Concept Of Fuzzy Number Research Articles

Relationship between efficiency in the traditional data envelopment analysis and possibility sets

In this paper, the relationship between possibility sets, a fuzzy number concept, and efficiency score in Data Envelopment Analysis (DEA) is dealt with. A new DEA model for handling crisp data using fuzzy concept is proposed. The model which is equivalent to a traditional DEA model is then extended to incorporate situations whereby some inputs, in a fuzzy sense, are almost discretionary variables. With this relationship, a new perspective of viewing and exploring other DEA models is now made possible.

Agility evaluation in fuzzy context: influence of decision-makers’ risk bearing attitude

Purpose – The purpose of this paper is to investigate the influence of decision-makers’ (DM) risk bearing attitudes and the effect of the decision-making environment on estimating the overall degree of agility of an organization. The present study explores an extended agility model in a specific organization's hierarchy and reflects how decision-making attitudes alter an organizational agility scenario. Design/methodology/approach – The concept of fuzzy logic has been explored in this paper. Based on DMs’ linguistic judgments, a fuzzy appropriateness rating as well as fuzzy priority weights have been determined for different levels of agile system hierarchy. Using a multi-grade fuzzy approach the overall agility index has been determined. The concept of fuzzy numbers ranking has been explored to show the effect of decision-making attitudes on agility estimations. Findings – Decision-making attributes, e.g. the category of DM (neutral, risk-averse and risk-taking), affect the quantitative evaluation of the overall agility degree, which is correlated with a predefined agility measurement scale. Research limitations/implications – This study explores a triangular fuzzy membership function to express DMs’ linguistic judgments as fuzzy representations. Apart from triangular fuzzy numbers, trapezoidal and Gaussian fuzzy numbers may also be used for agility evaluation. The model may be used in other agile industries for benchmarking and selection of the best approach. Practical implications – Selecting the right decision-making group to compute and analyze the agility level for a particular organization is an important managerial decision. In the case of benchmarking of various agile enterprises the decision-making group bearing the same attitude should be utilized. Originality/value – Agile system modeling and development of agility appraisement platforms have been attempted by previous researchers while the influence of DMs’ risk bearing attitudes, and the effect of the decision-making environment on estimating the overall degree of agility, have rarely been studied. In this context, the authors explore an exhaustive agility model for implementing in a case study and reveal how decision-making attitudes alter organizational agility scenarios.

Research on the Elevator System with Fault Diagnosis Method Based on Fuzzy Fault Tree

This paper is aimed at the security problems of elevator system.Fuzzy fault tree analytic method is applied to study the reliability of the elevator system.First of all, the elevator system is divided into four subsystems, and then the paper take elevator fall accident as the top event as a example, applying the ascending method for qualitative analysis to find out 7 minimum cut sets in the fault tree and 15 bottom event structure importance sorting. Finally, the fuzzy fault interval probability come out through introducing the concept of fuzzy number in fuzzy set theory, using the triangular fuzzy number to describe the probability of basic event occurrence in the fault tree, making an quantitative interval probability calculation in middle events and top events in the fault tree..The results show that the fuzzy fault tree is an effective and practical method for reliability analysis when we are difficult or unable to obtain the accurate probability of bottom events in terms of the elevator system. Compared with the traditional method of fault tree, the calculated result is more scientific and reasonable, closer to the engineering practice.

Fuzzy weights estimation method based on the linguistic expression of criteria relevance

In this article, the quantified expression of criteria weights in decision-making processes is considered. A decision maker is often able to express his or her preferences only linguistically. The concept of fuzzy numbers, or linguistic variables, is used in order to state these vague preferences. A fuzzy number is considered as one with a triangular membership function, which renders an approximate value of the weight of a particular criterion according to linguistic terms about its importance. To set the strict (crisp) value of weights, the optimization model based on the maximin principle is proposed in two modifications. The proposed approaches are compared with other methods. Finally, the introduced methods are applied to a rather illustrative but real case of investment decision making in the capital market. The main results are discussed.

Structural identification (St-Id) using finite element models for optimum sensor configuration and uncertainty quantification

Developments and advances in experimental technologies providing useful data make it possible to identify civil engineering structures and to obtain a more reliable model characterizing the existing condition for decision making. Analytical models such as Finite Element (FE) models, which are calibrated using structural health monitoring (SHM) data, better represent the existing structures' behavior under different loading conditions. However, the SHM data should include sufficient information about the structural parameters to be identified. In this study, a novel methodology is proposed in order to determine the optimum sensor configuration which provides adequate data for structural identification (St-Id). The success of the St-Id is investigated in a comparative fashion by comparing the model parameters calibrated using different sensor configurations. Uncertainties both in the mathematical model and the experimental data are taken into account using the fuzzy number concept. A so-called inverse fuzzy arithmetic technique is used to quantify the uncertainties in the updated parameters. The proximity of linkage values, which are the product of cluster analysis, is used to determine the optimal sensor configuration. The optimal sensor configuration is then verified by using the relative amount of uncertainty in the updating parameters resulting from the inverse propagation of the uncertainties. A hybrid evolutionary optimization algorithm is also proposed in order to efficiently minimize an objective function that consists of differences between the fuzzy experimental measurements and the analytical data. Genetic Algorithms (GA) and Harmony Search (HS) algorithm are combined to enhance the efficiency and the robustness of the optimization process. An analytical benchmark bridge structure developed for bridge health monitoring studies is used as the test structure to verify the proposed methodologies. Three different cases including the undamaged and the damage cases are considered. It has been shown that there is no significant difference between the St-Id results obtained by using a dense sensor configuration and the optimum configuration obtained by the proposed method in terms of accuracy.

A mathematical programming model for the fuzzy analytic network process—applications of international investment

Currently, the analytic network process (ANP) method is widely employed to consider the multiple criteria analysis problems with dependence and feedback effects. However, in order to extend the ANP to resolve the problem of uncertainty or human subjective judgment, the concepts of fuzzy numbers should be incorporated into the ANP to represent the subjective uncertain pairwise judgments. In this paper, therefore, we propose a novel fuzzy analytic network process (FANP) model by solving a mathematical programming problem. Unlike other FANPs, the proposed method does not require the reciprocity assumption of the weight ratios between criteria, and it can derive local and global weights simultaneously in a single model. Two numerical examples of international investment problems are used to demonstrate the proposed method.

Ranking alternatives in a preferential voting system using fuzzy concepts and data envelopment analysis

In this paper, a new method for aggregating the opinions of experts in a preferential voting system is proposed. The method, which uses fuzzy concept in handling crisp data, is computationally efficient and is able to completely rank the alternatives. Through this method, the number of votes for certain rank position that each alternative receives are first grouped together to form fuzzy numbers. The nearest point to a fuzzy number concept is then used to introduce an artificial ideal alternative. Data envelopment analysis is next used to find the efficiency scores of the alternatives in a pair-wise comparison with the artificial ideal alternative. Alternatives are rank based on these efficiency scores. If the alternatives are not completely ranked, a weight restriction method also based on fuzzy concept is used on the un-discriminated alternatives until they are completely ranked. Two examples are given for illustration of the method.

A new model for designing uncertain enterprise architecture

Article history: Received October 5, 2011 Received in Revised form January, 4, 2012 Accepted 5 January 2012 Available online 6 January 2012 C4ISR framework describes architecture in three views of information architecture and defines a set of products, which are main outputs of enterprise architecture design. Formats and templates, which are presented for C4ISR products, cannot describe uncertainty in process or data. Meanwhile, uncertainty in many information systems is unavoidable and using the concept of fuzzy numbers in architecture design helps architects handle uncertainty in process and data of organization. In this paper, we present a new template based on fuzzy-UML concept for some of C4ISR products such as Logical Data Model (OV-7), Operational Event/Trace Description (OV-6c) and Systems Event/Trace Description (SV-10c). To explain further, fictional Fast Pass system used at OilCo gas stations is used to demonstrate details of our proposed model. © 2012 Growing Science Ltd. All rights reserved.

Evaluate the fuzzy completion times in the fuzzy flow shop scheduling problems using the virus-evolutionary genetic algorithms

Abstract The scheduling problem with fuzzy processing times is concerned in this paper. A computational procedure is proposed to obtain the approximated membership function of fuzzy completion time for each schedule. The possibility and necessity measures will be used to propose the ranking concept of fuzzy numbers. Under this ordering among fuzzy numbers, we plan to minimize the fuzzy makespan and total weighted fuzzy completion time. Two types of formulations will be proposed by considering the different directions of ordering among fuzzy numbers. We shall apply the modified virus-evolutionary genetic algorithms to search for the best schedules. Three numerical examples are also provided to clarify the discussions in this paper using the commercial software MATLAB.

Asymptotic Behavior of Solutions for the Delay Semilinear Fuzzy Integrodifferential Systems

In this paper, we study the asymptotic behavior of solutions for the delay semilinear fuzzy integrodifferential systems on E¹ N by using the concept of fuzzy number whose values are normal, convex, upper semicontinuous and compactly supported interval in E¹ N

A Novel Human Error Probability Assessment Using Fuzzy Modeling

Human error is one of the significant factors contributing to accidents. Traditional human error probability (HEP) studies based on fuzzy number concepts are one of the contributions addressing such a problem. It is particularly useful under circumstances where the lack of data exists. However, the degree of the discriminability of such studies may be questioned when applied under circumstances where experts have adequate information and specific values can be determined in the abscissa of the membership function of linguistic terms, that is, the fuzzy data of each scenario considered are close to each other. In this article, a novel HEP assessment aimed at solving such a difficulty is proposed. Under the framework, the fuzzy data are equipped with linguistic terms and membership values. By establishing a rule base for data combination, followed by the defuzzification and HEP transformation processes, the HEP results can be acquired. The methodology is first examined using a test case consisting of three different scenarios of which the fuzzy data are close to each other. The results generated are compared with the outcomes produced from the traditional fuzzy HEP studies using the same test case. It is concluded that the methodology proposed in this study has a higher degree of the discriminability and is capable of providing more reasonable results. Furthermore, in situations where the lack of data exists, the proposed approach is also capable of providing the range of the HEP results based on different risk viewpoints arbitrarily established as illustrated using a real-world example.

Product selection in Internet business: a fuzzy approach

AbstractIn this paper, we propose a methodology which helps customers buy products through the Internet. This procedure takes into account the customer's level of desire in the product attributes, which are normally fuzzy, or in linguistically defined terms. The concept of fuzzy number will be used to measure the degree of similarities of the available products to that of the customer's requirements. The degrees of similarities so obtained over all the attributes give rise to the fuzzy probabilities and hence the fuzzy expected values of availing a product on the Internet as per the customer's requirement. Attribute‐wise the fuzzy expected values are compared with those of the available products on the Internet and the product that is closest to the customer's preference is selected as the best product. The multi‐attribute weighted average method is used here to evaluate and hence to select the best product.

Development of a fuzzy saturation index for sulfate scale prediction

An innovative approach established upon the concepts of fuzzy numbers and their processing system was developed to address the risk of sulfate deposition due to seawater injection as an enhanced oil recovery option. Uncertain parameters such as solubility product constant and free sulfate concentration are considered as fuzzy numbers. Appropriate modeling steps were performed with these fuzzy numbers to suggest a fuzzy saturation index. As a case study, anhydrite scaling tendency due to injection of Persian Gulf water into a selected well from Parsi field, southwestern Iran, is investigated via the proposed fuzzy saturation index. The proposed fuzzy approach provides a strict mathematical environment in which vague conceptual phenomena in scale prediction problem can rigorously be studied. It is able to deliver the maximum possible saturation index value and the whole set of possible values for the problem solution, preparing a wider perspective for the oilfield operator over the scale problem and the corresponding suitable prevention action.

Existence of Solutions for the Semilinear Fuzzy Integrodifferential Equations using by Successive Iteration

This paper is to investigate the existence theorem for the semilinear fuzzy integrodifferential equation in <TEX>$E_N$</TEX> by using the concept of fuzzy number whose values are normal, convex, upper semicontinuous and compactly supported interval in <TEX>$E_N$</TEX>. Main tool is successive iteration method.

Fuzzy approach to semi-parametric of a sample selection model

The sample selection model is studied in the context of semi-parametric methods. With the deficiency of the parametric model, such as inconsistent estimators etc, the semi-parametric estimation methods provide the best alternative to handle this deficiency. Semi-parametric of a sample selection model is an econometric model and has found interesting application in empirical studies. The issue of uncertainty and ambiguity still become are still major problem and are complicated in the modelling of a semi-parametric sample selection model as well as its parametric. This study, focuses on the context of fuzzy concept as a hybrid to the semi-parametric sample selection model. The best approach of accounting for uncertainty and ambiguity is to take advantage of the tools provided by the theory of fuzzy sets. It seems particularly appropriate for modelling vague concepts. Fuzzy sets theory and its properties, through the concept of fuzzy number, provide an ideal framework in order to solve the problem of uncertain data. In this paper, we introduce a fuzzy membership function for solving uncertain data of a semi-parametric sample selection model.

A probabilistic methodology for bridge deck condition assessment

Condition assessment is an essential step in bridge management. Various techniques are currently used during the inspection of a bridge to assess the conditions of bridge elements. Data collected through inspection is used to make important decisions regarding needs assessment and budgetallocation. However, inspection data is at best subjective and associated with uncertainty. This tends to create problems in the decision-making process. This paper presents a methodology to minimise the effect of such problems on the assessment of bridge decks condition. A bridge deck condition index is developed based on the remaining value of deteriorated quantities. A methodology is proposed that uses the fuzzy number concept and the Monte Carlo simulation technique to rate the deck condition taking into account the subjectivity and the uncertainty issues in the inspection process. The proposed methodology benefits from the bridge deck inspection's current practice. It produces a probabilistic rating that is consistent...

Controllability for the impulsive semilinear fuzzy integrodifferential equations with nonlocal conditions

In this paper. we study the controllability for the impulsive semilinear fuzzy integrodifferential control system with nonlocal conditions in EN by using the concept of fuzzy number whose values are normal, convex, upper semicontinuous and compactly supported interval in EN.

A strong consistency result for fuzzy relative frequencies interpreted as estimator for the fuzzy-valued probability

The unavoidable imprecision of measurements of continuous physical quantities can be modelled by using the concept of fuzzy numbers and fuzzy vectors. Concerning a quantitative usage of such data the classical concept of relative frequencies for real data has to be extended to so-called fuzzy relative frequencies for fuzzy data, whereby the fuzzy relative frequency of a set is a fuzzy number. Analogous to A. Dempster's interval-valued probabilities induced by multi-valued mappings fuzzy-valued probabilities induced by fuzzy random vectors are considered and analyzed. It is proved that fuzzy relative frequencies can be interpreted as strongly consistent estimator for the corresponding fuzzy-valued probability.

Controllability for the Semilinear Fuzzy Integrodifferential Equations with Nonlocal Conditions and Forcing Term with Memory

In this paper. we study the controllability for the semilinear fuzzy integrodifferential equations with nonlocal condition and forcing term with memory in E N by using the concept of fuzzy number whose values are normal, convex, upper semicontinuous and compactly supported interval in E N .

Existence and Uniqueness of Solutions for the Semilinear Fuzzy Integrodifferential Equations with Nonlocal Conditions and Forcing Term with Memory

Many authors have studied several concepts of fuzzy systems. Balasubramaniam and Muralisankar (2004) proved the existence and uniqueness of fuzzy solutions for the semilinear fuzzy integrodifferential equation with nonlocal initial condition. Recently, Park, Park and Kwun (2006) find the sufficient condition of nonlocal controllability for the semilinear fuzzy integrodifferential equation with nonlocal initial condition. In this paper, we study the existence and uniqueness of solutions for the semilinear fuzzy integrodifferential equations with nonlocal condition and forcing term with memory in <TEX>$E_{N}$</TEX> by using the concept of fuzzy number whose values are normal, convex, upper semicontinuous and compactly supported interval in <TEX>$E_{N}$</TEX>.