Showing papers on "Fuzzy number published in 2009"

On hesitant fuzzy sets and decision

Abstract: Intuitionistic Fuzzy Sets (IFS) are a generalization of fuzzy sets where the membership is an interval. That is, membership, instead of being a single value, is an interval. A large number of operations have been defined for this type of fuzzy sets, and several applications have been developed in the last years. In this paper we describe hesitant fuzzy sets. They are another generalization of fuzzy sets. Although similar in intention to IFS, some basic differences on their interpretation and on their operators exist. In this paper we review their definition, the main results and we present an extension principle, which permits to generalize existing operations on fuzzy sets to this new type of fuzzy sets. We also discuss their use in decision making.

Weapon selection using the AHP and TOPSIS methods under fuzzy environment

Abstract: The weapon selection problem is a strategic issue and has a significant impact on the efficiency of defense systems. On the other hand, selecting the optimal weapon among many alternatives is a multi-criteria decision-making (MCDM) problem. This paper develops an evaluation model based on the analytic hierarchy process (AHP) and the technique for order performance by similarity to ideal solution (TOPSIS), to help the actors in defence industries for the selection of optimal weapon in a fuzzy environment where the vagueness and subjectivity are handled with linguistic values parameterized by triangular fuzzy numbers. The AHP is used to analyze the structure of the weapon selection problem and to determine weights of the criteria, and fuzzy TOPSIS method is used to obtain final ranking. A real world application is conducted to illustrate the utilization of the model for the weapon selection problem. The application could be interpreted as demonstrating the effectiveness and feasibility of the proposed model.

Risk evaluation in failure mode and effects analysis using fuzzy weighted geometric mean

Abstract: Failure mode and effects analysis (FMEA) has been extensively used for examining potential failures in products, processes, designs and services. An important issue of FMEA is the determination of risk priorities of the failure modes that have been identified. The traditional FMEA determines the risk priorities of failure modes using the so-called risk priority numbers (RPNs), which require the risk factors like the occurrence (O), severity (S) and detection (D) of each failure mode to be precisely evaluated. This may not be realistic in real applications. In this paper we treat the risk factors O, S and D as fuzzy variables and evaluate them using fuzzy linguistic terms and fuzzy ratings. As a result, fuzzy risk priority numbers (FRPNs) are proposed for prioritization of failure modes. The FRPNs are defined as fuzzy weighted geometric means of the fuzzy ratings for O, S and D, and can be computed using alpha-level sets and linear programming models. For ranking purpose, the FRPNs are defuzzified using centroid defuzzification method, in which a new centroid defuzzification formula based on alpha-level sets is derived. A numerical example is provided to illustrate the potential applications of the proposed fuzzy FMEA and the detailed computational process of the FRPNs.

Fuzzy hierarchical TOPSIS for supplier selection

Abstract: This study simplifies the complicated metric distance method [L.S. Chen, C.H. Cheng, Selecting IS personnel using ranking fuzzy number by metric distance method, Eur. J. Operational Res. 160 (3) 2005 803-820], and proposes an algorithm to modify Chen's Fuzzy TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) [C.T. Chen, Extensions of the TOPSIS for group decision-making under fuzzy environment, Fuzzy Sets Syst., 114 (2000) 1-9]. From experimental verification, Chen directly assigned the fuzzy numbers [email protected]? and [email protected]? as fuzzy positive ideal solution (PIS) and negative ideal solution (NIS). Chen's method sometimes violates the basic concepts of traditional TOPSIS. This study thus proposes fuzzy hierarchical TOPSIS, which not only is well suited for evaluating fuzziness and uncertainty problems, but also can provide more objective and accurate criterion weights, while simultaneously avoiding the problem of Chen's Fuzzy TOPSIS. For application and verification, this study presents a numerical example and build a practical supplier selection problem to verify our proposed method and compare it with other methods.

Combination of interval-valued fuzzy set and soft set

Abstract: The soft set theory, proposed by Molodtsov, can be used as a general mathematical tool for dealing with uncertainty. By combining the interval-valued fuzzy set and soft set models, the purpose of this paper is to introduce the concept of the interval-valued fuzzy soft set. The complement, ''AND'' and ''OR'' operations are defined on the interval-valued fuzzy soft sets. The DeMorgan's, associative and distribution laws of the interval-valued fuzzy soft sets are then proved. Finally, a decision problem is analyzed by the interval-valued fuzzy soft set. Some numerical examples are employed to substantiate the conceptual arguments.

Long term supplier selection using a combined fuzzy MCDM approach: A case study for a telecommunication company

Abstract: With the globalization and the emergence of the extended enterprise of interdependent organizations, there has been a steady increase in the outsourcing of parts and services. This has led firms to give more importance to the purchasing function and its associated decisions. Since these decisions require a long term investment for the telecommunication industry especially and affect the strategic positioning of the companies in the sector, the selection of the proper supplier is one of the most important problems. Supplier selection is a multi-criteria problem which includes both tangible and intangible factors. This paper develops a supplier evaluation approach based on the analytic network process (ANP) and the technique for order performance by similarity to ideal solution (TOPSIS) methods to help a telecommunication company in the GSM sector in Turkey under the fuzzy environment where the vagueness and subjectivity are handled with linguistic terms parameterized by triangular fuzzy numbers. Contrary to conventional Fuzzy ANP (FANP) methodology in the literature, we use triangular fuzzy numbers in all pairwise comparison matrices in the FANP. Hence, criteria weights are calculated as the triangular fuzzy numbers and then these fuzzy criteria weights are inserted to the fuzzy TOPSIS methodology to rank the alternatives. This approach is demonstrated with a real world case study involving six main evaluation criteria that the company has determined to choose the most appropriate supplier. The study was followed by the sensitivity analyses of the results.

A new approach for ranking of trapezoidal fuzzy numbers

Abstract: Ranking fuzzy numbers plays an very important role in linguistic decision making and some other fuzzy application systems. Several strategies have been proposed for ranking of fuzzy numbers. Each of these techniques have been shown to produce non-intuitive results in certain cases. In this paper, we will introduce a new approach for ranking of trapezoidal fuzzy numbers based on the left and the right spreads at some @a-levels of trapezoidal fuzzy numbers. The calculation of the proposed method is far simpler and easier. Finally, some comparative examples are used to illustrate the advantage of the proposed method.

A causal and effect decision making model of service quality expectation using grey-fuzzy DEMATEL approach

Abstract: This research uses a solution based on a combined grey-fuzzy DEMATEL method to deal with the objective of the study. This study is aimed to present a perception approach to deal with real estate agent service quality expectation ranking with uncertainty. The ranking of best top five real estate agents might be a key strategic direction of other real estate agents prior to service quality expectation. The solving procedure is as follows: (i) the weights of criteria and alternatives are described in triangular fuzzy numbers; (ii) a grey possibility degree is used to result the ranking order for all alternatives; (iii) DEMATEL is used to resolve interdependency relationships among the criteria and (iv) an empirical example of real estate agent service quality ranking problem in customer expectation is used to resolve with this proposed method approach indicating that real estate agent R1 (CY real estate agent) is the best selection in terms of service quality in customer expectation.

Multicriteria fuzzy decision-making method based on a novel accuracy function under interval-valued intuitionistic fuzzy environment

Abstract: The interval-valued intuitionistic fuzzy weighted arithmetic average operator, the interval-valued intuitionistic fuzzy weighted geometric average operator, and an accuracy function of interval-valued intuitionistic fuzzy value are introduced in this paper. A novel accuracy function for interval-valued intuitionistic fuzzy sets (IVIFSs) is proposed by taking into account the unknown degree (hesitancy degree) of IVIFSs to overcome the situation of difficult decision of existing accuracy functions to the alternatives in some cases. To identify the best alternative in multicriteria decision-making problems, a multicriteria fuzzy decision-making method is established in which criterion values for alternatives are IVIFSs. We utilize the interval-valued intuitionistic fuzzy weighted aggregation operators to aggregate the interval-valued intuitionistic fuzzy information corresponding to each alternative, and then rank the alternatives and select the most desirable one(s) according to the accuracy degree of the aggregated the interval-valued intuitionistic fuzzy information corresponding to the new accuracy function. Finally, an illustrative example is given to verify the developed approach.

Extension of fuzzy TOPSIS method based on interval-valued fuzzy sets

Abstract: Decision making is one of the most complex administrative processes in management. In circumstances where the members of the decision making team are uncertain in determining and defining the decision making criteria, fuzzy theory provides a proper tool to encounter with such uncertainties. However, if decision makers cannot reach an agreement on the method of defining linguistic variables based on the fuzzy sets, the interval-valued fuzzy set theory can provide a more accurate modeling. In this paper the interval-valued fuzzy TOPSIS method is presented aiming at solving MCDM problems in which the weights of criteria are unequal, using interval-valued fuzzy sets concepts.

$\alpha$ -Plane Representation for Type-2 Fuzzy Sets: Theory and Applications

Abstract: This paper 1) reviews the alpha-plane representation of a type-2 fuzzy set (T2 FS), which is a representation that is comparable to the alpha-cut representation of a type-1 FS (T1 FS) and is useful for both theoretical and computational studies of and for T2 FSs; 2) proves that set theoretic operations for T2 FSs can be computed using very simple alpha-plane computations that are the set theoretic operations for interval T2 (IT2) FSs; 3) reviews how the centroid of a T2 FS can be computed using alpha-plane computations that are also very simple because they can be performed using existing Karnik Mendel algorithms that are applied to each alpha-plane; 4) shows how many theoretically based geometrical properties can be obtained about the centroid, even before the centroid is computed; 5) provides examples that show that the mean value (defuzzified value) of the centroid can often be approximated by using the centroids of only 0 and 1 alpha -planes of a T2 FS; 6) examines a triangle quasi-T2 fuzzy logic system (Q-T2 FLS) whose secondary membership functions are triangles and for which all calculations use existing T1 or IT2 FS mathematics, and hence, they may be a good next step in the hierarchy of FLSs, from T1 to IT2 to T2; and 7) compares T1, IT2, and triangle Q-T2 FLSs to forecast noise-corrupted measurements of a chaotic Mackey-Glass time series.

Fuzzy risk analysis based on ranking generalized fuzzy numbers with different heights and different spreads

Abstract: In this paper, we present a new method for fuzzy risk analysis based on ranking generalized fuzzy numbers with different heights and different spreads. First, we present a new method for ranking generalized fuzzy numbers. The proposed method considers the defuzzified values, the heights and the spreads for ranking generalized fuzzy numbers. Based on the proposed method for ranking generalized fuzzy numbers, we propose a fuzzy risk analysis algorithm to deal with fuzzy risk analysis problems. The proposed method provides a useful way for handling the fuzzy risk analysis problems.

Intuitionistic and interval-valued intutionistic fuzzy preference relations and their measures of similarity for the evaluation of agreement within a group

Abstract: Szmidt and Kacprzyk (Lecture Notes in Artificial Intelligence 3070:388---393, 2004a) introduced a similarity measure, which takes into account not only a pure distance between intuitionistic fuzzy sets but also examines if the compared values are more similar or more dissimilar to each other. By analyzing this similarity measure, we find it somewhat inconvenient in some cases, and thus we develop a new similarity measure between intuitionistic fuzzy sets. Then we apply the developed similarity measure for consensus analysis in group decision making based on intuitionistic fuzzy preference relations, and finally further extend it to the interval-valued intuitionistic fuzzy set theory.

Introduction to fuzzy soft groups

Abstract: In this paper, the concept of fuzzy soft group is introduced and in the meantime, some of their properties and structural characteristics are discussed and studied. Furthermore, definitions of fuzzy soft function and fuzzy soft homomorphism are defined and the theorems of homomorphic image and homomorphic pre-image are given. After that, the definition of normal fuzzy soft group is given and some of its basic properties are studied.

Some geometric aggregation functions and their application to dynamic multiple attribute decision making in the intuitionistic fuzzy setting

Abstract: The intuitionistic fuzzy set (IFS) characterized by a membership function and a non-membership function, was introduced by [K. Atanassov, "Intuitionistic fuzzy sets", Fuzzy Sets and Systems20 (1986) 87–96] as a generalization of Zadeh' fuzzy set [L. A. Zadeh, "Fuzzy sets", Information and Control8 (1965) 338–356] to deal with fuzziness and uncertainty. In this paper, the dynamic multiple attribute decision making (DMADM) problems with intuitionistic fuzzy information are investigated. The notions of intuitionistic fuzzy variable and uncertain intuitionistic fuzzy variable are defined, and two new aggregation operators called dynamic intuitionistic fuzzy weighted geometric (DIFWG) operator and uncertain dynamic intuitionistic fuzzy weighted geometric (UDIFWG) operator are proposed. Moreover, a procedure based on the DIFWG and IFWG operators is developed to solve the dynamic intuitionistic fuzzy multiple attribute decision making problems where all the decision information about attribute values takes the form of intuitionistic fuzzy numbers collected at different periods, and a procedure based on the UDIFWG and IIWG operators is developed for uncertain dynamic intuitionistic fuzzy multiple attribute decision making problems under interval uncertainty in which all the decision information about attribute values takes the form of interval-valued intuitionistic fuzzy numbers collected at different periods. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.

Improving Generalization of Fuzzy IF--THEN Rules by Maximizing Fuzzy Entropy

Abstract: When fuzzy IF-THEN rules initially extracted from data have not a satisfying performance, we consider that the rules require refinement. Distinct from most existing rule-refinement approaches that are based on the further reduction of training error, this paper proposes a new rule-refinement scheme that is based on the maximization of fuzzy entropy on the training set. The new scheme, which is realized by solving a quadratic programming problem, is expected to have the advantages of improving the generalization capability of initial fuzzy IF-THEN rules and simultaneously overcoming the overfitting of refinement. Experimental results on a number of selected databases demonstrate the expected improvement of generalization capability and the prevention of overfitting by a comparison of both training and testing accuracy before and after the refinement.

Polynomial Fuzzy Models for Nonlinear Control: A Taylor Series Approach

Abstract: Classical Takagi-Sugeno (T-S) fuzzy models are formed by convex combinations of linear consequent local models. Such fuzzy models can be obtained from nonlinear first-principle equations by the well-known sector-nonlinearity modeling technique. This paper extends the sector-nonlinearity approach to the polynomial case. This way, generalized polynomial fuzzy models are obtained. The new class of models is polynomial, both in the membership functions and in the consequent models. Importantly, T-S models become a particular case of the proposed technique. Recent possibilities for stability analysis and controller synthesis are also discussed. A set of examples shows that polynomial modeling is able to reduce conservativeness with respect to standard T-S approaches as the degrees of the involved polynomials increase.

An integrated fuzzy model for supplier management

Abstract: Supplier selection is a multi-criteria decision-making problem which consists of both qualitative and quantitative metrics. A lot of investigations have been published in the supplier selection area and it has been notified that in the majority of these publications supplier selection and evaluation and development have the same meaning. However, one needs integrated models to cover all of these stages. In addition, most of the proposed models focused on manufacturing environments and a few papers have been allocated for service industries. To our knowledge, no Internet service provider (ISP) selection and evaluation has been published up to now.In this paper, we propose a new framework on the basis of company's strategy for supplier management including supplier selection, evaluation, and development. In the first phase, quality function deployment (QFD) is utilized to rank the best ISPs based on qualitative criteria. Then, a quantitative model is adopted to consider quantitative metrics. Finally, we compose two models and select the best ISPs. In the next phase, we propose a novel algorithm to evaluate selected ISPs from three perspectives: customer, performance, and competition. Meanwhile, the fuzzy logic and triangular fuzzy numbers are utilized to deal with vagueness of human thought. Furthermore, a case study is conducted to illustrate the stages of ISP selection and evaluation. The implementation of the proposed model is easy and do not need optimization background.

Entropy of interval-valued fuzzy sets based on distance and its relationship with similarity measure

Abstract: This article proposes a new axiomatic definition of entropy of interval-valued fuzzy sets (IVFSs) and discusses its relation with similarity measure. First, we propose an axiomatic definition of entropy for IVFS based on distance which is consistent with the axiomatic definition of entropy of a fuzzy set introduced by De Luca, Termini and Liu. Next, some formulae are derived to calculate this kind of entropy. Furthermore we investigate the relationship between entropy and similarity measure of IVFSs and prove that similarity measure can be transformed by entropy. Finally, a numerical example is given to show that the proposed entropy measures are more reasonable and reliable for representing the degree of fuzziness of an IVFS.