Multi-attribute aggregation operators

This paper deals with the idea of aggregation. A new, enlarged notion of aggregation operator is given, along with a classification of classical properties into some main groups. The concept of multi-attribute aggregation operator, which incorporates many classical aggregation methods, is provided. An extension of different properties to multi-attribute aggregation operators is proposed.     

Design of fuzzy logic controllers based on generalized T-operators

Since Zadeh first proposed the basic principle of fuzzy logic controllers in 1968, the and operators have been popular in the design of fuzzy logic controllers. In this paper, the general concept of T-operators is introduced into the conventional design methods for fuzzy logic controllers so that a general and flexible methodology for the design of these fuzzy logic controllers is available. Then, by computer simulations, studies are made so as to determine the relations between the various T-operators and the performance of a fuzzy logic controller. It is concluded that the performance of the fuzzy logic controller for a given class of plants very much depends upon the choice of the T-operators.     

Distance measures with heavy aggregation operators

The use of distance measures and heavy aggregations in the ordered weighted averaging (OWA) operator is studied. We present the heavy ordered weighted averaging distance (HOWAD) operator. It is a new aggregation operator that provides a parameterized family of aggregation operators between the minimum distance and the total distance operator. Thus, it permits to analyze an aggregation from its usual average (normalized distance) to the sum of all distances available in the aggregation process. We analyze some of its main properties and particular cases such as the normalized Hamming distance, the weighted Hamming distance and the OWA distance (OWAD) operator. This approach is generalized by using quasi-arithmetic means obtaining the quasi-arithmetic HOWAD (Quasi-HOWAD) operator and with norms obtaining the heavy OWA norm (HOWAN). Further extensions to this approach are presented by using moving averages forming the moving HOWAD (HOWMAD) and the moving Quasi-HOWAN (Quasi-HOWMAN) operator. The applicability of the new approach is studied in a decision making model regarding the selection of national policies. We focus on the selection of monetary policies. The key advantage of this approach is that we can consider several sources of information that are independent between them.     

On generalized Bonferroni mean operators for multi-criteria aggregation

We introduce the idea of multi-criteria aggregation functions and describe a number of properties desired in such functions. We emphasize the importance of having an aggregation function capture the expressed interrelationship between the criteria. A number of standard aggregation functions are introduced. We next introduce the Bonferroni mean operator. We provide an interpretation of this operator as involving a product of each argument with the average of the other arguments, a combined averaging and “anding” operator. This allows us to suggest generalizations of this operator by replacing the simple averaging by other mean type operators as well as associating differing importances with the arguments.     

Continuous interval-valued intuitionistic fuzzy aggregation operators and their applications to group decision making

In this paper, we introduce a new operator called the continuous interval-valued intuitionistic fuzzy ordered weighted averaging (C-IVIFOWA) operator for aggregating the interval-valued intuitionistic fuzzy values. It combines the intuitionistic fuzzy ordered weighted averaging (IFOWA) operator and the continuous ordered weighted averaging (C-OWA) operator by a controlling parameter, which can be employed to diminish fuzziness and improve the accuracy of decision making. We further apply the C-IVIFOWA operator to the aggregation of multiple interval-valued intuitionistic fuzzy values and obtain a wide range of aggregation operators including the weighted C-IVIFOWA (WC-IVIFOWA) operator, the ordered weighted (OWC-IVIFOWA) operator and the combined C-IVIFOWA (CC-IVIFOWA) operator. Some desirable properties of these operators are investigated. And finally, we give a numerical example to illustrate the applications of these operators to group decision making under interval-valued intuitionistic fuzzy environment.     

Some induced ordered weighted averaging operators and their use for solving group decision-making problems based on fuzzy preference relations

In [R.R. Yager, D.P. Filev, Operations for granular computing: Mixing words and numbers, in: Proceedings of the FUZZ-IEEE World Congress on Computational Intelligence, Anchorage, 1998, pp. 123–128] Yager and Filev introduced the Induced Ordered Weighted Averaging (IOWA) operator. In this paper, we provide some IOWA operators to aggregate fuzzy preference relations in group decision-making (GDM) problems. These IOWA operators when guided by fuzzy linguistic quantifiers allow the introduction of some semantics or meaning in the aggregation, and therefore allow for a better control over the aggregation stage developed in the resolution process of the GDM problems. In particular, we present the Importance IOWA (I-IOWA) operator, which applies the ordering of the argument values based upon the importance of the information sources; the Consistency IOWA (C-IOWA) operator, which applies the ordering of the argument values based upon the consistency of the information sources; and the Preference IOWA (P-IOWA) operator, which applies the ordering of the argument values based upon the relative preference values associated to each one of them. We provide a procedure to deal with ‘ties’ in respect to the ordering induced by the application of one of these IOWA operators; it consists of a sequential application of the above IOWA operators. We also present a selection process for GDM problems based on the concept of fuzzy majority and the above three IOWA operators. Finally, we analyse the reciprocity and consistency properties of the collective fuzzy preference relations obtained using IOWA operators.     

Fuzzy set approach to the utility,preference relations,and aggregation operators

Score x = (x₁, … , x_n) describing an alternative α is modelled by means of a continuous quasi-convex fuzzy quantity μ_α = μ_x, thus allowing to compare alternatives (scores) by means of fuzzy ordering (comparison) methods. Applying some defuzzification method leads to the introduction of operators acting on scores. A special stress is put on the Mean of Maxima defuzzification method allowing to introduce several averaging aggregation operators. Moreover, our approach allows to introduce weights into above mentioned aggregation, even in the non-anonymous (non-symmetric) case. Finally, Ordered Weighted Aggregation Operators (OWAO) are introduced, generalizing the standard OWA operators.     

Generalized weighted exponential proportional aggregation operators and their applications to group decision making

We present a new aggregation operator called the generalized ordered weighted exponential proportional averaging (GOWEPA) operator, which is based on an optimal model. We study some properties and different families of the GOWEPA operator. We also generalize the GOWEPA operator. The key advantage of the GOWEPA operator is that it is an aggregation operator with theoretic basis on aggregation. Moreover, we propose an orness measure of the GOWEPA operator and indicate some properties of this orness measure. Furthermore, we introduce the least exponential squares method (LESM) to determine the GOWEPA operator weights based on its orness measure. In the end, we develop an application of the new approach in a case of group decision making in investment selection.     

The aggregation operations for decision making in probabilistic fuzzy environment

This paper deals with some important classes of aggregation operations on various kinds of sets applied to decision making problems.These operations are mainly based on general concepts such as triangular norms (t- and s-norms). In this paper we focus particularly on operations on probabilistic sets and their distribution function representation. The considerations are illustrated by means of numerical examples.     

Hesitant fuzzy information aggregation in decision making

As a generalization of fuzzy set, hesitant fuzzy set is a very useful tool in situations where there are some difficulties in determining the membership of an element to a set caused by a doubt between a few different values. The aim of this paper is to develop a series of aggregation operators for hesitant fuzzy information. We first discuss the relationship between intutionistic fuzzy set and hesitant fuzzy set, based on which we develop some operations and aggregation operators for hesitant fuzzy elements. The correlations among the aggregation operators are further discussed. Finally, we give their application in solving decision making problems.     

A general class of fuzzy operators,the demorgan class of fuzzy operators and fuzziness measures induced by fuzzy operators

In this paper we examine operators which can be derived from the general solution of functional equations on associativity. We define the characteristics of those functions f(x) which are necessary for the production of operators. We shall show, that with the help of the negation operator for every such function f(x) a function g(x) can be given, from which a disjunctive operator can be derived, and for the three operators the DeMorgan identity is fulfilled. For the fulfillment of the DeMorgan identity the necessary and sufficient conditions are given.We shall also show that an f_λ(x) can be constructed for every f(x), so that for the derived k_λ(x,y) and d_λ(x,y) lim_λ→∞k_λ(x,y) and lim_λ→∞d_λ(x,y) = max(x,y).As Yager's operator is not reducible, for every λ there exists an α, for which, in case x < α and y<α, k_λ(x,y) = 0.We shall give an f(x) which has the characteristics of Yager's operator, and which is strictly monotone.Finally we shall show, that with the help of all those f(x), which are necessary when constructing a k(x,y), an F(x) can be constructed which has the properties of the measures of fuzziness introduced by A. De Luca and S. Termini. Some classical fuzziness measures are obtained as special cases of our system.     

A new approach to fuzzy wavelet system modeling

In this paper, we propose simple but effective two different fuzzy wavelet networks (FWNs) for system identification. The FWNs combine the traditional Takagi–Sugeno–Kang (TSK) fuzzy model and discrete wavelet transforms (DWT). The proposed FWNs consist of a set of if–then rules and, then parts are series expansion in terms of wavelets functions. In the first system, while the only one scale parameter is changing with it corresponding rule number, translation parameter sets are fixed in each rule. As for the second system, DWT is used completely by using wavelet frames. The performance of proposed fuzzy models is illustrated by examples and compared with previously published examples. Simulation results indicate the remarkable capabilities of the proposed methods. It is worth noting that the second FWN achieves high function approximation accuracy and fast convergence.     

A general model of parameterized OWA aggregation with given orness level

The paper proposes a general optimization model with separable strictly convex objective function to obtain the consistent OWA (ordered weighted averaging) operator family. The consistency means that the aggregation value of the operator monotonically changes with the given orness level. Some properties of the problem are discussed with its analytical solution. The model includes the two most commonly used maximum entropy OWA operator and minimum variance OWA operator determination methods as its special cases. The solution equivalence to the general minimax problem is proved. Then, with the conclusion that the RIM (regular increasing monotone quantifier) can be seen as the continuous case of OWA operator with infinite dimension, the paper further proposes a general RIM quantifier determination model, and analytically solves it with the optimal control technique. Some properties of the optimal solution and the solution equivalence to the minimax problem for RIM quantifier are also proved. Comparing with that of the OWA operator problem, the RIM quantifier solutions are usually more simple, intuitive, dimension free and can be connected to the linguistic terms in natural language. With the solutions of these general problems, we not only can use the OWA operator or RIM quantifier to obtain aggregation value that monotonically changes with the orness level for any aggregated set, but also can obtain the parameterized OWA or RIM quantifier families in some specific function forms, which can incorporate the background knowledge or the required characteristic of the aggregation problems.     

Multiple-attribute decision support system based on fuzzy logic for performance assessment

This paper deals with the problem of assessing the performance of a set of production units, simultaneously considering different kinds of information, yielded by a Data Envelopment Analysis, a qualitative data analysis and an expert assessment. The tool for integrating heterogeneous data is a model that applies fuzzy logic to decision support systems. The results obtained are a holistic performance assessment of each unit of the set and a ranking order of the units.     

Robust design of rule-based fuzzy controllers

This paper deals with the design of stable and robust rule-based fuzzy control systems. New expressions to compute indices which provide a measure of the stability and robustness of fuzzy control systems are presented. The relation between the modification of the rules and the stability is studied through the so-called sensitivity indices. The paper presents procedures that make use of these indices to improve the design of fuzzy control systems, including the modification of the rules to obtain the global stability of an unstable system with multiple attractors, and to improve the dynamic behavior or the robustness of a non-linear plant. An example with a fuzzy controller for a system with non-linear damping and saturation in the actuation is presented to illustrate the design procedure.     

Optimal aggregation of fuzzy preference relations with an application to broadband internet service selection

This paper investigates the aggregation of multiple fuzzy preference relations into a collective fuzzy preference relation in fuzzy group decision analysis and proposes an optimization based aggregation approach to assess the relative importance weights of the multiple fuzzy preference relations. The proposed approach that is analytical in nature assesses the weights by minimizing the sum of squared distances between any two weighted fuzzy preference relations. Relevant theorems are offered in support of the proposed approach. Multiplicative preference relations are also incorporated into the approach using an appropriate transformation technique. An eigenvector method is introduced to derive the priorities from the collective fuzzy preference relation. The proposed aggregation approach is tested using two numerical examples. A third example involving broadband internet service selection is offered to illustrate that the proposed aggregation approach provides a simple, effective and practical way of aggregating multiple fuzzy preference relations in real-life situations.     

Selection of parameters for a fuzzy logic controller

The fuzzy logic controller is reviewed and its parameter are explicitly identified. The problem of initial selection and subsequent adjustment of the parameters are discussed in detail by example.