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.     

Linguistic labels for expressing fuzzy preference relations infuzzy group decision making

This paper proposes improvements to pairwise group decision making based on fuzzy preference relations in three ways. First, it extends the fuzzy preference relation representation using linguistic labels. Decision makers may express their preference relations in linguistic labels which are more practically implementable for solving group decision making problems. Second, it modifies the computational procedures by using fuzzy sets representation and computation, and by avoiding the use of strict threshold values. This allows natural representation, preserves the preference accuracy, and produces more intuitively meaningful solutions. Finally, it considers fuzzy criteria of the alternatives explicitly. Solutions are first derived based on each criterion, and then by using neat ordered weighted average (OWA) operator the final solutions which accommodate all criteria are determined. The proposed method is verified for solving fuzzy group decision making problems, i.e., advertising media selection cases.     

An integrated fuzzy MCDM approach for supplier evaluation and selection

A fuzzy multi-criteria group decision making approach that makes use of quality function deployment (QFD), fusion of fuzzy information and 2-tuple linguistic representation model is developed for supplier selection. The proposed methodology seeks to establish the relevant supplier assessment criteria while also considering the impacts of inner dependence among them. Two interrelated house of quality matrices are constructed, and fusion of fuzzy information and 2-tuple linguistic representation model are employed to compute the weights of supplier selection criteria and subsequently the ratings of suppliers. The proposed method is apt to manage non-homogeneous information in a decision setting with multiple information sources. The decision framework presented in this paper employs ordered weighted averaging (OWA) operator, and the aggregation process is based on combining information by means of fuzzy sets on a basic linguistic term set. The proposed framework is illustrated through a case study conducted in a private hospital in Istanbul.     

A new version of 2-tuple fuzzy linguistic representation model for computing with words

In this paper, we provide a new (proportional) 2-tuple fuzzy linguistic representation model for computing with words (CW), which is based on the concept of "symbolic proportion." This concept motivates us to represent the linguistic information by means of 2-tuples, which are composed by two proportional linguistic terms. For clarity and generality, we first study proportional 2-tuples under ordinal contexts. Then, under linguistic contexts and based on canonical characteristic values (CCVs) of linguistic labels, we define many aggregation operators to handle proportional 2-tuple linguistic information in a computational stage for CW without any loss of information. Our approach for this proportional 2-tuple fuzzy linguistic representation model deals with linguistic labels, which do not have to be symmetrically distributed around a medium label and without the traditional requirement of having "equal distance" between them. Moreover, this new model not only provides a space to allow a "continuous" interpolation of a sequence of ordered linguistic labels, but also provides an opportunity to describe the initial linguistic information by members of a "continuous" linguistic scale domain which does not necessarily require the ordered linguistic terms of a linguistic variable being equidistant. Meanwhile, under the assumption of equally informative (which is defined by a condition based on the concept of CCV), we show that our model reduces to Herrera and Mart/spl inodot//spl acute/nez's (translational) 2-tuple fuzzy linguistic representation model.     

A model of an information retrieval system with unbalanced fuzzy linguistic information

Most information retrieval systems based on linguistic approaches use symmetrically and uniformly distributed linguistic term sets to express the weights of queries and the relevance degrees of documents. However, to improve the system–user interaction, it seems more adequate to express these linguistic weights and degrees by means of unbalanced linguistic scales, that is, linguistic term sets with different discrimination levels on both sides of the middle linguistic term. In this contribution we present an information retrieval system that accepts weighted queries whose weights are expressed using unbalanced linguistic term sets. Then, the system provides the retrieved documents classified in linguistic relevance classes assessed on unbalanced linguistic term sets. To do so, we propose a methodology to manage unbalanced linguistic information and we use the linguistic 2‐tuple model as the representation base of the unbalanced linguistic information. Additionally, the linguistic 2‐tuple model allows us to increase the number of relevance classes in the output and also to improve the performance of the information retrieval system. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 1197–1214, 2007.     

基于梯形模糊隶属函数的复合语言多目标决策

对于一些复杂的决策问题, 使用比较语言比单一语言更能准确地表达专家的看法. 据此, 提出一种同时使用单一语言和比较语言的新算法. 根据上下文无关文法将比较语言表达转换为犹豫模糊语言术语集(HFLTS), 并应用有序加权算子(OWA) 计算出由梯形隶属函数表示的模糊语言术语集的模糊包络, 有效地简化了基于HFLTS 的词计算过程. 最后应用逼近理想解排序(TOPSIS) 方法进行决策.

     

Hierarchical semi-numeric method for pairwise fuzzy group decision making

Gradual improvements to a single-level semi-numeric method, i.e., linguistic labels preference representation by fuzzy sets computation for pairwise fuzzy group decision making are summarized. The method is extended to solve multiple criteria hierarchical structure pairwise fuzzy group decision-making problems. The problems are hierarchically structured into focus, criteria, and alternatives. Decision makers express their evaluations of criteria and alternatives based on each criterion by using linguistic labels. The labels are converted into and processed in triangular fuzzy numbers (TFNs). Evaluations of criteria yield relative criteria weights. Evaluations of the alternatives, based on each criterion, yield a degree of preference for each alternative or a degree of satisfaction for each preference value. By using a neat ordered weighted average (OWA) or a fuzzy weighted average operator, solutions obtained based on each criterion are aggregated into final solutions. The hierarchical semi-numeric method is suitable for solving a larger and more complex pairwise fuzzy group decision-making problem. The proposed method has been verified and applied to solve some real cases and is compared to Saaty's (1996) analytic hierarchy process (AHP) method.     

A new fuzzy operator and its application to topology design of distributed local area networks

Topology design of distributed local area networks can be classified as a hard combinatorial optimization problem. The problem has several conflicting objectives, such as cost, reliability, network delay, and number of hops between source and destination. These objectives can conveniently be expressed in linguistic terms - a key component of fuzzy logic. This paper presents an approach based on fuzzy logic that combines the conflicting objectives into a single optimization function. A new fuzzy operator, namely, the unified AND-OR (UAO) operator is also proposed, and a decision-making approach based on fuzzy rules and preference rules is introduced. The UAO operator is empirically compared with the well-known ordered weighted averaging (OWA) operator through application to an evolutionary algorithm. Results show that the UAO operator exhibits comparatively better performance than the OWA operator.     

Some q‐rung orthopair fuzzy Heronian mean operators in multiple attribute decision making

The generalized Heronian mean and geometric Heronian mean operators provide two aggregation operators that consider the interdependent phenomena among the aggregated arguments. In this paper, the generalized Heronian mean operator and geometric Heronian mean operator under the q‐rung orthopair fuzzy sets is studied. First, the q‐rung orthopair fuzzy generalized Heronian mean (q‐ROFGHM) operator, q‐rung orthopair fuzzy geometric Heronian mean (q‐ROFGHM) operator, q‐rung orthopair fuzzy generalized weighted Heronian mean (q‐ROFGWHM) operator, and q‐rung orthopair fuzzy weighted geometric Heronian mean (q‐ROFWGHM) operator are proposed, and some of their desirable properties are investigated in detail. Furthermore, we extend these operators to q‐rung orthopair 2‐tuple linguistic sets (q‐RO2TLSs). Then, an approach to multiple attribute decision making based on q‐ROFGWHM (q‐ROFWGHM) operator is proposed. Finally, a practical example for enterprise resource planning system selection is given to verify the developed approach and to demonstrate its practicality and effectiveness.     

Selected issues of frame of knowledge representation realized by means of linguistic labels

The article concentrates on selected aspects of knowledge representation. It is considered how fuzzy sets viewed as linguistic labels (information granules) determine a representation frame. the representation scheme is discussed with respect to its perception level and a scope of individual labels. Both the features can be handled by fuzzy sets and easily modeled by changing associated parameters of corresponding membership functions. Problems of prototype determination in the original space (in which the objects are characterized) as well as in the space of linguistic labels are studied. It is argued that the space of grades of membership functions is more suitable to capture a notion of the prototype. Different aspects of matching are also brought into account.     

Interpreting linguistically quantified propositions

We discuss the idea of a linguistic quantifier and fuzzy set representations of these objects. We describe two formalisms for evaluating the truth of linguistically quantified propositions such as Most winter days are cold. the first approach is based upon a probabilistic interpretation and the second is based upon a logical interpretation, and uses a generalization of the “and” and “or” operations via OWA operators. We suggest an application of these quantified statements for the representation of the quotient operator in fuzzy relational data bases. © 1994 John Wiley & Sons, Inc.     

A method based on preference degrees for handling hybrid multiple attribute decision making problems

In this paper, we investigate hybrid multiple attribute decision making problems with various forms of attribute values (real numbers, linguistic labels, interval numbers, intuitionistic fuzzy numbers and interval intuitionistic fuzzy numbers). We propose a method based on preference degrees which may take the forms of fuzzy numbers, intuitionistic fuzzy numbers and interval intuitionistic fuzzy numbers. The method first normalizes various forms of attribute values into preference degrees, and then uses a preference degree-based weighted averaging operator to aggregate the normalized preference degrees. Meanwhile, for convenience of calculation, a new linguistic representation model is presented, whose feasibility is verified by comparing it with the traditional 4-tuple linguistic representation model, and from our model, the mapping relationship between interval intuitionistic fuzzy numbers and linguistic labels can be constructed. Finally, we illustrate the rationality and practicality of the proposed method by an application example.     

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 power average operator for unbalanced linguistic term sets

In order to aggregate linguistic values of unbalanced linguistic term sets, this paper introduces the linguistic proportional 2-tuple power average operator, which can reflect the relationship among the aggregated values by considering the support for each value from others. Its advantage regarding other linguistic power average operators enables it to be used in such cases in which the linguistic term sets are not necessarily to be balanced, and the membership functions of the linguistic terms are utilized in the computational processes. In this operator, a linguistic proportional 2-tuple is represented by a normalized numerical representation. Some properties of the operator are discussed. A group decision making model based on the proposed operator is introduced. Finally an illustrative example is presented.     

Rule Base Reduction and Genetic Tuning of Fuzzy Systems Based on the Linguistic 3-tuples Representation

Recently, a new linguistic rule representation model was presented to perform a genetic lateral tuning of membership functions. It is based on the linguistic 2-tuples representation model, that allows the symbolic translation of a label considering an unique parameter. It involves a reduction of the search space that eases the derivation of optimal models. This work presents a new symbolic representation with three values (s, α, β), respectively representing a label, the lateral displacement and the amplitude variation of the support of this label. Based on this new representation we propose a new method for fine tuning of membership functions that is combined with a rule base reduction method in order to extract the most useful tuned rules. This approach makes use of a modified inference system that consider non-covered inputs in order to improve the final fuzzy model generalization ability, specially in highly non-linear problems with noise points. Additionally, we analyze the proposed approach showing its behavior in two real-world applications. Supported by the Spanish Ministry of Science and Technology under Projects TIC-2002-04036-C05-01 and TIN-2005-08386-C05-01.     

结合类标签关联度的有序核判别回归学习

有序离散类标号通常由原始连续标号按一定规则映射得到，因 此它们彼此间是存在关联信息的，现有有序回归方法对此类关联信息的考虑仍然较少。 首先提出一类有序标号间关联度的量化表示,进而将其与典型有序回归方法(Kernel discrim inant learning for ordinal regression, KDLOR) 相结合，设计出了一种结合类标号关联度的有序核判别回归学习方法(Kernel discriminant learning for ordinal regression using label membership，LM KDLOR),最后通过在 多 个标准有序回归数据集上的对比实验验证了所提方法的有效性。     

A Fuzzy Linguistic Methodology to Deal With Unbalanced Linguistic Term Sets

Many real problems dealing with qualitative aspects use linguistic approaches to assess such aspects. In most of these problems, a uniform and symmetrical distribution of the linguistic term sets for linguistic modeling is assumed. However, there exist problems whose assessments need to be represented by means of unbalanced linguistic term sets, i.e., using term sets that are not uniformly and symmetrically distributed. The use of linguistic variables implies processes of computing with words (CW). Different computational approaches can be found in the literature to accomplish those processes. The 2-tuple fuzzy linguistic representation introduces a computational model that allows the possibility of dealing with linguistic terms in a precise way whenever the linguistic term set is uniformly and symmetrically distributed. In this paper, we present a fuzzy linguistic methodology in order to deal with unbalanced linguistic term sets. To do so, we first develop a representation model for unbalanced linguistic information that uses the concept of linguistic hierarchy as representation basis and afterwards an unbalanced linguistic computational model that uses the 2-tuple fuzzy linguistic computational model to accomplish processes of CW with unbalanced term sets in a precise way and without loss of information.     

Weighted‐selective aggregated majority‐OWA operator and its application in linguistic group decision making

This paper focuses on the aggregation operations in the group decision‐making model based on the concept of majority opinion. The weighted‐selective aggregated majority‐OWA (WSAM‐OWA) operator is proposed as an extension of the SAM‐OWA operator, where the reliability of information sources is considered in the formulation. The WSAM‐OWA operator is generalized to the quantified WSAM‐OWA operator by including the concept of linguistic quantifier, mainly for the group fusion strategy. The QWSAM‐IOWA operator, with an ordering step, is introduced to the individual fusion strategy. The proposed aggregation operators are then implemented for the case of alternative scheme of heterogeneous group decision analysis. The heterogeneous group includes the consensus of experts with respect to each specific criterion. The exhaustive multicriteria group decision‐making model under the linguistic domain, which consists of two‐stage aggregation processes, is developed in order to fuse the experts’ judgments and to aggregate the criteria. The model provides greater flexibility when analyzing the decision alternatives with a tolerance that considers the majority of experts and the attitudinal character of experts. A selection of investment problem is given to demonstrate the applicability of the developed model.     

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.     

A Proposal for the Genetic Lateral Tuning of Linguistic Fuzzy Systems and Its Interaction With Rule Selection

Linguistic fuzzy modeling allows us to deal with the modeling of systems by building a linguistic model which is clearly interpretable by human beings. However, since the accuracy and the interpretability of the obtained model are contradictory properties, the necessity of improving the accuracy of the linguistic model arises when complex systems are modeled. To solve this problem, one of the research lines in recent years has led to the objective of giving more accuracy to linguistic fuzzy modeling without losing the interpretability to a high level. In this paper, a new postprocessing approach is proposed to perform an evolutionary lateral tuning of membership functions, with the main aim of obtaining linguistic models with higher levels of accuracy while maintaining good interpretability. To do so, we consider a new rule representation scheme base on the linguistic 2-tuples representation model which allows the lateral variation of the involved labels. Furthermore, the cooperation of the lateral tuning together with fuzzy rule reduction mechanisms is studied in this paper, presenting results on different real applications. The obtained results show the good performance of the proposed approach in high-dimensional problems and its ability to cooperate with methods to remove unnecessary rules.