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.     

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 Multigranularity Linguistic Group Decision‐Making Method Based on Hesitant 2‐Tuple Sets

Hesitant fuzzy linguistic term set (HFLTS) is a very useful technology in dealing with decision‐making problems where people have hesitancy in providing their linguistic assessments. Distinct methods have been developed to aid decision making with HFLTSs, yet there is little research involving the issue that how to deal with the multigranularity hesitant fuzzy linguistic information. The aim of this paper is to develop the aggregation method for multigranularity hesitant fuzzy linguistic information and solve the linguistic group decision problem with different linguistic term sets. To do so, we first modify the translation functions and aggregation operators in the existing 2‐tuple linguistic representation models so as to aggregate linguistic terms from different linguistic term sets. Then, we introduce the notion of hesitant 2‐tuple sets to make computation of HFLTSs without loss of information, and develop some new operators to aggregate HFLTSs from different linguistic term sets. Using these operators, we propose a method to deal with multigranularity linguistic group decision‐making problems with different situations where importance weights of either criteria or experts are known or unknown. Finally, the multigranularity linguistic group decision‐making model is implemented to the healthcare waste treatment in West China Hospital to validate its effectiveness and efficiency in aiding decision‐making process.     

An Intuitionistic 2‐Tuple Linguistic Information Model and Aggregation Operators

Dealing with uncertainty is always a challenging problem, and different tools have been proposed to deal with it. Fuzzy sets was presented to manage situations in which experts have some membership value to assess an alternative. The fuzzy linguistic approach has been applied successfully to many problems. The linguistic information expressed by means of 2‐tuples, which were composed by a linguistic term and a numeric value assessed in [ ? 0.5, 0.5). Linguistic values was used to assess an alternative and variable in qualitative settings. Intuitionistic fuzzy sets were presented to manage situations in which experts have some membership and nonmembership value to assess an alternative. In this paper, the concept of an I2LI model is developed to provide a linguistic and computational basis to manage the situations in which experts assess an alternative in possible and impossible linguistic variable and their translation parameter. A method to solve the group decision making problem based on intuitionistic 2‐tuple linguistic information (I2LI) by the group of experts is formulated. Some operational laws on I2LI are introduced. Based on these laws, new aggregation operators are introduced to aggregate the collective opinion of decision makers. An illustrative example is given to show the practicality and feasibility of our proposed aggregation operators and group decision making method.     

A communication model based on the 2-tuple fuzzy linguistic representation for a distributed intelligent agent system on Internet

 Internet users are assisted by means of distributed intelligent agents in the information gathering process to find the fittest information to their needs. In this paper we present a distributed intelligent agent model where the communication of the evaluation of the retrieved information among the agents is carried out by using linguistic operators based on the 2-tuple fuzzy linguistic representation as a way to endow the retrieval process with a higher flexibility, uniformity and precision. The 2-tuple fuzzy linguistic representation model allows to make processes of computing with words without loss of information.     

Fusion of imprecise qualitative information

In this paper, we present a new 2-tuple linguistic representation model, i.e. Distribution Function Model (DFM), for combining imprecise qualitative information using fusion rules drawn from Dezert-Smarandache Theory (DSmT) framework. Such new approach allows to preserve the precision and efficiency of the combination of linguistic information in the case of either equidistant or unbalanced label model. Some basic operators on imprecise 2-tuple labels are presented together with their extensions for imprecise 2-tuple labels. We also give simple examples to show how precise and imprecise qualitative information can be combined for reasoning under uncertainty. It is concluded that DSmT can deal efficiently with both precise and imprecise quantitative and qualitative beliefs, which extends the scope of this theory.     

A maximizing consensus approach for alternative selection based on uncertain linguistic preference relations

In alternative selection problems managed by multiple experts in uncertain situations achieving consensus is a desirable objective as incorrect selection may adversely affect stakeholder outcomes. This paper develops an approach to solve consensus problems when expert preference information is in the form of uncertain linguistic preference relations. First, definitions for aggregation operators and group consensus level based on a 2-tuple linguistic representation model are provided. Then, in order to obtain the weights of the experts under the assumption of incomplete weights information, an optimization model is developed which seeks maximum consensus from the current expert preferences in the group. If the consensus level reached does not meet predefined requirements, a consensus reaching algorithm is presented which can automatically achieve the goal. To determine the parameters for the proposed algorithm, a simulation procedure is presented. Finally, an investment company optimal selection example is provided to show the properties of the proposed approach. A comparative study and discussion of the proposed approach are also conducted.     

Combination of Qualitative Information with 2-Tuple Linguistic Representation in DSmT

Modern systems for information retrieval,fusion and management need to deal more and more with information coming from human experts usually expressed qualitatively in natural language with linguistic labels.In this paper,we propose and use two new 2-Tuple linguistic representation models(i.e.,a distribution function model(DFM) and an improved Herrera-Martínez's model) jointly with the fusion rules developed in Dezert-Smarandache Theory(DSmT),in order to combine efficiently qualitative information expres...     

A model based on linguistic 2-tuples for dealing with multigranularhierarchical linguistic contexts in multi-expert decision-making

In those problems that deal with multiple sources of linguistic information we can find problems defined in contexts where the linguistic assessments are assessed in linguistic term sets with different granularity of uncertainty and/or semantics (multigranular linguistic contexts). Different approaches have been developed to manage this type of contexts, that unify the multigranular linguistic information in an unique linguistic term set for an easy management of the information. This normalization process can produce a loss of information and hence a lack of precision in the final results. In this paper, we shall present a type of multigranular linguistic contexts we shall call linguistic hierarchies term sets, such that, when we deal with multigranular linguistic information assessed in these structures we can unify the information assessed in them without loss of information. To do so, we shall use the 2-tuple linguistic representation model. Afterwards we shall develop a linguistic decision model dealing with multigranular linguistic contexts and apply it to a multi-expert decision-making problem.     

Two-tuple linguistic utility aggregation operator and its applications to group decision-making

This paper aims to develop an aggregation operator for two-tuple linguistic information based on utility function, which characterizes the influence of decision makers' psychological factors on the linguistic aggregation process. First, we propose a new two-tuple linguistic ordered utility aggregation (TOU) operator, and then, we investigate its properties that are suitable for any utility function. Subsequently, we derive a specific form of the TOU operator, which is called the two-tuple linguistic generalized ordered weighted utility averaging-hyperbolic absolute risk aversion (TOHU) operator, under the hyperbolic absolute risk aversion utility function. Then, we further investigate its families including a wide range of aggregation operators. To determine the weights of the TOHU operator, which take the form of two-tuple linguistic, we establish an optimization weighting model by combining the information of input arguments and subjective considerations of decision makers. Furthermore, we propose a two-tuple linguistic aggregation method to deal with the multiple attribute group decision-making (MAGDM) problem based on the TOHU operator. Finally, we provide an example to demonstrate the application of the TOHU operator to MAGDM.     

Hesitant 2-tuple linguistic Bonferroni operators and their utilization in group decision making

Hesitant 2-tuple linguistic variable realizes a graded information approach to characterize the uncertainty of human cognition. This study is concerned with the development of new aggregation operators and aims to design a new group decision making approach to address the information fusion involving the interrelationship between aggregated terms and the prioritization relationship among decision makers under hesitant 2-tuple linguistic situation. Firstly, hesitant 2-tuple linguistic Bonferroni mean (H2TLBM) operator and prioritized weighted hesitant 2-tuple linguistic Bonferroni mean (PWH2TLBM) operator are established. Subsequently, some pertinent properties and special forms of the developed operators are studied in detail. To employ the proposed operators to solve group decision making problems, a novel TODIM (an acronym in Portuguese of interactive and multiple attribute decision making) method based on possibility degree is developed under the situation of hesitant 2-tuple linguistic information. The designed decision making method not only inherits the merits of the traditional TODIM approach, but also characterizes the interrelationship of criteria. The detailed process of solving problems is exemplified to highlight the practicality and feasibility of the designed method. Furthermore, comparative analysis with other methods is carried out to further offer insights on the designed decision method.     

A novel semi-quantitative Fuzzy Cognitive Map model for complex systems for addressing challenging participatory real life problems

Fuzzy Cognitive Maps (FCM) are a promising approach for socio-ecological systems modelling. FCMs represent problem knowledge extracted from different stakeholders in the form of connected factors/variables with imprecise cause-effect relationships and many feedback loops. These typically large maps are condensed and aggregated to obtain a summary view of the system. However, representation, condensation and aggregation of previous FCM models are qualitative due to lack of appropriate quantitative methods. This study tackles these drawbacks by developing a semi-quantitative FCM model consisting of robust methods for adequately and accurately representing and manipulating imprecise data describing a complex problem involving stakeholders for pragmatic decision making. The model starts with collecting qualitative imprecise data from relevant stakeholders. These data are then transformed into stakeholder perceptions/FCMs with different causal relationship formats (linguistic or numeric) which the proposed model then represents in a unified format using a 2-tuple fuzzy linguistic representation model which allows combining imprecise linguistic and numeric values with different granularity and/or semantic without loss of information. The proposed model then condenses large FCMs using a semi-quantitative method that allows multi-level condensation. In each level of condensation, groups of similar variables are subjectively condensed and the corresponding imprecise connections are computationally condensed using robust calculations involving credibility weights assigned to variables (variables’ importance). The model then uses a quantitative fuzzy method to aggregate perceptions/FCMs into a stakeholder group or social perception/FCM based on the 2-tuple model and credibility weights assigned to FCMs (stakeholders’ importance). Thereafter, the structure of produced FCMs is analysed using graph theory indices to examine differences in perceptions between stakeholders or groups. Finally, the model applies various what-if policy scenario simulations on group FCMs using a dynamical systems approach with neural networks and analyses scenario outcomes to provide appropriate recommendations to decision makers. An example application illustrates method’s effectiveness and usefulness.     

区间二元语义Bonferroni集成算子及其决策应用

区间二元语义值是一种常用的不确定环境下决策信息表达形式。考虑到决策信息的交叉影响作用,定义了区间二元语义值的Bonferroni平均算子以及相应的加权形式,在此基础上,给出了组合形式的区间二元语义值的加权Bonferroni平均算子的概念,并研究了算子的幂等性、单调性等数学性质,给出了基于C-I2TLWBA算子区间二元语义值的集成模型和决策应用。实例表明了该模型具有较好的有效性。     

基于Choquet 积分的直觉不确定语言信息集结算子及其应用

基于直觉不确定语言信息,针对属性间不严格相互独立且具有较大关联度的群决策问题,提出了两种基于直觉不确定语言信息的Choquet积分算子.首先,分析了因属性关联使得以往直觉不确定语言信息集结算子失效的现象,对此引入模糊测度,提出了直觉不确定语言的Choquet加权算术平均算子(IULCWA)和直觉不确定语言的Choquet加权几何平均算子(IULCGM);然后,证明了算子的相关性质,研究了属性间相关的、属性值为直觉不确定语言数的多属性群决策方法;最后,通过实例分析说明了以往直觉不确定语言信息集结算子的局限性以及新算子的有效性.     

Type‐1 OWA Unbalanced Fuzzy Linguistic Aggregation Methodology: Application to Eurobonds Credit Risk Evaluation

In decision making, a widely used methodology to manage unbalanced fuzzy linguistic information is the linguistic hierarchy (LH), which relies on a linguistic symbolic computational model based on ordinal 2‐tuple linguistic representation. However, the ordinal 2‐tuple linguistic approach does not exploit all advantages of Zadeh's fuzzy linguistic approach to model uncertainty because the membership function shapes are ignored. Furthermore, the LH methodology is an indirect approach that relies on the uniform distribution of symmetric linguistic assessments. These drawbacks are overcome by applying a fuzzy methodology based on the implementation of the type‐1 ordered weighted average (T1OWA) operator. The T1OWA operator is not a symbolic operator and it allows to directly aggregate membership functions, which in practice means that the T1OWA methodology is suitable for both balanced and unbalanced linguistic contexts and with heterogeneous membership functions. Furthermore, the final output of the T1OWA methodology is always fuzzy and defined in the same domain of the original unbalanced fuzzy linguistic labels, which facilitates its interpretation via a visual joint representation. A case study is presented where the T1OWA operator methodology is used to assess the creditworthiness of European bonds based on real credit risk ratings of individual Eurozone member states modeled as unbalanced fuzzy linguistic labels.     

SICTQUAL: A fuzzy linguistic multi-criteria model to assess the quality of service in the ICT sector from the user perspective

The Information and Communication Technologies (ICTs) play an important role in the economic development, making it necessary to assess the quality of service perceived by consumers in this sector. The most effective quality assessment from the consumer perspective is still to be researched, yet the most common approach is oriented towards quantitative indicators. This study proposes to use a two-dimensional model that combines the widely accepted segmentation of ICTs with elements from the SERVQUAL quality model. This model, useful in multi-criteria decision-making situations, has been developed using the 2-tuple linguistic representation and fuzzy logic principles. This methodology prevents data loss during processing and provides relevant information through 16 indicators related to the quality of service. Besides, an expert-based mechanism is defined for the use of historical information extracted from completed surveys. As a practical case, this mechanism is applied to the historical information of a telecommunications company for assessing the quality of the service provided to its customers.     

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.     

Multiple attribute group decision-making methods based on trapezoidal fuzzy two-dimension linguistic power generalized aggregation operators

On the basis of two-dimension uncertain linguistic variables, in this paper, we further presented a trapezoidal fuzzy two-dimension linguistic variable in which the first dimensional linguistic uncertain information is extended to trapezoidal fuzzy number. First, the definition, operational laws, characteristics, expectation, comparative method and distance of trapezoidal fuzzy two-dimension linguistic information are proposed. Then, the trapezoidal fuzzy two-dimension linguistic power generalized aggregation operator and the trapezoidal fuzzy two-dimension linguistic power generalized weighted aggregation (TF2DLPGWA) operator are developed, and some properties and special cases of these operators are analyzed. Furthermore, based on the TF2DLPGWA operator and the comparative formula of the trapezoidal fuzzy two-dimension linguistic variables, an approach to group decision making with trapezoidal fuzzy two-dimension linguistic variables is established. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.     

How “OPTIMUS” is a city in terms of energy optimization? e-SCEAF: A web based decision support tool for local authorities

Nowadays cities tend to become “Smarter”, usually disregarding the issues of energy efficiency and sustainability. Therefore, optimizing energy use in a city remains a challenge and respective decision support systems are important to guide local authorities toward that direction. This paper provides a holistic approach presenting a Smart City Energy Assessment Framework (SCEAF) along with a specific web based decision support tool, the so-called e-SCEAF, which can provide local authorities with fruitful results for assessing the energy behavior and performance of their city. The tool merges heterogeneous information, such as clearly quantifiable energy related indicators, the related city policy context performance and the integration of smart infrastructure. This multi-source information fusion is based on the 2-tuple linguistic representation model of Herrera and Martínez. This particular model has been widely used in decision problems and was mainly selected due to the fact that it provides linguistic results that are accurate and easy to understand by the cities’ local authorities. The performance, usefulness and effectiveness of the SCEAF framework and the e-SCEAF tool are tested on a real life application in three different cities, Savona (Italy), Sant Cugat del Vallès (Spain) and Zaanstad (The Netherlands). In this respect, the role of fusion methods and algorithms for merging multiple information will be evaluated in a “real life environment”.