Induced and uncertain heavy OWA operators

In this paper, we analyse in detail the ordered weighted averaging (OWA) operator and some of the extensions developed about it. We specially focus on the heavy aggregation operators. We suggest some new extensions about the OWA operator such as the induced heavy OWA (IHOWA) operator, the uncertain heavy OWA (UHOWA) operator and the uncertain induced heavy OWA (UIHOWA) operator. For these three new extensions, we consider some of their main properties and a wide range of special cases found in the weighting vector such as the heavy weighted average (HWA) and the uncertain heavy weighted average (UHWA). We further generalize these models by using generalized and quasi-arithmetic means obtaining the generalized heavy weighted average (GHWA), the induced generalized HOWA (IGHOWA) and the uncertain IGHOWA (UIGHOWA) operator. Finally, we develop an application of the new approach in a decision-making problem.     

Quantile-induced uncertain heavy ordered weighted averaging operator and the application in incentive evaluation problems

To uncertain evaluation problems, we integrate incentive management into the aggregation process and propose an aggregation operator called quantile-induced uncertain heavy ordered weighted averaging (QI-UHOWA) operator, which is an extension of the quantile-induced heavy ordered weighted averaging (QI-HOWA) operator. We provide an approach for determining the quantile order-inducing variables by using the technique for order preference by similarity to ideal solution method and the Hamming distance. In this case, the quantile values are measurements of relative developments of alternatives. Furthermore, we analyze the main properties of the operator including commutativity, boundedness, and monotonicity with uniform development space. The QI-UHOWA weighting vector is calculated using the maximum entropy measure with a given level of incentive attitude. We further expand the weighting method to the case of hierarchical stimulation. Moreover, the QI-UHOWA operator is generalized using the quasi-arithmetic mean. Finally, a numerical example regarding the selection of the optimal candidate(s) is given. The aggregation results are compared with those of the UOWA and QI-UOWA operator to illustrate the validity of the QI-UHOWA operator.     

Quantile-induced vector-based heavy OWA operator and the application in dynamic decision making

To the incentive problems in dynamic decision making, we propose a new type of aggregation operator denoted the quantile-induced vector-based heavy ordered weighted averaging (QI-VHOWA) operator. The main characteristic of the operator is that the arguments are aggregated using the form of vector. Additionally, the decision maker's incentive expectation is integrated into the aggregation process by various segmented incentive coefficients. We calculate the quantile measures of the argument vectors based on the technique for order of preference by similarity to ideal solution method. We determine the QI-VHOWA weighting vector by considering the location position of an alternative's performance as well as the development trend. The primary properties of the operator are discussed, including commutativity, boundness, and monotonicity under certain conditions. Finally, a numerical example regarding the evaluation of employees' performances in multiple periods is provided. The results are compared with that of the vector-based OWA and vector-based weighted arithmetic averaging operators. It is found that the incentive effectiveness of the QI-VHOWA is the most significant. The use of the QI-VHOWA operator is helpful to guide the long-term development of an alternative.     

Heavy Moving Averages and Their Application in Econometric Forecasting

This paper presents the heavy ordered weighted moving average (HOWMA) operator. It is an aggregation operator that uses the main characteristics of two well-known techniques: the heavy ordered weighted averaging (OWA) and the moving averages. Therefore, this operator provides a parameterized family of aggregation operators from the minimum to the total operator and includes the OWA operator as a special case. It uses a heavy weighting vector in the moving average formulation and it represents the information available and the knowledge of the decision maker about the future scenarios of the phenomenon, according to his attitudinal character. Some of the main properties of this operator are studied, including a wide range of families of HOWMA operators such as the heavy moving average and heavy weighted moving average operators. The HOWMA operator is also extended using generalized and quasi-arithmetic means. An example concerning the foreign exchange rate between US dollars and Mexican pesos is also presented.     

New decision-making techniques and their application in the selection of financial products

We develop a new approach that uses the ordered weighted averaging (OWA) operator in the selection of financial products. In doing so, we introduce the ordered weighted averaging distance (OWAD) operator and the ordered weighted averaging adequacy coefficient (OWAAC) operator. These aggregation operators are very useful for decision-making problems because they establish a comparison between an ideal alternative and available options in order to find the optimal choice. The objective of this new model is to manipulate the attitudinal character of previous methods based on distance measures, so that the decision maker can select financial products according to his or her degree of optimism, which is also known as the orness measure. The main advantage of using the OWA operator is that we can generate a parameterized family of aggregation operators between the maximum and the minimum. Thus, the analysis developed in the decision process by the decision maker is much more complete, because he or she is able to select the particular case in accordance with his or her interests in the aggregation process. The paper ends with an illustrative example that shows results obtained by using different types of aggregation operators in the selection of financial products.     

A method for fuzzy group decision making based on induced aggregation operators and Euclidean distance

In this paper, we present the fuzzy‐induced Euclidean ordered weighted averaging distance (FIEOWAD) operator. It is an extension of the ordered weighted averaging (OWA) operator that uses the main characteristics of the induced OWA (IOWA), the Euclidean distance and uncertain information represented by fuzzy numbers. The main advantage of this operator is that it is able to consider complex attitudinal characters of the decision maker by using order‐inducing variables in the aggregation of the Euclidean distance. Moreover, it is able to deal with uncertain environments where the information is very imprecise and can be assessed with fuzzy numbers. We study some of its main properties and particular cases such as the fuzzy maximum distance, fuzzy minimum distance, fuzzy‐normalized Euclidean distance (FNED), fuzzy‐weighted Euclidean distance (FWED), and fuzzy Euclidean ordered weighted averaging distance (FEOWAD) operator. Finally, we present an application of the operator to a group decision‐making problem concerning the selection of strategies.     

Behavioral ordered weighted averaging operator and the application in multiattribute decision making

This paper introduces a new type of behavioral ordered weighted averaging (BOWA) operator, to incorporate decision maker’s gains and losses behavior tendency into the information aggregation process. The main characteristic of this BOWA operator is that it considers behavioral weights and ordered weights in the same formulation. We further provide a calculation method of the behavioral weights, in which various psychological preferences of different attribute types of the decision maker can be expressed intuitively. In addition, we discuss some particular cases of BOWA operator and its main properties. Finally, a numerical example is used to illustrate the use of the proposed method.     

Study on the ranking problems in multiple attribute decision making based on interval‐valued intuitionistic fuzzy numbers

This paper puts forward a new ranking method for multiple attribute decision‐making problems based on interval‐valued intuitionistic fuzzy set (IIFS) theory. First, the composed ordered weighted arithmetic averaging operator and composed ordered weighted geometric averaging operator are extended to the IIFSs in which they are, respectively, named interval‐valued intuitionistic fuzzy composed ordered weighted arithmetic averaging (IIFCOWA) operator and interval‐valued intuitionistic composed ordered weighted geometric averaging (IIFCOWG) operator. Afterwards, to compare interval‐valued intuitionistic fuzzy numbers, we define the concepts of the maximum, the minimum, and ranking function. Some properties associated with the concepts are investigated. Using the IIFCOWA or IIFCOWG operator, we establish the detailed steps of ranking alternatives (or attributes) in multiple attribute decision making. Finally, an illustrative example is provided to show that the proposed ranking method is feasible in multiple attribute decision making.     

Implicit Elicitation of Attitudinal Character in the OWA Operator

Ordered weighted averaging (OWA) operators are well recognized as aggregation operators and are successfully applied to real world problems. The OWA operator weights are also known to play an important role in the aggregation, and thus, they heavily affect the final aggregation results. In this paper, we attempt to elicit a hidden attitudinal character from a decision‐maker through a simple question about his or her preference of alternatives for the purpose of alleviating the burden of specifying an attitudinal character. A paired comparison of alternatives in a decision‐making problem yields a precise (or uncertain) attitudinal character, which can be used to derive OWA operator weights via one of the well‐established weight generating methods.     

A novel aggregation method for Pythagorean fuzzy multiple attribute group decision making

As an extension of fuzzy set, a Pythagorean fuzzy set has recently been developed to model imprecise and ambiguous information in practical group decision‐making problems. The aim of this paper is to introduce a novel aggregation method for the Pythagorean fuzzy set and analyze possibilities for its application in solving multiple attribute decision‐making problems. More specifically, a new Pythagorean fuzzy aggregation operator called the Pythagorean fuzzy induced ordered weighted averaging‐weighted average (PFIOWAWA) operator is developed. This operator inherits main characteristics of both ordered weighted average operator and induced ordered weighted average to aggregate the Pythagorean fuzzy information. Some of main properties and particular cases of the PFIOWAWA operator are studied. A method based on the proposed operator for multiple attribute group decision making is developed. Finally, we present a numerical example of selection of research and development projects to illustrate applicability of the new approach in a multiple attribute group decision‐making problem.     

Linguistic continuous ordered weighted distance measure and its application to multiple attributes group decision making

This paper develops a new method for group decision making and introduces a linguistic continuous ordered weighted distance (LCOWD) measure. It is a new distance measure that combines the linguistic continuous ordered weighted averaging (LCOWA) operator with the ordered weighted distance (OWD) measure considering the risk attitude of decision maker. Moreover, it also can relieve the influence of extremely large or extremely small deviations on the aggregation results by assigning them smaller weights. These advantages make it suitable to deal with the situations where the input arguments are represented with uncertain linguistic information. Some of the main properties of the LCOWD measure and different particular cases are studied. The applicability of the new approach is also analyzed focusing on a group decision making problem.     

广义犹豫模糊信息集成及其多属性群决策

在犹豫模糊环境下,主要研究了基于阿基米德范数的广义信息集成算法,并提出了一种新的多属性群决策方法。基于阿基米德T-范数和S-范数,定义了广义犹豫模糊运算法则;运用新定义的广义犹豫模糊运算法则,提出了广义犹豫模糊有序加权平均(G-HFOWA)算子,研究了其优良性质;探讨了在某些特殊情况下,广义犹豫模糊有序加权平均算子将转化为一些常见的犹豫模糊信息集成算子,包括犹豫模糊有序加权平均算子、犹豫模糊Einstein有序加权平均算子、犹豫模糊Hamacher有序加权平均算子以及犹豫模糊Frank有序加权平均算子;基于广义信息集成算子,构建了一种新的犹豫模糊多属性群决策方法,并将其应用于区域经济协调发展研究过程中,以验证提出的决策方法是可行的与有效的。     

Uncertain induced aggregation operators and its application in tourism management

We develop a new decision making approach for dealing with uncertain information and apply it in tourism management. We use a new aggregation operator that uses the uncertain weighted average (UWA) and the uncertain induced ordered weighted averaging (UIOWA) operator in the same formulation. We call it the uncertain induced ordered weighted averaging - weighted averaging (UIOWAWA) operator. We study some of the main advantages and properties of the new aggregation such as the uncertain arithmetic UIOWA (UA-UIOWA) and the uncertain arithmetic UWA (UAUWA). We study its applicability in a multi-person decision making problem concerning the selection of holiday trips. We see that depending on the particular type of UIOWAWA operator used, the results may lead to different decisions.     

Generalized aggregation operators for intuitionistic fuzzy sets

The generalized ordered weighted averaging (GOWA) operators are a new class of operators, which were introduced by Yager (Fuzzy Optim Decision Making 2004;3:93–107). However, it seems that there is no investigation on these aggregation operators to deal with intuitionistic fuzzy or interval‐valued intuitionistic fuzzy information. In this paper, we first develop some new generalized aggregation operators, such as generalized intuitionistic fuzzy weighted averaging operator, generalized intuitionistic fuzzy ordered weighted averaging operator, generalized intuitionistic fuzzy hybrid averaging operator, generalized interval‐valued intuitionistic fuzzy weighted averaging operator, generalized interval‐valued intuitionistic fuzzy ordered weighted averaging operator, generalized interval‐valued intuitionistic fuzzy hybrid average operator, which extend the GOWA operators to accommodate the environment in which the given arguments are both intuitionistic fuzzy sets that are characterized by a membership function and a nonmembership function, and interval‐valued intuitionistic fuzzy sets, whose fundamental characteristic is that the values of its membership function and nonmembership function are intervals rather than exact numbers, and study their properties. Then, we apply them to multiple attribute decision making with intuitionistic fuzzy or interval‐valued intuitionistic fuzzy information. © 2009 Wiley Periodicals, Inc.     

Using Induced Ordered Weighted Averaging (IOWA) Operators for Aggregation in Cross‐Efficiency Evaluations

This paper proposes an enhancement of the cross‐efficiency evaluation through the aggregation of cross‐efficiencies by using a particular type of induced ordered weighted averaging (IOWA) operator. The use of a weighted average of cross‐efficiencies for the calculation of the cross‐efficiency scores, instead of the usual arithmetic mean, allows us to introduce some flexibility into the analysis. In particular, the main purpose of the approach we present is to provide aggregation weights that reflect the decision maker (DM) preferences regarding the relative importance that should be attached to the cross‐efficiencies provided by the different decision‐making units. To do it, an ordering is to be induced in the rows of the matrix of cross‐efficiencies, so the IOWA operator weights can be attached accordingly to the elements in each of the columns. The DM can thus incorporate his/her preferences by means of the choice of the variable that induces such ordering, and he/she may also adjust the importance to be attached to the most preferred cross‐efficiencies with the level of orness that is used when the aggregation weights are obtained.     

Induced aggregation operators in decision making with the Dempster‐Shafer belief structure

In this study, we analyze the induced aggregation operators. The analysis begins with a revision of some basic concepts such as the induced ordered weighted averaging operator and the induced ordered weighted geometric operator. We then analyze the problem of decision making with Dempster‐Shafer (D‐S) theory of evidence. We suggest the use of induced aggregation operators in decision making with the D‐S theory. We focus on the aggregation step and examine some of its main properties, including the distinction between descending and ascending orders and different families of induced operators. Finally, we present an illustrative example in which the results obtained with different types of aggregation operators can be seen. © 2009 Wiley Periodicals, Inc.     

The induced generalized aggregation operators for intuitionistic fuzzy sets and their application in group decision making

In this paper, we present the induced generalized intuitionistic fuzzy ordered weighted averaging (I-GIFOWA) operator. It is a new aggregation operator that generalized the IFOWA operator, including all the characteristics of both the generalized IFOWA and the induced IFOWA operators. It provides a very general formulation that includes as special cases a wide range of aggregation operators for intuitionistic fuzzy information, including all the particular cases of the I-IFOWA operator, GIFOWA operator and the induced intuitionistic fuzzy ordered geometric (I-IFOWG) operator. We also present the induced generalized interval-valued intuitionistic fuzzy ordered weighted averaging (I-GIIFOWA) operator to accommodate the environment in which the given arguments are interval-valued intuitionistic fuzzy sets. Further, we develop procedures to apply them to solve group multiple attribute decision making problems with intuitionistic fuzzy or interval-valued intuitionistic fuzzy information. Finally, we present their application to show the effectiveness of the developed methods.     

Some methods for strategic decision‐making problems with immediate probabilities in Pythagorean fuzzy environment

In this article, a new decision‐making model with probabilistic information and using the concept of immediate probabilities has been developed to aggregate the information under the Pythagorean fuzzy set environment. In it, the existing probabilities have been modified by introducing the attitudinal character of the decision maker by using an ordered weighted average operator. Based on it, we have developed some new probabilistic aggregation operator with Pythagorean fuzzy information, namely probabilistic Pythagorean fuzzy weighted average operator, immediate probability Pythagorean fuzzy ordered weighted average operator, probabilistic Pythagorean fuzzy ordered weighted average, probabilistic Pythagorean fuzzy weighted geometric operator, immediate probability Pythagorean fuzzy ordered weighted geometric operator, probabilistic Pythagorean fuzzy ordered weighted geometric, etc. Furthermore, we extended these operators by taking interval‐valued Pythagorean fuzzy information and developed their corresponding aggregation operators. Few properties of these operators have also been investigated. Finally, an illustrative example about the selection of the optimal production strategy has been given to show the utility of the developed method.     

Induced choquet ordered averaging operator and its application to group decision making

Yager (Fuzzy Sets Syst 2003;137:59–69) extended the idea of order‐induced aggregation to the Choquet aggregation and defined a more general type of Choquet integral operator called the induced Choquet ordered averaging (I‐COA) operator, which take as their argument pairs, in which one component called order‐inducing variable is used to induce an ordering over the second components called argument variable and then aggregated. The aim of this paper is to develop the I‐COA operator. Some of its properties are investigated. We show its relationship to the induced‐ordered weighted averaging operator. Finally, we provide some I‐COA operators to aggregate fuzzy preference relations in group decision‐making problems. © 2009 Wiley Periodicals, Inc.     

A ranking method for multiple attribute decision-making problems based on the possibility degrees of trapezoidal intuitionistic fuzzy numbers

To solve multiple attribute decision-making problems with attribute values or decision values characterized by trapezoidal intuitionistic fuzzy numbers (TIFNs), we define a trapezoidal intuitionistic fuzzy induced ordered weighted arithmetic averaging (TIFIOWA) operator, which is an extension of the induced ordered weighted arithmetic averaging operator. We derive and prove some related properties and conclusions of the TIFIOWA operator. To compare the TIFNs, we define possibility degrees of the TIFNs. Based on the possibility degrees of the TIFNs and the TIFIOWA operator, we construct a new method to determine the order of alternatives in multiple attribute decision making and to choose the best alternative. Finally, a numerical example shows that the developed method is feasible and effective.