Fuzzy linguistic induced OWA Minkowski distance operator and its application in group decision making

The Minkowski distance is a distance measure that generalizes a wide range of other distances such as the Euclidean and the Hamming distance. In this paper, we develop a new decision making model using induced ordered weighted averaging operators and the Minkowski distance of the fuzzy linguistic variables. Then, the authors introduce a new aggregation operator called the fuzzy linguistic induced ordered weighted averaging Minkowski distance (FLIOWAMD) operator by defining a fuzzy linguistic variable distance. It is an induced generalized aggregation operator that utilizes induced OWA operator, Minkowski distance measures and uncertain information represented as fuzzy linguistic variables. Some of its main properties and particular cases are studied. And a further generalization that uses quasi-arithmetic means also is presented. A method based on the FLIOWAMD operator for decision making is presented. At last, we end the paper with a numerical example of the new method.     

Fuzzy Linguistic Induced Euclidean OWA Distance Operator and its Application in Group Linguistic Decision Making

In this paper, we develop a new method for group linguistic decision making, in which the attribute values take the form of fuzzy linguistic information, namely the fuzzy linguistic induced Euclidean ordered weighted averaging distance (FLIEOWAD) operator. This operator is an extension of the IOWA operator that utilizes induce OWA operator, Euclidean distance measures, and uncertain information represented as fuzzy linguistic variables. Then, some of its main properties by utilizing some operational laws of fuzzy linguistic variables are studied. Thus, a method based on the FLIEOWAD operator for decision making is presented. Finally, a numerical example is used to illustrate the applicability and effectiveness of the proposed method.     

The uncertain induced quasi‐arithmetic OWA operator

We present the uncertain induced quasi‐arithmetic OWA (Quasi‐UIOWA) operator. It is an extension of the OWA operator that uses the main characteristics of the induced OWA (IOWA), the quasi‐arithmetic OWA (Quasi‐OWA) and the uncertain OWA (UOWA) operator. Thus, this generalization uses quasi‐arithmetic means, order inducing variables in the reordering process and uncertain information represented by interval numbers. A key feature of the Quasi‐UIOWA operator is that it generalizes a wide range of aggregation operators such as the uncertain quasi‐arithmetic mean, the uncertain weighted quasi‐arithmetic mean, the UOWA, the uncertain weighted generalized mean, the uncertain induced generalized OWA (UIGOWA), the Quasi‐UOWA, the uncertain IOWA, the uncertain induced ordered weighted geometric (UIOWG), and the uncertain induced ordered weighted quadratic averaging (UIOWQA) operator. We study some of the main properties of this approach including how to obtain a wide range of particular cases. We further generalize the Quasi‐UIOWA operator by using discrete Choquet integrals. We end the article with an application of the new approach in a decision making problem about investment selection. © 2010 Wiley Periodicals, Inc.     

Uncertain Induced Heavy Aggregation Distance Operator and its Application to Decision Making

We introduce a new decision-making approach for dealing with uncertain information and apply it to decision making. We have developed the uncertain induced heavy ordered weighted averaging distance (UIHOWAD) operator. It is a new aggregation operator that generalizes a wide range of uncertain aggregation operators such as the uncertain minimum distance, the uncertain weighted Hamming distance (UWHD), the uncertain OWA distance (UOWAD) operator, and the uncertain heavy OWA distance (UHOWAD) operator. We studied some of its main properties and different particular cases. We also present its applicability in a decision-making problem concerning the selection of investments.     

Fuzzy induced generalized aggregation operators and its application in multi-person decision making

We present a wide range of fuzzy induced generalized aggregation operators such as the fuzzy induced generalized ordered weighted averaging (FIGOWA) and the fuzzy induced quasi-arithmetic OWA (Quasi-FIOWA) operator. They are aggregation operators that use the main characteristics of the fuzzy OWA (FOWA) operator, the induced OWA (IOWA) operator and the generalized (or quasi-arithmetic) OWA operator. Therefore, they use uncertain information represented in the form of fuzzy numbers, generalized (or quasi-arithmetic) means and order inducing variables. The main advantage of these operators is that they include a wide range of mean operators such as the FOWA, the IOWA, the induced Quasi-OWA, the fuzzy IOWA, the fuzzy generalized mean and the fuzzy weighted quasi-arithmetic average (Quasi-FWA). We further generalize this approach by using Choquet integrals, obtaining the fuzzy induced quasi-arithmetic Choquet integral aggregation (Quasi-FICIA) operator. We also develop an application of the new approach in a strategic multi-person decision making problem.     

Pythagorean Fuzzy Multiattribute Group Decision Making with Probabilistic Information and OWA Approach

The aim of this paper is to develop a Pythagorean fuzzy multiattribute group decision making (MAGDM) method based on probabilistic information and the ordered weighted averaging (OWA) approach. The Pythagorean fuzzy probabilistic ordered weighted averaging (PFPOWA) operator is presented. It is a new aggregation operator that considers the probabilities and the OWA in the same formulation. Therefore, it is able to take into account the degree of importance that each concept has in the particular problem considered. Some main properties and different particular cases of the PFPOWA operators are studied. Moreover, a method based on the proposed operator for multiattribute group decision making is put forward. Finally, an example showing analysis of a supplier selection is given to verify the effectiveness and practicability of the proposed method.     

Some induced intuitionistic fuzzy aggregation operators applied to multi-attribute group decision making

In this paper, we define various induced intuitionistic fuzzy aggregation operators, including induced intuitionistic fuzzy ordered weighted averaging (OWA) operator, induced intuitionistic fuzzy hybrid averaging (I-IFHA) operator, induced interval-valued intuitionistic fuzzy OWA operator, and induced interval-valued intuitionistic fuzzy hybrid averaging (I-IIFHA) operator. We also establish various properties of these operators. And then, an approach based on I-IFHA operator and intuitionistic fuzzy weighted averaging (WA) operator is developed to solve multi-attribute group decision-making (MAGDM) problems. In such problems, attribute weights and the decision makers' (DMs') weights are real numbers and attribute values provided by the DMs are intuitionistic fuzzy numbers (IFNs), and an approach based on I-IIFHA operator and interval-valued intuitionistic fuzzy WA operator is developed to solve MAGDM problems where the attribute values provided by the DMs are interval-valued IFNs. Furthermore, induced intuitionistic fuzzy hybrid geometric operator and induced interval-valued intuitionistic fuzzy hybrid geometric operator are proposed. Finally, a numerical example is presented to illustrate the developed approaches.     

THE FUZZY GENERALIZED OWA OPERATOR AND ITS APPLICATION IN STRATEGIC DECISION MAKING

We present the fuzzy generalized ordered weighted averaging (FGOWA) operator. It is an extension of the GOWA operator for uncertain situations where the available information is given in the form of fuzzy numbers. This generalization includes a wide range of mean operators such as the fuzzy average (FA), the fuzzy OWA (FOWA), and the fuzzy generalized mean (FGM). We also develop a further generalization by using quasi-arithmetic means that we call the quasi-FOWA operator. The article ends with an illustrative example where we apply the new approach in the selection of strategies.     

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.     

Fuzzy Entropic Ordered Weighted Averaging Operator and Its Application in Group Decision Making

In the paper, we develop a new method for multiple attribute group decision making) for fuzzy numbers. The fuzzy entropic weighted averaging (FEOWA) operator is an extension of the entropic ordered weighted averaging operator, which unifies the fuzzy entropy and the ordered weighted averaging operator in the same formulation. Then, some of its main properties by utilizing some operational laws of fuzzy numbers are studied. We also present the generalized entropic ordered weighted averaging operator and the fuzzy generalized entropic ordered weighted averaging operator. Moreover, a method based on the FEOWA operator for decision making is presented. Finally, a numerical example illustrates the applicability and effectiveness of the proposed method.     

On aggregating uncertain information by type‐2 OWA operators for soft decision making

Yager's ordered weighted averaging (OWA) operator has been widely used in soft decision making to aggregate experts' individual opinions or preferences for achieving an overall decision. The traditional Yager's OWA operator focuses exclusively on the aggregation of crisp numbers. However, human experts usually tend to express their opinions or preferences in a very natural way via linguistic terms. Type‐2 fuzzy sets provide an efficient way of knowledge representation for modeling linguistic terms. In order to aggregate linguistic opinions via OWA mechanism, we propose a new type of OWA operator, termed type‐2 OWA operator, to aggregate the linguistic opinions or preferences in human decision making modeled by type‐2 fuzzy sets. A Direct Approach to aggregating interval type‐2 fuzzy sets by type‐2 OWA operator is suggested in this paper. Some examples are provided to delineate the proposed technique. © 2010 Wiley Periodicals, Inc.     

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.     

Induced generalized intuitionistic fuzzy OWA operator for multi-attribute group decision making

With respect to multi-attribute group decision making (MAGDM) problems in which both the attribute weights and the decision makers (DMs) weights take the form of real numbers, attribute values provided by the DMs take the form of intuitionistic fuzzy numbers, a new group decision making method is developed. Some operational laws, score function and accuracy function of intuitionistic fuzzy numbers are introduced at first. Then a new aggregation operator called induced generalized intuitionistic fuzzy ordered weighted averaging (IG-IFOWA) operator is proposed, which extend the induced generalized ordered weighted averaging (IGOWA) operator introduced by Merigo and Gil-Lafuente [Merigo, J. M., & Gil-Lafuente, A. M. (2009). The induced generalized OWA operator. Information Sciences, 179, 729-741] to accommodate the environment in which the given arguments are intuitionistic fuzzy sets that are characterized by a membership function and a non-membership function. Some desirable properties of the IG-IFOWA operator are studied, such as commutativity, idempotency, monotonicity and boundary. And then, an approach based on the IG-IFOWA and IFWA (intuitionistic fuzzy weighted averaging) operators is developed to solve MAGDM problems with intuitionistic fuzzy information. Finally, a numerical example is used to illustrate the developed approach.     

Density-clusters ordered weighted averaging operator based on generalized trapezoidal fuzzy numbers

To the problem of multi-attribute decision making with fuzzy numbers, this paper proposes a new type of operator called the density-clusters ordered weighted averaging (OWA) operator based on generalized trapezoidal fuzzy (GTF) numbers. This operator is abbreviated as the GTF-DOWA operator. A primary characteristic of the GTF-DOWA operator is that it considers the implicit structure of the GTF numbers to be aggregated by grouping the numbers to various local clusters. We discuss the grouping methods of the GTF numbers using the centroids of the numbers. The cluster weights are determined by the combined consideration of the decision maker's attitude and the scale of each local cluster. In addition, we discuss the primary properties of the GTF-DOWA operator. Finally, a numerical example regarding the selection of optimal alternative is provided. The aggregations of the GTF-DOWA operator are compared with those of the weighted arithmetic averaging (WAA) operator and the OWA operator based on GTF numbers to illustrate the validity of the GTF-DOWA operator.     

The induced generalized OWA operator

We present the induced generalized ordered weighted averaging (IGOWA) operator. It is a new aggregation operator that generalizes the OWA operator, including the main characteristics of both the generalized OWA and the induced OWA operator. This operator uses generalized means and order-inducing variables in the reordering process. It provides a very general formulation that includes as special cases a wide range of aggregation operators, including all the particular cases of the IOWA and the GOWA operator, the induced ordered weighted geometric (IOWG) operator and the induced ordered weighted quadratic averaging (IOWQA) operator. We further generalize the IGOWA operator via quasi-arithmetic means. The result is the Quasi-IOWA operator. Finally, we present a numerical example to illustrate the new approach in a financial decision-making problem.     

Hesitant interval-valued Pythagorean fuzzy VIKOR method

In this article, we investigate multiple attribute decision-making problems with hesitant interval-valued Pythagorean fuzzy information. First, the concepts of hesitant interval-valued Pythagorean fuzzy set are defined, and the operation laws, the score function, and accuracy function have been developed. Then several distance measures for hesitant interval-valued Pythagorean fuzzy values have been presented including the Hamming distance, Euclidean distance, and generalized distance, and so on. Based on the operational laws, a series of aggregation operators have been developed including the hesitant interval-valued Pythagorean fuzzy weighted averaging (HIVPFWA) operator, the hesitant interval-valued Pythagorean fuzzy geometric weighted averaging (HIVPFGWA) operator, the hesitant interval-valued Pythagorean fuzzy ordered weighed averaging (HIVPFOWA) operator, and hesitant interval-valued Pythagorean fuzzy ordered weighed geometric averaging (HIVPFOWGA) operator. By using the generalized mean operator, we also develop the generalized hesitant interval-valued Pythagorean fuzzy weighed averaging (GHIVPFWA) operator, the generalized hesitant interval-valued Pythagorean fuzzy weighed geometric averaging (GHIVPFWGA) operator, the generalized hesitant interval-valued Pythagorean fuzzy ordered weighted averaging (GHIVPFOWA) operator, and generalized hesitant interval-valued Pythagorean fuzzy ordered weighted geometric averaging (GHIVPFOWGA) operator operator. We further develop several hybrid aggregation operators including the hesitant interval-valued Pythagorean fuzzy hybrid averaging (HIVPFHA) operator and the generalized hesitant interval-valued Pythagorean fuzzy hybrid averaging (GHIVPFHA) operator. Based on the distance measures and the aggregation operators, we propose a hesitant interval-valued Pythagorean fuzzy VIKOR method to solve multiple attribute decision problems with multiple periods. Finally, an illustrative example for evaluating the metro project risk is given to demonstrate the feasibility and effectiveness of the proposed method.     

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.     

Type‐Reduction of General Type‐2 Fuzzy Sets: The Type‐1 OWA Approach

For general type‐2 fuzzy sets, the defuzzification process is very complex and the exhaustive direct method of implementing type‐reduction is computationally expensive and turns out to be impractical. This has inevitably hindered the development of type‐2 fuzzy inferencing systems in real‐world applications. The present situation will not be expected to change, unless an efficient and fast method of deffuzzifying general type‐2 fuzzy sets emerges. Type‐1 ordered weighted averaging (OWA) operators have been proposed to aggregate expert uncertain knowledge expressed by type‐1 fuzzy sets in decision making. In particular, the recently developed alpha‐level approach to type‐1 OWA operations has proven to be an effective tool for aggregating uncertain information with uncertain weights in real‐time applications because its complexity is of linear order. In this paper, we prove that the mathematical representation of the type‐reduced set (TRS) of a general type‐2 fuzzy set is equivalent to that of a special case of type‐1 OWA operator. This relationship opens up a new way of performing type reduction of general type‐2 fuzzy sets, allowing the use of the alpha‐level approach to type‐1 OWA operations to compute the TRS of a general type‐2 fuzzy set. As a result, a fast and efficient method of computing the centroid of general type‐2 fuzzy sets is realized. The experimental results presented here illustrate the effectiveness of this method in conducting type reduction of different general type‐2 fuzzy sets.     

A Novel Intuitionistic Fuzzy Induced Ordered Weighted Euclidean Distance Operator and Its Application for Group Decision Making

In the paper, we develop the novel intuitionistic fuzzy induced ordered weighted Euclidean distance (NIFIOWED) operator based on the generalized intuitionistic fuzzy distance for multiple attribute group decision making problems. The NIFIOWED operator's attribute values take the form of Atanassov's intuitionistic fuzzy numbers(A‐IFNs), and the principal component x of A‐IFN is taken into account first. The prime properties of the NIFIOWED operator are investigated. Finally, a new method and a numerical example are provided to reveal the availability and practicability of the NIFIOWED operator.     

基于语言型混合算子的模糊信息聚合方法

在多属性决策过程中经常会用到聚合算子,有序加权平均聚合(OWA)算子是最常用的聚合算子之一,通常用于聚合确切的数值.然而,现实世界部分信息的不确定性以及决策者对一些信息的模糊性,使得部分信息不能用确切的数值表示,从而导致OWA算子及其扩展算子向着多元化发展.对此,给出一种语言型混合有序加权平均聚合(LHOWA)算子,同时研究该算子所应具备的一些基本性质,并给出一种基于该算子的语言型信息聚合方法,用于多属性决策过程中模糊信息的聚合.最后,通过一个煤矿安全评价的算例对所提出方法的优越性进行了验证.