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In this note, a fuzzy inventory model with multiple items is considered. Economic order quantities (EOQs) are developed for these items. The costs involved in inventory are always assumed to be exact, otherwise called as crisp or hard, but in practice these costs are not exact or precise but vary over a range. In such cases an application of fuzzy set theory plays a vital role in obtaining the EOQ. An application of this model to manpower planning is studied with an example; sensitivity analysis is also made.

In most real-world situations for transportation planning decision (TPD) problems, environmental coefficients and parameters are imprecise/fuzzy in nature, and the decision maker (DM) generally faces a multi-objective TPD problem in a fuzzy environment. This work develops an interactive fuzzy linear programming (FLP) method for solving TPD problems with fuzzy goals, available supply and forecast demand. The proposed method attempts simultaneously to minimize the total production and transportation costs and the total delivery time with reference to available supply, machine capacities and budget constraints at each source, as well as forecast demand and warehouse space constraints at each destination. In addition, the proposed method provides a systematic framework that facilitates the DM interactively to modify the imprecise data and related parameters until a satisfactory solution is derived. An industrial case is used to demonstrate the feasibility of applying the proposed method to real-world TPD problems. Especially, several significant characteristics of the proposed FLP method are presented in contrast to those of the main TPD methods.

Face recognition, as a research hot topic, still faces many challenges. This paper proposes a new face recognition method by fusing the advantages of fuzzy set theory, sub-image method and random sampling technique. In this method, we partition an original image into some sub-images to improve the robustness to different facial variations, and extract local features from each sub-image by using fuzzy 2D-Linear Discriminant analyzis (LDA) which makes use of the class information hidden in neighbor samples. In order to increase the diversity of component classifiers and retain as much as the structural information of the row vectors, we further randomly sample row vectors from each sub-image before performing fuzzy 2D-LDA. Experimental results on Yale A, ORL, AR and Extended Yale B face databases show its superiority to other related state-of-the-art methods on the different variations such as illumination, occlusion and facial expression. Furthermore, we analyze the diversity of our proposed method by virtue of Kappa diversity-error analyzis and frequency histogram and results show that the proposed method can construct more diverse component classifiers than other methods.

In common language, as well as in knowledge–based systems, the truth of a proposition can be evaluated in a qualitative manner using adverbs usually represented on a scale of symbolic degrees. To combine or aggregate such symbolic degrees, we may need scales of different precision levels. We propose to model small variations inside a degree scale using linguistic modifiers in a symbolic framework. We formally define such modifiers and we distinguish three families: reinforcing, weakening and central modifiers. We also introduce the original notion of intensity rate associated to a linguistic degree on a scale base. After that, we propose a generalization of our modifiers, so we obtain more sophisticated tools. These have been used, in particular, in an application on colorimetry that allows us to alter the color slightly. The importance of our work is that most of our linguistic modifiers verify some interesting properties on their intensity rate: notably, they assume a certain order relation.

The aim of this paper is to o study the evolution of positive HIV population for manifestation of AIDS, the Acquired Immunodeficiency Syndrome.

For this purpose, we suggest a methodology to combine a macroscopic HIV positive population model with an individual microscopic model. The first describes the evolution of the population whereas the second the evolution of HIV in each individual of the population. This methodology is suggested by the way that experts use to conduct public policies, namely, to act at the individual level to observe and verify the manifest population.

The population model we address is a differential equation system whose transference rate from asymptomatic to symptomatic population is found through a fuzzy rule-based system. The transference rate depends on the CD4+ level, the main T lymphocyte attacked by the HIV retrovirus when it reaches the bloodstream. The microscopic model for a characteristic individual in a population is used to obtain the CD4+ level at each time instant. From the CD4+ level, its fuzzy initial value, and the macroscopic population model, we compute the fuzzy values of the proportion of asymptomatic population at each time instant t using the extension principle. Next, centroid defuzzification is used to obtain a solution that represents the number of infected individuals. This approach provides a method to find a solution of a non-autonomous differential equation from an autonomous equation, a fuzzy initial value, the extension principle, and center of gravity defuzzification. Simulation experiments show that the solution given by the method suggested in this paper fits well to AIDS population data reported in the literature.

Fuzzy clustering is an approach using the fuzzy set theory as a tool for data grouping, which has advantages over traditional clustering in many applications. Many fuzzy clustering algorithms have been developed in the literature including fuzzy c-means and possibilistic clustering algorithms, which are all objective-function based methods. Different from the existing fuzzy clustering approaches, in this paper, a general approach of fuzzy clustering is initiated from a new point of view, in which the memberships are estimated directly according to the data information using the fuzzy set theory, and the cluster centers are updated via a performance index. This new method is then used to develop a generalized approach of possibilistic clustering to obtain an infinite family of generalized possibilistic clustering algorithms. We also point out that the existing possibilistic clustering algorithms are members of this family. Following that, some specific possibilistic clustering algorithms in the new family are demonstrated by real data experiments, and the results show that these new proposed algorithms are efficient for clustering and easy for computer implementation.

Recommender systems are systems capable of assisting users by quickly providing them with relevant resources according to their interests or preferences. The efficacy of a recommender system is strictly connected with the possibility of creating meaningful user profiles, including information about user preferences, interests, goals, usage data and interactive behavior. In particular, analysis of user preferences is important to predict user behaviors and make appropriate recommendations. In this paper, we present a fuzzy framework to represent, learn and update user profiles. The representation of a user profile is based on a structured model of user cognitive states, including a competence profile, a preference profile and an acquaintance profile. The strategy for deriving and updating profiles is to record the sequence of accessed resources by each user, and to update preference profiles accordingly, so as to suggest similar resources at next user accesses. The adaption of the preference profile is performed continuously, but in earlier stages it is more sensitive to updates (plastic phase) while in later stages it is less sensitive (stable phase) to allow resource recommendation. Simulation results are reported to show the effectiveness of the proposed approach.

Fuzzy set theory and probability theory are complementary for soft computing, in particular object-oriented systems with imprecise and uncertain object properties. However, current fuzzy object-oriented data models are mainly based on fuzzy set theory or possibility theory, and lack of a rigorous algebra for querying and managing uncertain and fuzzy object bases. In this paper, we develop an object base model that incorporates both fuzzy set values and probability degrees to handle imprecision and uncertainty. A probabilistic interpretation of relations on fuzzy sets is introduced as a formal basis to coherently unify the two types of measures into a common framework. The model accommodates both class attributes, representing declarative object properties, and class methods, representing procedural object properties. Two levels of property uncertainty are taken into account, one of which is value uncertainty of a definite property and the other is applicability uncertainty of the property itself. The syntax and semantics of the selection and other main data operations on the proposed object base model are formally defined as a full-fledged algebra.

An approach to distance sensor data integration that obtains a robust interpretation of the robot environment is presented in this paper. This approach consists in obtaining patterns of fuzzy distance zones from sensor readings; comparing these patterns in order to detect non-working sensors; and integrating the patterns obtained by each kind of sensor in order to obtain a final pattern that detects obstacles of any sort. A dissimilarity measure between fuzzy sets has been defined and applied to this approach. Moreover, an algorithm to classify orientation reference systems (built by corners detected in the robot world) as open or closed is also presented. The final pattern of fuzzy distances, resulting from the integration process, is used to extract the important reference systems when a glass wall is included in the robot environment. Finally, our approach has been tested in an ActivMedia Pioneer 2 dx mobile robot using the Player/Stage as the control interface and promising results have been obtained.

Safety Culture describes how safety issues are managed within an enterprise. How to make safety culture strong and sustainable? How to be sure that safety is a prime responsibility or main focus for all types of activity? How to improve safety culture and how to identify the most vulnerable issues of safety culture? These are important questions for safety culture. Huge amount of studies focus on identifying and building the hierarchy of the main indicators of safety culture. However, there are only few methods to assess an organization's safety culture and those methods are often straightforward.

In this paper we describe a novel approach for safety culture assessment by using Belief Degree-Distributed Fuzzy Cognitive Maps (BDD-FCMs). Cognitive maps were initially presented for graphical representation of uncertain causal reasoning. Later Kosko suggested Fuzzy Cognitive Maps FCMs in which users freely express their opinions in linguistic terms instead of crisp numbers. However, it is not always easy to assign some linguistic term to a causal link. By using BDD-FCMs, causal links are expressed by belief structures which enable getting the links evaluations with distributions over the linguistic terms. In addition, we propose a general framework to construct BDD-FCMs by directly using belief structures or other types of structures such as intervals, linguistic terms, or crisp numbers. The proposed framework provides a more flexible tool for causal reasoning as it handles different structures to evaluate causal links.

We first investigate the fundamental properties of the mechanical system as related to the control design. Then a new robust control is proposed for mechanical systems with fuzzy uncertainty. Fuzzy set theory is used to describe the uncertainty in the mechanical system. The desirable system performance is deterministic. The proposed control is deterministic and is not the usual if-then rules-based. The resulting controlled system is uniformly bounded and uniformly ultimately bounded proved via the Lyapunov minimax approach. The resulting control design is systematic and is able to render the deterministic performance. A mechanical system is chosen for demonstration.

Uncertainty is unavoidable and addressing the same is inevitable. That everything is available at our doorstep is due to a well-managed modern global supply chain, which takes place despite its efficiency and effectiveness being threatened by various sources of uncertainty originating from the demand side, supply side, manufacturing process, and planning and control systems. This paper addresses the demand- and supply-rooted uncertainty. In order to cope with uncertainty within the constrained multi-objective supply chain network, this paper develops a fuzzy goal programming methodology, with solution procedures. The probabilistic fuzzy goal multi-objective supply chain network (PFG-MOSCN) problem is thus formulated and then solved by three different approaches, namely, simple additive goal programming approach, weighted goal programming approach, and pre-emptive goal programming approach, to obtain the optimal solution. The proposed work links fuzziness in transportation cost and delivery time with randomness in demand and supply parameters. The results may prove to be important for operational managers in manufacturing units, interested in optimizing transportation costs and delivery time, and implicitly, in optimizing profits. A numerical example is provided to illustrate the proposed model.

The paper defines four fuzzy project scheduling models under inflation condition without or with budget limit. The activity time is described by fuzzy relation or fuzzy variables. The models can be solved in the forms of crisp LP or NLP after using the concept of α-cut.

An approach using defuzzifying methods is proposed for the fuzzy multiple attribute decision-making (MADM) problems. The computing effectiveness of the proposed defuzzifying methods combined with the simple additive weighting (SAW) method and the technique for order preference by similarity to ideal solution (TOPSIS) method are evaluated based on a comparison to the improved fuzzy weighted average (IFWA) followed by a ranking method. Both SAW and TOPSIS methods are two of classic MADM methods. The purpose of this application is to make the method easier to program and data easier to manipulate. This results in a more practical method for fuzzy decisions. A numerical example and experiment are discussed to demonstrate the implementation of the methods in different input conditions.

Identification of important design requirements for product development is critical because it leads to successful products with shorter development time. Quality Function Deployment (QFD) is a tool to help the product development team to systematically determine the design requirements for developing a product with higher customer satisfaction. Therefore, determining the Importance rating of Engineering Characteristics should be robust and reliable. Generally, in QFD charts the relationships between Customer Attributes and Engineering Characteristics can be defined using linguistic variables that have three values: Weak, Medium and Strong. Reversing priority of results (rank reversing) is possible when various scales such as 1-3-5 or 1-3-9 are employed. In this paper, the effect of using fuzzy numbers in rank reverse reduction is studied. For this study a statistical experiment for measuring rank reverse with fuzzy numbers was designed. This experiment was replicated for 7 sets, which included symmetrical and non-symmetrical triangular and trapezoidal fuzzy sets with various degrees of fuzziness. This experiment was extended for cases involving relative importance for Customer Attributes with various fuzzy sets used for weights of importance. The results showed a major reduction in rank reversal using symmetrical membership functions. Furthermore, results did not depend on system fuzziness, and there were not any major differences between the use of triangular and trapezoidal membership functions.

The required level of operating reserve to be maintained by an electric power system can be determined by deterministic and probabilistic techniques. The power system parameters such as failure and repair rates used in the probabilistic models basically come from historical operation records, which are necessarily limited and subject to errors. There is considerable data uncertainty that exists in these parameters. This paper presents the application of fuzzy sets, which is recognized as a potential tool to include data uncertainty in normal calculations, for evaluation of spinning reserve is illustrated. In conventional reliability evaluation method, loads are deterministic values. The failure rate of the generating units is represented as triangular fuzzy number. The fuzzy set is used to represent consumer's demand, which is the deterministic load, as fuzzy loads. The concept is extended for evaluating the fuzzy based well-being indices using different criterion for the generating system. The fz-forced outage rate (FOR) and fz-availability of a unit in service are evaluated using fuzzy Sets and fuzzy interval arithmetic to find the fuzzy well-being states, which are designated as healthy, marginal and at risk. The concept is illustrated for a Roy Billinton's Test System (RBTS) and IEEE RTS. Impact of outage level and deterministic criteria is also illustrated. The proposed method can be applied to the operation of deregulated power system in which operating reserve is served as an important issue with respect to stable and reliable operation.

The fire-fighting system is one of the proactive technical barriers related to liquefied petroleum gas storage tank safety. This paper presents an integrated approach that uses fuzzy set theory, an improved-dependent uncertain ordered weighted averaging operator and fault tree analysis to handle uncertainty in the unavailability assessment of fire-fighting systems. In this study, the center of area is used to defuzzify triangular fuzzy numbers. Furthermore, for the fire-fighting system fault tree, importance analysis, including Fussell–Vesely importance measure and risk reduction worth of basic events, are performed to identify the weak links of the fire-fighting system. In addition, a real case study on a fire-fighting system for a liquefied petroleum gas storage system in an LPG unit in Algeria is provided to illustrate the effectiveness of the proposed methodology. The research results show that the proposed methodology makes it possible to assess the unavailability of the entire system by analyzing weak links. Consequently, some suggestions are given to take preventive–corrective actions in advance, in order to reduce the failure probability of fire-fighting system and assist the practitioners in setting priorities for improving safety procedures in liquefied petroleum gas storage tanks. The study provides references for analyzing safety barriers in a complex system.

Preventive maintenance of any system should depend on its starting, ending and operating conditions. Systems working with a minimum permissible reliability should be maintained at predetermined points to ensure its reliability do not fall below the permissible level. For any period, the starting condition of a system and the operating condition can be specified using fuzzy sets. Since the condition of the system at the end of a period depends on its starting condition and the operating condition during the period, linguistic variables are also required to specify it. This paper describes how to select periods of maintenance and the types of maintenance for such a system. The model utilizes the fuzzy set theory to determine the period length and the type of maintenance.

Classification problems affect all organizations. Important decisions affecting an organization's effectiveness include predicting the success of job applicants and the matching and assignment of individuals from a pool of applicants to available positions. In these situations, linear mathematical models are employed to optimize the allocation of an organization's human resources.

Use of linear techniques may be problematic, however, when relationships between predictor and criterion are nonlinear. As an alternative, we developed a fuzzy associative memory (FAM: a rule-based system based on fuzzy sets and logic) and used it to derive predictive (classification) equations composed of measures of job experience and job performance. The data consisted of two job experience factors used to predict measures of job performance for four US Air Force job families. The results indicated a nonlinear relationship between experience and performance for three of the four data sets. The overall classification accuracy was similar for the two systems, although the FAM provided better classification for two of the jobs. We discuss the apparent nonlinear relationships between experience and performance, and the advantages and implications of using these systems to develop and describe behavioral models.

As international corporate activities increase, the staffing of their operations involves more strategic concerns. However, foreign assignments have many differences, and dissatisfaction with host country is a known cause of expatriate failure. This study distinguishes from previous studies, which focused on the expatriate selection process from the viewpoint of the human resource managers. From the view of expatriate candidate's points, this paper describes a fuzzy analytic hierarchy process (fuzzy AHP) to determine the weighting of subjective judgments. When the expatriate assignments are evaluated from various aspects, such as employee personal factors, employee competencies, job characteristics, family factors, environmental factors and organization relocation support activities, it can be regarded as an fuzzy multiple criteria decision making (FMCDM) problem. Since expatriate candidates cannot clearly estimate the relative importance of each considered criterion in terms of numerical values, fuzziness is applicable. Consequently, this paper uses triangular fuzzy numbers by fuzzy AHP to establish weights for expatriate candidates, thus determining the relative importance for criteria of expatriate assignments. From the insights of this study, this article addresses this expatriate problem and offers guidelines for managers concerned with a successful expatriate assignment program.