2-tuple Linguistic Representation Research Articles

Assigning Method for Decision Power Based on Linguisitc 2-tuple Judgment Matrices

Decision power is very important in group decision making, which effects the final decision making result. When there exists uncertainty in group decision making, it is easy for an expert to express his/her preferences using fuzzy linguistic term such as ‘good’, ‘very good’. The linguistic 2-tuple representation model was selected to represent fuzzy linguistic term for its accuracy in representing fuzzy terms and less loss of information in processing. To obtain the objective decision power in group decision making where the experts express their opinions using linguistic 2-tuple judgment matrices, the paper put forward a new approach to assign decision power based on element consistency level. And the method for calculating the contribution degree of each expert was also provided. The proposed method thought of calculating the different weight to aggregate different element according to the element consistent level. An illustrated example was used to demonstrate the proposed method. And a GDSS based on the method was also developed to simplify the application in VB.NET. The GDSS was applied to building non-financial performance system for listed company in small and medium enterprise board in China, which showed its reasonability.

A Dynamic Sensory Quality Evaluation Model Based on Panel Data and Linguistic Information Processing

The sensory quality evaluation processes are widely used for many industrial products, which is evaluated according to the knowledge acquired via human senses (such as sight, taste, touch, smell). Because the evaluation information acquired by our senses is involving uncertainty, vagueness and imprecision, and the sensory quality information of products always has the panel data characteristic, so the sensory quality evaluation and certification is a multi-feature group decision-making problem based on panel linguistic information processing. This paper presents a proposed method for the development of accredited sensory evaluation methods, and shows the application of the linguistic 2-tuple representation model and its advantages. It involved several steps: gathering of sensory information from experts; computing a collective evaluation for each feature; computing collective evaluations for each object; dynamic aggregation; sensory evaluation and quality certification with global evaluation result.

A case-based reasoning method for capacity identification in the Choquet integral: Application to cyclic construction operations

The estimation of productivity rates in cyclic construction processes is a crucial task in the planning of construction projects. Since the productivity depends on many factors, the main ones should be selected by taking into account the possible interactions between them. For this aim, we adopted the Choquet integral to define fuzzy weights of criteria or coalition of criteria called capacities. In the literature, many approaches of capacity identification in the Choquet integral are proposed. However, these approaches require information, which is always hardly provided by the decision-maker and necessitates the determination of utility functions. Furthermore, they usually deal with a set of objects having a small cardinality. In this study, we use the Case-Based Reasoning (CBR) for capacity identification in concreting operations by developing a new quadratic program. By this way, a selection of “major” criteria is first performed to which a 2-tuple linguistic representation model is applied in order to unify quantitative and qualitative information. Then, a causal model is used to estimate the overall score of the new case. As this work demonstrates, the developed methodology can provide a good tool for capacity identification that is able to justify its choices clearly and consistently in the concreting operations.

The OWA-based consensus operator under linguistic representation models using position indexes

When using linguistic approaches to solve decision problems, we need linguistic representation models. The symbolic model, the 2-tuple fuzzy linguistic representation model and the continuous linguistic model are three existing linguistic representation models based on position indexes. Together with these three linguistic models, the corresponding ordered weighted averaging operators, such as the linguistic ordered weighted averaging operator, the 2-tuple ordered weighted averaging operator and the extended ordered weighted averaging operator, have been developed, respectively. In this paper, we analyze the internal relationship among these operators, and propose a consensus operator under the continuous linguistic model (or the 2-tuple fuzzy linguistic representation model). The proposed consensus operator is based on the use of the ordered weighted averaging operator and the deviation measures. Some desired properties of the consensus operator are also presented. In particular, the consensus operator provides an alternative consensus model for group decision making. This consensus model preserves the original preference information given by the decision makers as much as possible, and supports consensus process automatically, without moderator.

Incorporating linguistic, probabilistic, and possibilistic information in a risk‐based approach for ranking contaminated sites

Different types of uncertain information-linguistic, probabilistic, and possibilistic-exist in site characterization. Their representation and propagation significantly influence the management of contaminated sites. In the absence of a framework with which to properly represent and integrate these quantitative and qualitative inputs together, decision makers cannot fully take advantage of the available and necessary information to identify all the plausible alternatives. A systematic methodology was developed in the present work to incorporate linguistic, probabilistic, and possibilistic information into the Preference Ranking Organization METHod for Enrichment Evaluation (PROMETHEE), a subgroup of Multi-Criteria Decision Analysis (MCDA) methods for ranking contaminated sites. The identification of criteria based on the paradigm of comparative risk assessment provides a rationale for risk-based prioritization. Uncertain linguistic, probabilistic, and possibilistic information identified in characterizing contaminated sites can be properly represented as numerical values, intervals, probability distributions, and fuzzy sets or possibility distributions, and linguistic variables according to their nature. These different kinds of representation are first transformed into a 2-tuple linguistic representation domain. The propagation of hybrid uncertainties is then carried out in the same domain. This methodology can use the original site information directly as much as possible. The case study shows that this systematic methodology provides more reasonable results.

Computing the Numerical Scale of the Linguistic Term Set for the 2-Tuple Fuzzy Linguistic Representation Model

When using linguistic approaches to solve decision problems, we need the techniques for computing with words (CW). Together with the 2-tuple fuzzy linguistic representation models (i.e., the Herrera and Martinez model and the Wang and Hao model), some computational techniques for CW are also developed. In this paper, we define the concept of numerical scale and extend the 2-tuple fuzzy linguistic representation models under the numerical scale. We find that the key of computational techniques based on linguistic 2-tuples is to set suitable numerical scale with the purpose of making transformations between linguistic 2-tuples and numerical values. By defining the concept of the transitive calibration matrix and its consistent index, this paper develops an optimization model to compute the numerical scale of the linguistic term set. The desired properties of the optimization model are also presented. Furthermore, we discuss how to construct the transitive calibration matrix for decision problems using linguistic preference relations and analyze the linkage between the consistent index of the transitive calibration matrix and one of the linguistic preference relations. The results in this paper are pretty helpful to complete the fuzzy 2-tuple representation models for CW.

Multiattribute Group Decision Making Method Using Extended Linguistic Variables

The aim of this paper is to use the concept of extended linguistic variables to develop a new methodology for solving multiattribute group decision making problems under linguistic assessments. In this methodology, using the generalized induced ordered weighted averaging operator and extended linguistic variables, linguistic ratings of each alternative on all attributes for each decision maker are aggregated into a comprehensive assessment, which is not always a linguistic term in the linguistic term set designated a priori. Comprehensive assessments of each alternative on all decision makers are similarly aggregated into a comprehensive assessment of the alternative for the group. An optimal linguistic term in the linguistic term set which approaches the comprehensive assessment of each alternative for the group as close as possible is computed and an extended 2-tuple fuzzy linguistic representation is obtained for the alternative. The ranking order of alternatives for the group is generated according to the extended 2-tuple fuzzy linguistic representations. A numerical example is examined to demonstrate applicability and implementation process of the methodology proposed in this paper.

A fuzzy MCDM approach for personnel selection

Many individual attributes considered for personnel selection such as organizing ability, creativity, personality, and leadership exhibit vagueness and imprecision. The fuzzy set theory appears as an essential tool to provide a decision framework that incorporates imprecise judgments inherent in the personnel selection process. In this paper, a fuzzy multi-criteria decision making (MCDM) algorithm using the principles of fusion of fuzzy information, 2-tuple linguistic representation model, and technique for order preference by similarity to ideal solution (TOPSIS) is developed. The proposed method is apt to manage information assessed using both linguistic and numerical scales in a decision making problem with multiple information sources. Furthermore, it enables managers to deal with heterogeneous information. The decision making framework presented in this paper employs ordered weighted averaging (OWA) operator that encompasses several operators as the aggregation operator since it can implement different aggregation rules by changing the order weights. The aggregation process is based on the unification of information by means of fuzzy sets on a basic linguistic term set (BLTS). Then, the unified information is transformed into linguistic 2-tuples in a way to rectify the problem of loss information of other fuzzy linguistic approaches. The computational procedure of the proposed framework is illustrated through a personnel selection problem reported in an earlier study.

Extension of TOPSIS method for 2-tuple linguistic multiple attribute group decision making with incomplete weight information

With respect to linguistic multiple attribute group decision making problems with incomplete weight information, a new method is proposed. In the method, the 2-tuple linguistic representation developed in recent years is used to aggregate the linguistic assessment information. In order to get the weight vector of the attribute, we establish an optimization model based on the basic ideal of traditional technique for order performance by similarity to ideal solution, by which the attribute weights can be determined. Then, the optimal alternative(s) is determined by calculating the shortest distance from the 2-tuple linguistic positive ideal solution, and on the other side, the farthest distance of the 2-tuple linguistic negative ideal solution. The method has exact characteristic in linguistic information processing. It avoided information distortion and losing, which occur formerly in the linguistic information processing. Finally, a numerical example is used to illustrate the use of the proposed method. The result shows the approach is simple, effective, and easy to calculate.

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-Martinez’s model) jointly with the fusion rules developed in Dezert-Smarandache Theory (DSmT), in order to combine efficiently qualitative information expressed in term of qualitative belief functions. The two models both preserve the precision and improve the efficiency of the fusion of linguistic information expressing the global expert’s opinion. However, DFM is more general and efficient than the latter, especially for unbalanced linguistic labels. Some simple examples are also provided to show how the 2-Tuple qualitative fusion rules are performed and their advantages.

Qualitative reasoning by computing with words in Herrera-Martínez’s linguistic model

Most of modern systems for information retrieval, fusion and management have to deal with more and more qualitative information (by linguistic labels) besides information expressed quantitatively (by numbers), since human reports are better and easier expressed in natural language than with numbers. In this paper, Herrera-Martinez’s 2-Tuple linguistic representation model is extended for reasoning with uncertain and qualitative information in Dezert-Smarandache Theory (DSmT) framework, in order to overcome the limitations of current approaches, i.e., the lack of precision in the final results of linguistic information fusion according to 1-Tuple representation (q1). The linguistic information which expresses the expert’s qualitative beliefs is expressed by means of mixed 2 Tuples (equidistant linguistic labels with a numeric biased value). Together with the 2-Tuple representation model, some basic operators are presented to carry out the fusion operation among qualitative information sources. At last, through simple example how 2-Tuple qualitative DSmT-based (q2 DSmT) fusion rules can be used for qualitative reasoning and fusion under uncertainty, which advantage is also showed by comparing with other methods.

A fuzzy linguistic method for evaluating collaboration satisfaction of NPD team using mutual-evaluation information

Collaboration satisfaction of new product development (NPD) team is a key factor that affects the performance of team. The evaluation of collaboration satisfaction is a useful work for managers to control the operational process of NPD team so as to promote the performance. This paper investigates a fuzzy linguistic method for evaluating collaboration satisfaction of NPD team. The concept of collaboration satisfaction of NPD team is deduced and the collaborative working relationship between members is described. A research perspective is then proposed, i.e., collaboration satisfaction of NPD team can be measured by mutual satisfaction of members. After that, we construct an evaluation hierarchy with two perspectives and extending criteria. With respect to each criterion, the mutual-evaluation matrix with linguistic terms is obtained from mutual evaluation of members based on working relationship. A fuzzy linguistic approach based on 2-tuple linguistic representation model is proposed to evaluate collaboration satisfaction of NPD team. Finally, an example is used to demonstrate the potential of the proposed method.

PROMETHEE-MD-2T method for project selection

Project selection is a real problem of multicriteria group decision making (MCGDM) where each decision maker expresses his/her preferences depending on the nature of the alternatives and on his/her own knowledge over them. Thus, information, as much quantitative as qualitative, coexists. The traditional methods of MCGDM developed for project selection usually discriminates in favour of quantitative information at the expense of qualitative information, and this is due to the capability to integrate this first type of information inside their procedure. In this article, two new multicriteria 2-tuple group decision methods called “Preference Ranking Organisation Method for Enrichment Evaluation Multi Decision maker 2-Tuple-I and II” (PROMETHEE-MD-2T-I and II) are presented. They are able to integrate inside their procedure both quantitative and qualitative information in an uncertain context. This has been performed by integrating a 2-tuple linguistic representation model dealing with non-homogeneous and imprecise information data made up by valued intervals, numerical and linguistic values into the aggregation operators of Promethee methods. Although they have been developed for project selection problems, these proposed methods can be applied to all kinds of decision-making problems with heterogeneous and multigranular information. Therefore, the application of these methods to real problems will lead to better results in MCGDM. It offers to the decision makers simpler and wider application of the aggregation operators of the Promethee multicriteria method without sacrificing any of its advantageous properties and by taking into account the imprecision of data. A numerical simulation of the proposed method is carried out to show its possibilities.

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.

Extracting complex linguistic data summaries from personnel database via simple linguistic aggregations

A linguistic data summary of a given data set is desirable and human consistent for any personnel department. To extract complex linguistic data summaries, the LOWA operator is used from fuzzy logic and some numerical examples are also provided in this paper. To obtain a complex linguistic data summary with a higher truth degree, genetic algorithms are applied to optimize the number and membership functions of linguistic terms and to select a part of truth degrees for aggregations, in which linguistic terms are represented by the 2-tuple linguistic representation model.

Learning the membership function contexts for mining fuzzy association rules by using genetic algorithms

Different studies have proposed methods for mining fuzzy association rules from quantitative data, where the membership functions were assumed to be known in advance. However, it is not an easy task to know a priori the most appropriate fuzzy sets that cover the domains of quantitative attributes for mining fuzzy association rules. This paper thus presents a new fuzzy data-mining algorithm for extracting both fuzzy association rules and membership functions by means of a genetic learning of the membership functions and a basic method for mining fuzzy association rules. It is based on the 2-tuples linguistic representation model allowing us to adjust the context associated to the linguistic term membership functions. Experimental results show the effectiveness of the framework.

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.

A group decision-making aggregation process

Within the frame of decision aid literature, decision making problems with multiple sources of information have drawn the attention of researchers from a wide spectrum of disciplines. In decision situations with multiple individuals, each one has his own knowledge of the decision problem alternatives. The use of information assessed in different domains is not a seldom situation. This non-homogeneous information can be represented by values belonging to domains with different nature as linguistic, numerical and interval valued or can be values assessed in label sets with different granularity and multigranular linguistic information. Decision processes for solving these problems are composed by two steps: aggregation and exploitation. The main problem to deal with non-homogeneous contexts is the aggregation manner of the information assessed in these contexts. The purpose of this paper is to address this problem and establish a procedure to aggregate individual opinions into a common decision to deal with non-homogeneous contexts. This process combines at the same time numerical, interval valued and linguistic information. Since subjectivity, vagueness and imprecision enter into the assessments of experts, the 2-tuple fuzzy linguistic representation model is used to deal with the fuzziness of human judgment.

An Approach to Computing With Words Based on Canonical Characteristic Values of Linguistic Labels

Herrera and Martinez initiated a 2-tuple fuzzy linguistic representation model for computing with words (CW), which offers a computationally feasible method for aggregating linguistic information (that are represented by linguistic variables with equidistant labels) through counting indexes of the corresponding linguistic labels. Lawry introduced an alternative approach to CW based on mass assignment theory that takes into account the underlying definitions of the words. Recently, we provided a new (proportional) 2-tuple fuzzy linguistic representation model for CW that is an extension of Herrera and Martinez's model and takes into account the underlying definitions of linguistic labels of linguistic variables in the process of aggregating linguistic information by assigning canonical characteristic values (CCVs) of the corresponding linguistic labels. In this paper, we study further into CW based on CCVs of linguistic labels to provide a unifying link between Lawry's framework and Herrera and Martinez's 2-tuple framework as well as allowing for computationally feasible CW. Our approach is based on a formal definition of CCV functions of a linguistic variable (which is introduced under the context of its proportional 2-tuple linguistic representation model as continuation of our earlier works) and on a group voting model that is for the probabilistic interpretation of the (whole) semantics of the ordered linguistic terms set of an arbitrary linguistic variable. After the general framework developed in the former part of this paper, we focus on a particular linguistic variable - probability. We show that, for a linguistic probability description, the expectation of its posterior conditional probability is a canonical characteristic value of the linguistic probability description. Then, a calculus for reasoning with linguistic syllogisms and inference from linguistic information is introduced. It is investigated under the context that linguistic quantifiers in such linguistic syllogisms can be arbitrary linguistic probability description and that the related linguistic information can be linguistic facts, overfacts, or underfacts. Intrinsically, our approach to this calculus is with computing with words based on canonical characteristic values of linguistic labels.

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.