Linguistic Computational Model Research Articles

Fuzzy encoding and decoding approaches for 2-TCLE and their applications in multi-criteria decision making

In order to incorporate linguistic information into decision making, it is necessary to apply computing with words (CW) techniques. Traditional CW models use only single and simple linguistic terms to represent both input and output, which limits the flexibility in information processing. Recent researches on computing with comparative linguistic expression, including extension models, has partially overcome this limitation. Nonetheless, the flexibility of linguistic information expression remains limited due to the discrete distributions of primary terms. A complete CW framework should include both encoding and decoding technologies for linguistic information, but previous researches have primarily focused on fuzzy encoding approaches, while ignoring fuzzy decoding techniques for linguistic expressions. To improve the accuracy and interpretability of CW in dealing with linguistic expressions, this research proposes a novel model called 2-tuple comparative linguistic expression (2-TCLE). To establish a framework for studying fuzzy representations of linguistic expressions, both fuzzy encoding and decoding approaches for 2-TCLE will be presented in a systematic manner that are performed to match each other. A novel linguistic computational model for dealing with 2-TCLE is presented and then applied to solve a multi-criteria group decision making case study.

Enhanced linguistic computational models and their similarity with Yager’s computing with words

A generalized computational framework for Computing with Words (CWW) using linguistic information (LI) was proposed by Prof. Yager. This framework is based on three steps: translation, manipulation and retranslation. Other works have independently proposed the Linguistic Computational Models (LCMs) to express the semantics of LI using Type-1 Fuzzy Sets and Ordinal term sets. The former is called the extension principle, and the latter, the symbolic method. We found that a high degree of similarity can be drawn between these methodologies and Yager’s CWW framework, but no discussion exists in the literature of the similarity drawn between them. Further, the extension principle has a drawback: it considers LI to be equally weighted in the aggregation phase. Also, Intuitionistic fuzzy sets (IFSs) and rough sets have gained popularity to model semantics of LI, but no CWW methodologies have been proposed using them. Thus, the novel contributions of this work are twofold. Firstly, showing the similarity of the linguistic computational models based on extension principle and symbolic method, to the Yager’s generalized CWW framework. Secondly, proposing a new augmented flexible weighting for LCM based on the extension principle and two novel CWW methodologies based on IFS and rough sets.

Consensus reaching for group decision making with multi-granular unbalanced linguistic information: A bounded confidence and minimum adjustment-based approach

In group decision making problems, there exist the situations that decision makers may use unbalanced linguistic term sets that are not uniformly and symmetrically distributed to provide their linguistic assessments over alternatives. Moreover, due to the difference in knowledge and culture backgrounds, it is also possible that multi-granular linguistic term sets may also be used by decision makers. How to manage multi-granular unbalanced linguistic information in consensus-based group decision making has becoming an important topic in linguistic decision making. In this paper, we first revise Herrera’s unbalanced linguistic term sets and propose a simplified linguistic computational model to fuse multi-granular unbalanced linguistic terms. Afterwards, for multi-criteria group decision making problems with multi-granular unbalanced linguistic information, we develop two optimization models to generate adjustment advice for decision makers who have to change his/her opinions in consensus reaching process, which consider both the bounded confidence levels and minimum adjustment of decision makers’ linguistic assessments. Moreover, an algorithm is further proposed to help decision makers reach consensus in group decision making. Eventually, an application example for ERP system supplier selection and some simulation results are presented to illustrate and justify the consensus reaching algorithm.

An optimal Best-Worst prioritization method under a 2-tuple linguistic environment in decision making

Multi-criteria group decision making (MCGDM) deals with decision makers who evaluate alternatives over several criteria. MCGDM problems evolve in tandem with the progress of our society. Such progress has given rise to the large-scale group decision making (LS-GDM) problems in which hundreds of decision makers may participate in the decision process and new challenges to face such as groups’ formation and polarization opinions. Most real world MCGDM problems present changing contexts with uncertainty that cannot be modeled by numerical values. Under these circumstances, the use of linguistic variables and computing with words (CW) processes have provided successfully results. Concretely, the 2-tuple linguistic computational model stands out because its precise linguistic computations and high interpretability. On the other hand, pairwise comparison is a widely used elicitation technique in MCGDM, but a large number of comparisons might lead inconsistent decision makers’ preferences. The Best-Worst method (BWM) reduces the number of pairwise comparisons and the inconsistency in decision makers’ opinions. Several BWM approaches have been proposed to manage linguistic information but none of them take advantage of the 2-tuple linguistic computational process based on the CW approach, which would allow to obtain precise and understandable results. This paper aims to present an extended 2-tuple BWM to reduce the number of pairwise comparisons in MCGDM problems and model the uncertainty associated with them to accomplish accuracy computations and obtaining interpretable results. Moreover, we apply our proposal to LS-GDM scenarios in which polarization opinions and sub-groups identification, ignored from any of BWM proposals, are considered. Finally, the new model is applied to several illustrative MCGDM problems.

A dual linguistic scale-based digitization and exploitation method for scrap steel remanufacturing process selection

Language is a preferred way for evaluators to express their opinions. As an important part of qualitative decision making, computing with words mainly focuses on transferring linguistic information to numerical values for operations. A significant challenge is how to model the meaning of linguistic information given by evaluators. This study aims to explore the principle of an evaluator to judge alternatives over different kinds of criteria and establish linguistic scale functions to simulate the personalized semantics of linguistic terms. In addition a dual linguistic scale in the form of linguistic terms and numerical meanings is developed to represent decision information. We then develop a method called the dual linguistic scale-based digitization and exploitation method to deduce the ranking of alternatives for multiple criteria decision-making problems, which considers the personalized cognition of evaluators and the personalized requirements of decision-makers for the trade-offs between criteria A case study concerning the scrap steel remanufacturing is conducted to demonstrate the validity of the proposed method. The results demonstrate that linguistic computational models have an influence on the ranking results of alternatives.

Materials Selection Using a 2-tuple Linguistic Multi-criteria Method

The materials selection can affect the design component radically, with effect on the manufacturing systems efficiency, environmental impact issues, and customer satisfaction. There are different methods employed for materials selection; however, two steps are usual for most of these methods: screening and ranking. The ranking step identifies among materials candidates those that can perform the function the best as possible. Multi-criteria methods have been widely employed to materials selection, especially in the ranking step. Most of these methods take advantage of fuzzy numbers and linguistic variables to process qualitative information and information with uncertainties. One of the approaches that have been developed to solve issues related to make decisions in multi-criteria methods using linguistic information is the 2-tuple linguistic computational model. The main advantage of this approach is taking the “loss of information” away, which provides a higher precision on results. This paper aims to present a multi-criteria method for materials selection ranking step based on 2-tuple linguistic variables. The steps and several equations needed to apply the proposed method are described. Two case studies are presented and compare results with other methods to demonstrate the proposed method potential.

A Method Adjusting Consistency and Consensus for Group Decision-Making Problems with Hesitant Fuzzy Linguistic Preference Relations Based on Discrete Fuzzy Numbers

In each hesitant fuzzy linguistic preference relation, experts may express their opinions through comparison linguistic information combined with a discrete fuzzy number. In this paper, a hesitant fuzzy linguistic computational model based on discrete fuzzy numbers whose support is a subset of consecutive natural numbers is proposed, which enriches the flexibility of group decision-making. First, some main concepts related to discrete fuzzy numbers and an aggregation function of individual subjective linguistic preference relations are introduced. Then, a consistency measure is presented to check and improve the consistency in a given matrix. Further, in order to achieve the predefined degree of consensus and to arrive at the final result, a consensus-reaching process based on the interactive feedback mechanism is defined. Meanwhile, a revised formula is introduced to calculate the consistency and the degree of consensus in a preference relation matrix. Besides, an illustrative example and comparative analysis are conducted through the proposed calculation process and the optimization algorithm. Finally, the analysis on the threshold values is made to help the decision-maker determine critical consensus level. The proposed method can address both consistency and consensus, and the results confirmed the effectiveness of the proposed method and its potential use in the qualitative decision-making problems.

Managing Multigranular Linguistic Distribution Assessments in Large-Scale Multiattribute Group Decision Making

Linguistic large-scale group decision making (LGDM) problems are more and more common nowadays. In such problems a large group of decision makers are involved in the decision process and elicit linguistic information that are usually assessed in different linguistic scales with diverse granularity because of decision makers' distinct knowledge and background. To keep maximum information in initial stages of the linguistic LGDM problems, the use of multi-granular linguistic distribution assessments seems a suitable choice, however to manage such multigranular linguistic distribution assessments, it is necessary the development of a new linguistic computational approach. In this paper it is proposed a novel computational model based on the use of extended linguistic hierarchies, which not only can be used to operate with multi-granular linguistic distribution assessments, but also can provide interpretable linguistic results to decision makers. Based on this new linguistic computational model, an approach to linguistic large-scale multi-attribute group decision making is proposed and applied to a talent selection process in universities.

A 2-tuple linguistic multi-period decision making approach for dynamic green supplier selection

La selección de proveedores verdes tiene como objetivo la elección del mejor proveedor, entre varias alternativas, teniendo en cuenta no solo criterios tradicionales como el costo y la calidad del servicio o producto, sino considerando también la capacidad de producir estos productos o servicios cumpliendo estándares o regulaciones ambientales y con el menor impacto en el medio ambiente. En contextos reales de selección verde, en ocasiones no basta con una única evaluación estática de los proveedores y se necesita considerar la evolución de los proveedores en diferentes momentos y por supuesto algunos parámetros no son constantes en el tiempo, más bien son dinámicos y varían de un período a otro. En consecuencia, las decisiones acerca de los proveedores tienen lugar en un entorno dinámico, donde la decisión final se toma luego de un proceso de exploración. Además, la información disponible es vaga o imprecisa que no implica la incertidumbre probabilística. En tales situaciones, el uso del modelo lingüístico 2-tupla proporciona una forma adecuada para representar las evaluaciones lingüísticas por medio de variables lingüísticas y modelar la incertidumbre. En este trabajo, la atención principal se centra en encontrar el proveedor adecuado utilizando un enfoque de toma de decisiones multicriterio y multiperíodo, basado en el modelo computacional 2-tupla lingüística.

New types of computational perceptions: Linguistic descriptions in deforestation analysis

Abstract Automatic linguistic description of the available data about complex phenomena is a challenging task that is receiving the attention of data scientists in recent years. As an evolution of previous research results, there is a need of creating new linguistic computational models that allow us dealing with more complex phenomena and more complex descriptions of a growing amount of heterogeneous and real-time data. This paper contributes to this field by presenting three new ways of describing added-value information automatically extracted from data. Also, we extend previous computational models by including a description of the reliability of the available input data. Namely, we face this challenge by using a new implementation of the concept of Z-number proposed by Zadeh. We demonstrate the possibilities of the proposed extension with a practical application. The application generates automatic linguistic reports about the deforestation evolution in the Amazon region, e.g., “The deforestation last month was high. Because of the cloudiness, the reliability of this information is moderate”. Additionally, we evaluate the quality of the generated linguistic descriptions through fuzzy rating scale-based questionnaires. Moreover, we have also made a comparative study between reports generated with and without the new contributions introduced in this paper. The results show that the new types of computational perceptions introduced in this paper are ready to help data scientists to automatically generate good quality reports.

A Method for Unbalanced Linguistic Term Sets and its Application in Group Decision Making

In most decision-making problems where linguistic assessments are used, the assessments are assumed to be based on uniform and symmetrically distributed linguistic term sets. However, there exist decision-making problems whose assessments are unbalanced linguistic term sets. We propose a new linguistic computational model based on symbolic models. Firstly, we develop a representation model of unbalanced linguistic term sets. The values expressed by unbalanced linguistic terms are converted into a special linguistic domain, which is a basic equal-distance linguistic term set. We propose a computational model for group decision making. We then design a consensus model to reach an acceptable consensus level based on our representation model for unbalanced linguistic term sets. Finally, numerical examples are illustrated. The new method enriches the assessment of decision makers and makes computation easier.

Connecting the linguistic hierarchy and the numerical scale for the 2-tuple linguistic model and its use to deal with hesitant unbalanced linguistic information

The 2-tuple linguistic representation model is widely used as a basis for computing with words (CW) in linguistic decision making problems. Two different models based on linguistic 2-tuples (i.e., the model of the use of a linguistic hierarchy and the numerical scale model) have been developed to address term sets that are not uniformly and symmetrically distributed, i.e., unbalanced linguistic term sets (ULTSs). In this study, we provide a connection between these two different models and prove the equivalence of the linguistic computational models to handle ULTSs. Further, we propose a novel CW methodology where the hesitant fuzzy linguistic term sets (HFLTSs) can be constructed based on ULTSs using a numerical scale. In the proposed CW methodology, we present several novel possibility degree formulas for comparing HFLTSs, and define novel operators based on the mixed 0–1 linear programming model to aggregate the hesitant unbalanced linguistic information.

2-dimension linguistic computational model with 2-tuples for multi-attribute group decision making

The 2-dimension linguistic information includes two common linguistic labels. One dimension is used for describing the evaluation result of alternatives provided by the decision maker, and the other is used for describing the self-assessment of the decision maker on the reliability of the given evaluation result. In order to deal with comparability and incomparability of 2-dimension linguistic labels (2DLLs), a 2-dimension linguistic lattice implication algebra (2DL-LIA) is constructed as a linguistic evaluation set with lattice structure. In this paper, a 2DLL is firstly represented by two 2-tuples in a 2DL-LIA for more precise computing and aggregating 2-dimension linguistic information. This model allows a continuous representation of 2DLL on its domain, therefore, it can represent any continuous 2-dimension linguistic information obtained in the aggregation process. Next, two new 2-dimension linguistic aggregation operators, including 2-dimension linguistic weighted arithmetic aggregation (2DLWAA) operator and 2-dimension linguistic ordered weighted arithmetic aggregation (2DLOWAA) operator, are developed, and then some desirable properties of the operators are studied. Subsequently, based on 2DLWAA and 2DLOWAA operators, a decision making approach is provided to solve multi-attribute group decision making (MAGDM) problem with 2DLL assessment. Finally, an illustrative example is provided to show the concrete steps of the developed decision making approach and to demonstrate the practicality and the flexibility of this proposal by comparing with existing decision making approaches.

A model based on subjective linguistic preference relations for group decision making problems

In a group decision making problem, experts often express their opinions through the so-called preference relations. In recent years, several different definitions of preference relations depending on the framework and the nature of the problem have been introduced. These approaches vary from interval-valued fuzzy preference relations to incomplete fuzzy linguistic preference relations. In this paper, a novel definition of preference relation, the so-called subjective linguistic preference relation, is proposed. These preference relations are based on the concept of subjective evaluations, introduced in the linguistic computational model based on discrete fuzzy numbers. In this framework, the experts have more flexibility to express their opinions and the solid mathematical background of this model is a guarantee of no loss of information. Finally, an example of a multi-expert decision making problem with a hierarchical multi-granular linguistic context is analyzed to illustrate the potential of the proposed method and its advantages with respect to other methods.

An Approach to Hesitant Fuzzy Group Decision Making with Multi-Granularity Linguistic Information

The 2-tuple linguistic computational model is an important tool to deal with linguistic information. To extend the application of hesitant fuzzy linguistic term sets and avoid information loss, this paper introduces hesitant fuzzy 2-tuple linguistic term sets that are expressed by using several symbolic numbers in [0,1]. Considering the order relationship between hesitant fuzzy 2-tuple linguistic term sets, measures of expected value and variance are defined. Meanwhile, several induced generalized hesitant fuzzy 2-tuple linguistic aggregation operators are defined, by which the comprehensive attribute values of alternatives can be obtained. Then, models for the optimal weight vector on a decision maker set, on an attribute set and on their ordered sets are constructed, respectively. Furthermore, an approach to multi-granularity group decision making with hesitant fuzzy linguistic information is developed. Finally, an example is selected to illustrate the feasibility and practicality of the proposed procedure.

Linguistic Computational Model Based on 2-Tuples and Intervals

Herrera and Martínez initiated a 2-tuple fuzzy linguistic representation model for computing with words. Moreover, Wang and Hao further developed a new 2-tuple fuzzy linguistic representation model to deal with the linguistic term sets that are not uniformly and symmetrically distributed. This study proposes another linguistic computational model based on 2-tuples and intervals, which we call an interval version of the 2-tuple fuzzy linguistic representation model. The proposed model possesses three steps: 1) interval numerical scale; 2) computation based on interval numbers; and 3) a generalized inverse operation of the interval numerical scale. The first step transforms linguistic terms into interval numbers, based on which the second step is executed with output as an interval number. Finally, this number is then mapped into the interval of the linguistic 2-tuples by the generalized inverse operation. This study also generalizes the numerical scale approach, presented in the Wang and Hao model, to set the interval numerical scale, by considering the context where semantics of linguistic terms are defined by interval type-2 fuzzy sets (IT2 FSs). In order to compare the proposed model with the existing linguistic computational model based on IT2 FSs, we have conducted extensive simulations. The simulations demonstrate that the results obtained by our proposal are consistent with the results of the linguistic computational model based on IT2 FSs (in some sense) in a vast majority of cases.

A new linguistic computational model based on discrete fuzzy numbers for computing with words

In recent years, several different linguistic computational models for dealing with linguistic information in processes of computing with words have been proposed. However, until now all of them rely on the special semantics of the linguistic terms, usually fuzzy numbers in the unit interval, and the linguistic aggregation operators are based on aggregation operators in [0,1]. In this paper, a linguistic computational model based on discrete fuzzy numbers whose support is a subset of consecutive natural numbers is presented ensuring the accuracy and consistency of the model. In this framework, no underlying membership functions are needed and several aggregation operators defined on the set of all discrete fuzzy numbers are presented. These aggregation operators are constructed from aggregation operators defined on a finite chain in accordance with the granularity of the linguistic term set. Finally, an example of a multi-expert decision-making problem in a hierarchical multi-granular linguistic context is given to illustrate the applicability of the proposed method and its advantages.

A Fuzzy Knowledge Fusion Framework for Terms Conflict Resolution in Concurrent Engineering

Due to the increased complexity of engineering products and design process, concurrent engineering practices still face enormous challenges. Design teams often provide the knowledge involving multiple disciplines in natural language at conceptual design stage. As a result, conflicts often arise during communications. To increase the efficiency of design process, it is necessary to avoid interpretation conflicts. This article presents a system framework to resolve terminology conflicts. First, a semantic hierarchical structure of knowledge is proposed. Knowledge is decomposed into terms and predicates. Second, a fuzzy knowledge fusion framework is proposed to identify and resolve terminology conflicts. The conflict is resolved by unifying the usage of terminologies. By using the fuzzy linguistic computational model based on extension principle to measure the similarity of terms, the terminology conflict problem is converted into a linguistic decision-making problem. Finally, the methodology is applied to a piece of automotive electronics knowledge. The best term to describe electronic control unit is identified.

Computing with words in decision making: foundations, trends and prospects

Computing with Words (CW) methodology has been used in several different environments to narrow the differences between human reasoning and computing. As Decision Making is a typical human mental process, it seems natural to apply the CW methodology in order to create and enrich decision models in which the information that is provided and manipulated has a qualitative nature. In this paper we make a review of the developments of CW in decision making. We begin with an overview of the CW methodology and we explore different linguistic computational models that have been applied to the decision making field. Then we present an historical perspective of CW in decision making by examining the pioneer papers in the field along with its most recent applications. Finally, some current trends, open questions and prospects in the topic are pointed out.

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.