Generalized OWA Aggregation Operators

We extend the ordered weighted averaging (OWA) operator to a provide a new class of operators called the generalized OWA (GOWA) operators. These operators add to the OWA operator an additional parameter controlling the power to which the argument values are raised. We look at some special cases of these operators. One important case corresponds to the generalized mean and another special case is the ordered weighted geometric operator.     

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.     

Order selection and pricing methods using flexible quantity and fuzzy approach for buyer evaluation

This paper presents the methods for order selection and pricing of manufacturer (supplier) with make-to-order basis when orders exceed production capacity. By quoting the concepts of triangular fuzzy numbers and linguistic variables, a fuzzy approach to evaluating buyers by taking into account both positive and negative criteria is proposed. According to the classified results of buyers, the orders will be produced with priority, declined, or determined by MIP model. The fixed quantity MIP model and flexible quantity MIP model are employed to determine the produced orders along with the production quantity and the reference amount for price reduction. By applying the concept of TOPSIS, the closeness coefficients for satisfaction grades of orders and for ranking values of buyers are used as the adjusting rates in the final pricing MIP model to set segmented price.     

Induced aggregation operators in the VIKOR method and its application in material selection

In this paper, a hybrid decision making approach integrating induced aggregation operators into VIKOR is proposed for tackling multicriteria problems with conflicting and noncommensurable (different units) criteria. For doing so, we develop a new distance aggregation operator called the induced ordered weighted averaging standardized distance (IOWASD) operator. It is an aggregation operator that provides a wide range of standardized distance measures between the maximum and the minimum by using the induced OWA (IOWA) operator. The main advantage of the IOWA-based VIKOR (IOWA-VIKOR) is that it is able to reflect the complex attitudinal character of the decision maker by using order inducing variables and provide much more complete information for decision making. We also studied some of the IOWASD’s main properties and different particular cases and further generalized it by using the induced generalized OWA (IGOWA) operator. Finally, we apply the integrated IOWA-VIKOR method in a multi-criteria decision making problem regarding the selection of materials and the results are compared for different types of standardized distance aggregation operators.     

Multi-criteria decision-making methods based on intuitionistic fuzzy sets

In this paper we present new methods for solving multi-criteria decision-making problem in an intuitionistic fuzzy environment. First, we define an evaluation function for the decision-making problem to measure the degrees to which alternatives satisfy and do not satisfy the decision-maker’s requirement. Then, we introduce and discuss the concept of intuitionistic fuzzy point operators. By using the intuitionistic fuzzy point operators, we can reduce the degree of uncertainty of the elements in a universe corresponding to an intuitionistic fuzzy set. Furthermore, a series of new score functions are defined for multi-criteria decision-making problem based on the intuitionistic fuzzy point operators and the evaluation function and their effectiveness and advantage are illustrated by examples.     

A Decision Making Method for the Quality Identification of Wines Based on Fuzzy Soft Sets

Quality identification of wines is a crucial one for wine industry. The paper aims to give a decision making approach based on soft fuzzy sets for it. First, based on fuzzy soft sets, calculation steps are given to solve decision making problems. The grey relative coefficient between each alternative with the ideal alternative is calculated by grey relational analysis (GRA). Then, a relative relational degree is defined to determine ranking orders of all alternatives. Finally, an application of our proposed approach demonstrates its practicality and effectiveness in the quality identification of red wines.     

A fuzzy framework for defining dynamic playlist generation heuristics

We study a dynamic way of automatically generating sequences of songs in this paper. Starting from a given seed song, a sequence is generated on-the-fly while listening to the music. During this process, the user can express his or her dislike for the currently played song by pressing a skip button. When the current song is finished or skipped, a heuristic is used to choose the next song to be played. We introduce fuzzy set theory as a formalism for defining such heuristics, because this allows us to make the definitions systematic, formal, and intuitively clear. By doing this, we obtain a general unified framework that includes all heuristics introduced previously by other authors. We compare these existing heuristics with several novel ones by means of extensive experimental evaluations. Moreover, we demonstrate that the presented formal framework can be used to easily generate variations of a heuristic that perform significantly better under specific circumstances.     

Probability density functions based weights for ordered weighted averaging (OWA) operators: An example of water quality indices

This paper explores the application of ordered weighted averaging (OWA) operators to develop water quality index, which incorporates an attitudinal dimension in the aggregation process. The major thrust behind selecting the OWA operator for aggregation of multi-criteria is its capability to encompass a range of operators bounded between minimum and maximum. A new approach for generating OWA weight distributions using probability density functions (PDFs) is proposed in this paper. The basic parameters (mean and standard deviation) of the probability density functions can be determined using the number of criteria (e.g., water quality indicators) in the aggregation process.     

Normalizing rank aggregation method for priority of a fuzzy preference relation and its effectiveness

The aim of this paper is to show that the normalizing rank aggregation method can not only be used to derive the priority vector for a multiplicative preference relation, but also for the additive transitive fuzzy preference relation. To do so, a simple functional equation between fuzzy preference’s element and priority weight is derived firstly, then, based on the equation, three methods are proposed to prove that the normalizing rank aggregation method is simple and effective for deriving the priority vector. Finally, a numerical example is used to illustrate the proposed methods.     

Fuzzy rule generation methods for high-level computer vision

In many decision making systems involving multiple sources, the decisions made may be considered as the result of a rule-based system in which the decision rules are usually enumerated by experts or generated by a learning process. In this paper, we discuss the various issues involved in the generation of fuzzy rules automatically from training data for high-level computer vision. Features are treated as linguistic variables that appear in the antecedent clauses of the rules. We present methods to generate the corresponding linguistic labels (values) and their membership functions. Rules are generated by constructing a minimal approximate fuzzy aggregation network and then training the network using gradient descent methods. Several examples are given.     

A fuzzy approach for selecting project membership to achieve cognitive style goals

Decision makers select employees for a project to match a particular set of goals pertaining to the multiple criteria mix of skills and competencies needed. Cognitive style influences how a person gathers and evaluates information and consequently, provides skills and competencies toward problem solving. The proposed fuzzy set-based model facilitates the manager’s selection of employees who meet the project goal(s) for the preferred cognitive style. The paper presents background information on cognitive styles and fuzzy logic with an algorithm developed based on belief in the fuzzy probability of a cognitive style fitting a defined goal. An application is presented with analysis and conclusions stated.     

A comparison of two methods for determining the weights of belonging to fuzzy sets

Saaty has solved a basic problem in fuzzy set theory using an eigenvector method to determine the weights of belonging of each member to the set. In this paper, a weighted least-square method is utilized to obtain the weights. This method has the advantage that it involves the solution of a set of simultaneous linear algebraic equations and is thus conceptually easier to understand than the eigenvector method. Examples are given for estimating the relative wealth of nations and the relative amount of foreign trade of nations. Numerical solutions are obtained using both the eigenvector method and the weighted least-square method, and the results are compared.Partial support of this research was provided by NIH Grant No. GM-23732.     

A fuzzy simple additive weighting system under group decision-making for facility location selection with objective/subjective attributes

This work presents a new fuzzy multiple attributes decision-making (FMADM) approach, i.e., fuzzy simple additive weighting system (FSAWS), for solving facility location selection problems by using objective/subjective attributes under group decision-making (GDM) conditions. The proposed system integrates fuzzy set theory (FST), the factor rating system (FRS) and simple additive weighting (SAW) to evaluate facility locations alternatives. The FSAWS is applied to deal with both qualitative and quantitative dimensions. The FSAWS process considers the importance of each decision-maker, and the total scores for alternative locations are then derived by homo/heterogeneous group of decision-makers. Finally, a numerical example illustrates the procedure of the proposed FSAWS.     

A mathematical model for identifying an optimal waste management policy under uncertainty

In the municipal solid waste (MSW) management system, there are many uncertainties associated with the coefficients and their impact factors. Uncertainties can be normally presented as both membership functions and probabilistic distributions. This study develops a scenario-based fuzzy-stochastic quadratic programming (SFQP) model for identifying an optimal MSW management policy and for allowing dual uncertainties presented as probability distributions and fuzzy sets being communicated into the optimization process. It can also reflect the dynamics of uncertainties and decision processes under a complete set of scenarios. The developed method is applied to a case study of long-term MSW management and planning. The results indicate that reasonable solutions have been generated. They are useful for identifying desired waste-flow-allocation plans and making compromises among system cost, satisfaction degree, and constraint-violation risk.     

A novel two-phase group decision making approach for construction project selection in a fuzzy environment

This paper considers a construction project problem under multiple criteria in a fuzzy environment and proposes a new two-phase group decision making (GDM) approach. This approach integrates a modified analytic network process (ANP) and an improved compromise ranking method, known as VIKOR. To take uncertainty and risk into account, a new decision making approach is presented with multiple fuzzy information by a group of experts, and a risk attitude for each expert is incorporated that can be expressed linguistically. First, a modified fuzzy ANP method is introduced to address the problem of dependence as well as feedback among conflicting criteria and to determine their relative importance. Then, a fuzzy VIKOR method is extended to rank potential projects on the basis of their overall performance. An illustrative example from the literature is provided for the construction project problem to demonstrate the effectiveness and feasibility of the proposed approach. The computational results show that the proposed two-phase GDM approach is suitable to cope with imprecision and subjectivity for the complicated decision making problem. Finally, the associated results of the proposed approach with risk attitudes and without risk attitudes are compared with the results reported by Cheng and Li [1], and the merits are highlighted.