case of fuzzy number, but also the new and interesting mathematical construct designed by Fuzzy Complex Numbers, which is much more than a correlate of Complex Numbers in Mathematical Analysis. The selected perspective attempts here that of advancing through axiomatic descriptions.

New probability theory compatible with the new conception of modern thermodynamics. Economics and crisis of debts

We show that G\"odel's negative results concerning arithmetic, which date back to the 1930s, and the ancient "sand pile" paradox (known also as "sorites paradox") pose the questions of the use of fuzzy sets and of the effect of a measuring device on the experiment. The consideration of these facts led, in thermodynamics, to a new one-parameter family of ideal gases. In turn, this leads to a new approach to probability theory (including the new notion of independent events). As applied to economics, this gives the correction, based on Friedman's rule, to Irving Fisher's "Main Law of Economics" and enables us to consider the theory of debt crisis.

Wiener quantization of economics as an analog of the quantization of thermodynamics

We show that Godel’s negative results concerning arithmetic, which date back to the 1930s, and the ancient “sand pile” paradox pose the questions of the use of fuzzy sets and of the effect of a measuring device on the experiment. The consideration of these facts led, in thermodynamics, to a new one-parameter family of ideal gases and, in economics, to the correction, based on Friedman’s rule, to Irving Fisher’s “Main Law of Economics.” We introduce the notion of viscosity (braking) in economics. By analogy toWiener quantization, we study the Wiener (tunnel) quantization of economics as well as the tunnel geometric quantization of economics. We also consider debt crises, the stratification of society, and Islamic revolutions from the point of view of Human Thermodynamics.

Evaluation of photovoltaic cells in a multi-criteria decision making process

The requirements to satisfy the energy needs of today without compromising those of future generations have forced humans to adopt rules that permit a better use of the available resources, of which the sun is an inexhaustible energy source. Amongst the energy sources that offer the possibility of exploiting the resources offered by the Earth, solar energy has acquired great strength. Photovoltaic energy has presented a major evolution and it is forecasted as being an important contributor to power generation and an alternative to other non-renewable energy sources. The high cost of solar electricity is today the main reason why electricity from photovoltaic systems has not been introduced in a more widespread way. In this context, the aim of this paper is the study and analysis of the decision criteria to be used when searching for the best photovoltaic cell, studying both the criteria that exert most influence or their manufacture (defined by quantitative and qualitative values) and the alternatives which will be the decision problem to be solved; each alternative will correspond to one type of photovoltaic cell. Thus, relevant information has been provided by three experts and the TOPSIS method has been used to aggregate all the information combined with the use of fuzzy sets which will model the use of linguistic labels in the process.

A characterization of electrocardiogram signals through optimal allocation of information granularity

We propose and develop a concept of a granular representation of a collection of signals (patterns) where a prototype (representative) of such numeric signals is formed as a certain information granule (say, a set, fuzzy set, rough set, and alike) instead of a single numeric entity. As being more abstract, the granular format of the representative of the family of signals is more in rapport with the nature of the representation task itself. It is instrumental in quantifying the diversity of data and capture their inherent distribution characteristics. In the realization of the granular representation of the signals, we introduce a certain level of granularity (supplied in advance), which in the construction of the granular representative is regarded as an essential important modeling asset. A two-phase design is developed whose ultimate goal is to optimally allocate (distribute) the predefined level of granularity to the individual elements of the universe of discourse over which the signals are described. Given the nature of the required optimization, the ensuing optimization problem is solved by engaging a machinery of population-based optimization, namely Particle Swarm Optimization (PSO). Furthermore a number of information granularity distribution protocols are proposed. The numerical experiments completed for synthetic data and ECG MIT-BIH database signals are used to demonstrate the performance of the overall optimization algorithm and quantify the effectiveness of the allocation of information granularity realized by the PSO. An area under curve (AUC) criterion is proposed as a measure to express the quality of the overall optimization framework. For both synthetic as well as ECG signals, it is shown that the method endowed with the PSO identifies the best prototype and spans the lower and upper bounds of its granular counterpart. In addition to the numeric quantification of the best (optimized) granular prototype, the method helps visualizing its bounds. The relative difference in mapping performance between the best and the weakest granular prototypes is in the range of 18% (for normal ECG complexes) and over 26% in case of complexes of premature ventricular contraction. A complete algorithm of the construction of granular prototypes is presented. Treating the granular prototype as a template of a given class of electrocardiogram (ECG) signals, a matching process is facilitated and used as a basis for the design of signal classification algorithms. Various realizations of granular prototypes can be completed with the use of fuzzy sets or rough sets.

Designing and Modeling Fuzzy Control Systems

Fuzzy logic provides a formal framework for constructing systems exhibiting both good numeric performance (precision) and linguistic representation (interpretability). Fuzzy modeling—meaning the construction of fuzzy systems—is an arduous task, demanding the identification of many parameters. This paper analyses the fuzzy-modeling problem and different approaches to coping with it, focusing on evolutionary fuzzy modeling— the design of fuzzy inference systems using evolutionary algorithms. The purpose of this paper is twofold. We first provide an overview of the standard approach to constructing a fuzzy control system and then identify a wide variety of relevant system modeling techniques. The later part of the paper deals with discussing Fuzzy modeling problem – curse of dimensionality and techniques to solve the problem. The paper provides an introduction to the use of fuzzy sets and fuzzy logic for the approximation of functions and modeling of static and dynamic systems. The concept of a fuzzy system is first explained. Afterwards, the motivation and practical relevance of fuzzy modeling are highlighted.

Gradualness, uncertainty and bipolarity: Making sense of fuzzy sets

This paper discusses basic notions underlying fuzzy sets, especially gradualness, uncertainty, vagueness and bipolarity, in order to clarify the significance of using fuzzy sets in practice. Starting with the idea that a fuzzy set may represent either a precise gradual composite entity or an epistemic construction refereeing to an ill-known object, it is shown that each of this view suggests a different use of fuzzy sets. Then, it is argued that the usual phrase fuzzy number is ambiguous as it induces some confusion between gradual extensions of real numbers and gradual extensions of interval calculations. The distinction between degrees of truth that are compositional and degrees of belief that cannot be so is recalled. The truth-functional calculi of various extensions of fuzzy sets, motivated by the desire to handle ill-known membership grades, are shown to be of limited significance for handling this kind of uncertainty. Finally, the idea of a separate handling of membership and non-membership grades put forward by Atanassov is cast in the setting of reasoning about bipolar information. This intuition is different from the representation of ill-known membership functions and leads to combination rules differing from the ones proposed for handling uncertainty about membership grades.

The Use of Fuzzy Sets in the Evaluation of the Effectiveness of Earth Dam Reinforcement

This paper shows the use of fuzzy logic to evaluate the effectiveness of the reinforcement of Santa Branca dam. The embankment reinforcement was found imperative once the dam had shown signs of instability process, as undesirable seepage and unexpected movements, just after the first impoundment. Stability analyses were carried out considering fuzzy variation of the strength parameters in order to assessing the non-random uncertainties associated with their evaluation. These uncertainties are mostly connected to values varying within a specified interval, whose boundaries express the possibility of occurrences that, in turns, account for vagueness in information. Finally, the fuzzy Factor of Safety distribution resulting from these analyses is then compared to pre-defined fuzzy class intervals in order to classify the failure potentiality of the embankment, before and after the reinforcement has been constructed, reflecting, thus, its effectiveness.

Fuzzy for Excel, User Manual

Software Fuzzy for Excel (further for abridgment - the FE) is intended for the solving of analytical problems in uncertainty conditions in environment of widespread software Microsoft Excel. It is the fourth version of the software which has been developed by consulting group INEX-FT (Ukraine). The FE is based on using of algorithms of fuzzy technology for the solving of analytical problems in uncertainty conditions. By means of the FE the user can solve three types of analytical problems: - any calculations with use of fuzzy numbers; - problems of evaluation and classification of alternatives (problem of correlation of alternatives to the described classes); - problems of forecast.The FE solves the first problems type with use of algorithm of arithmetic operations according to principle of entropy maximum of decision. The FE solves the second problems type with use of fuzzy sets and fuzzy measures. Here the FE provides support of network-like structure of criteria of evaluation and classification. The FE solves the third problems type with using of forecast algorithm of composite events influence. It is fundamentally new forecast algorithm. The algorithm differs from widespread algorithms that this algorithm uses the information about events which have occurred in the past and are expected in the future.The FE has been created in the form of usual add-in of software Microsoft Excel. The FE does not demand special knowledge of fuzzy mathematics. The FE work is hidden from the user who, however, should understand the uncertainty nature in analytical problem and should have some skills of interpretation of fuzzy numbers.The FE contains the multitude of functions and tools (macro definitions). Functions of the FE create fuzzy numbers and execute various operations with them. Functions of the FE also execute a wide spectrum of operations with fuzzy sets and fuzzy measures. The majority of functions works both with fuzzy and with traditional numbers. Rules of a call and use of FE-functions are traditional. Tools of the FE provide the visual analysis of calculations results (including 3D-graphics), the solving of a forecasting problem and also the solving of auxiliary problems.The FE has the full and restricted version. The restricted version differs from the full version only by cells range (A1:F6) in which the FE supports an executing of functions and tools.

Using fuzzy operators to address the complexity in decision making of water resources redistribution in two neighboring river basins

This paper emphasizes the use of fuzzy sets for incorporating objective and subjective uncertainties to address coevolutionary alignment of a suite of water resources redistribution alternatives in a transboundary channel–reservoir system. The highlighted decision making complexity arises from the interactions between two neighboring water systems (i.e., the Tseng-Wen and Kao-Ping River Basins, South Taiwan) where a pending diversion plan has been under intensive debate for over a decade. While the local stakeholders make uncertain science linked with uncertain politics resulting in endless delay of the diversion plan, the environmental advocacy groups stress the increasing concern of loss of biological integrity due to changes of land use when sharing water resources across the boundary. Consequently, there is a need to generate a novel integration that enables us to consider a vast number of internal weirs, water intakes, reservoirs, drainage ditches, and transfer pipelines within the basin and bring out the connectivity via diversion between these two neighboring river basins under uncertainty. To explore the managerial implications with varying risk perception and risk attitude, four types of fuzzy operators tailored for the fuzzy multi-objective decision analysis depict greater flexibility in representing the complexity of possible trade-offs among those alternatives. These trade-offs in the multi-objective evaluation context are constrained by physical, chemical, socioeconomic, managerial, and technical factors reflecting the needs for adaptive water resources management. Findings indicates that the use of fuzzy operators is instructive, which could provide unique guidance for enlightening the potential barriers in sustainable water resources management at the regional scale.

Soft Querying Of Standard and Uncertain Databases

We provide a framework for querying of databases. We model a query as a collection of required conditions and an imperative for combining an object's satisfaction to the individual conditions to get its overall satisfaction. We investigate tools that can enrich this process by enabling the inclusion of more human focused considerations. We discuss how to include flexible conditions with the use of fuzzy sets. We describe some more sophisticated techniques for aggregating the satisfactions of the individual conditions based on the inclusion of importances and the use of the OWA operator. We introduce a new method for aggregating the individual satisfactions that can model a lexicographic relation between the individual requirements. In addition to considering more human focused aspects of the query we look at databases in which the information in the database can have some probabilistic or possibilistic uncertainty.

Fuzzy inference system for the risk assessment of liquefied natural gas carriers during loading/offloading at terminals

A multiple attribute risk assessment approach using a fuzzy inference system is developed in this work. The approach is based on the use of fuzzy sets, a rule base and a fuzzy inference engine. Traditional input probabilities and consequences used in risk assessment are represented by fuzzy sets to take into account uncertainties associated with the assignment of their values. The output risk values can be presented as crisp values or fuzzy sets with associated degree of membership. The fuzzy inference system FIS is used as an alternative approach to qualitative risk matrix techniques currently used in many industries and by ship classification societies. Two approaches for fuzzy inference are adopted. These include the Mamdani approach in which output risk values are fuzzy sets and the Sugeno method of fuzzy inference, in which output risk values are constant or linear. The use of a fuzzy set approach is particularly suited for handling multiple attribute risk problems with imprecise data. It improves upon existing qualitative methods and allows the ranking of risk alternatives based on a unified fuzzy risk index measure. Results show that while the Mamdani method is intuitive and well suited to human input, the Sugeno method is computationally more efficient and guarantees continuity of the final risk output surface. Results also show that computed risk values using a fuzzy risk index measure are consistent with those obtained using a qualitative risk matrix approach. The proposed methodology is also applicable to other ship operating modes such as transit in open sea and/or entering/leaving port. A case study for a liquefied natural gas LNG ship loading/offloading at the terminal is presented to demonstrate the developed approach capability.

Improving the Accuracy of Effort Estimation through Fuzzy Set Representation of Size

Problem statement: The precision and reliability of the effort estimation is very important for the competitiveness of software companies. The uncertainty at the input level of the Constructive Cost Model (COCOMO) yields uncertainty at the output, which leads to gross estimation error in the effort estimation. Fuzzy logic-based cost estimation models are more appropriate when vague and imprecise information was to be accounted for and was used in this research to improve the effort estimation accuracy. This study proposed to extend the COCOMO by incorporating the concept of fuzziness into the measurements of size. The main objective of this research was to investigate the role of size in improving the effort estimation accuracy by characterizing the size of the project using trapezoidal function which gave superior transition from one interval to another. Approach: The methodology adopted in this study was use of fuzzy sets rather than classical intervals in the COCOMO. Using fuzzy sets, size of a software project can be specified by distribution of its possible values and these fuzzy sets were represented by membership functions. Though, Triangular membership functions (TAMF) was used in the literature to represent the size, but it was not appropriate to clear the vagueness in the project size. Therefore, to get a smoother transition in the membership function, the size of the project, its associated linguistic values were represented by trapezoidal shaped MF and rules. Results: After analyzing the results attained by means of applying COCOMO, triangular and trapezoidal MF models to the COCOMO dataset, it had been found that proposed model was performing better than ordinal COCOMO and trapezoidal function was performing better than triangular function, as it demonstrated a smoother transition in its intervals and the achieved results were closer to the actual effort. The relative error for COCOMO using trapezoidal function is lower than that of the error obtained using TAMF. Conclusion: From the experimental results, it was concluded that, by fuzzifying the project size using TPMF, the accuracy of effort estimation can be improved and the estimated effort can be very close to the actual effort.

Ground of requirements to the perspective standards of armament and military technique with the use of fuzzy sets

The analysis of the existent scientifically-methodical approaches is conducted to ground performance requirements to the perspective models of armament and military materiel. It is set that in modern terms on initial design stages they do not allow to fully take into account the vagueness of basic data and ambiguousness of description of process of the use of perspective standards of armament and military materiel. Offered approach is based on the use of concept of fuzzy set allowing to ground performance requirements to the perspective models of armament and military materiel in modern terms.