A MAGDM ALGORITHM FOR DECISION-MAKING PROBLEMS ON FUZZY SOFT SETS USING A COEFFICIENT CORRELATION AND AN ENTROPY MEASURE FOR DETERMINING THE WEIGHT OF PARAMETERS

In statistics, the correlation coefficient concept aims to show how strong the linear relationship between two variables is. Sometimes the data collected relates to everyday life problems whose value is uncertain. Therefore, the concept of correlation coefficient must be developed on the fuzzy sets and the fuzzy soft sets environment. In this study, a decision-making algorithm was designed on fuzzy soft sets using the concept of the correlation coefficient. The method used is MAGDM, where the parameter weights are determined using entropy measures. Using this method, the algorithm of our decision-making problem is more realistic and general. The final section gives an example of a decision-making problem and a numerical illustration using the designed algorithm

Multiple-Attribute Decision-Making Method Using Similarity Measures of Hesitant Linguistic Neutrosophic Numbers Regarding Least Common Multiple Cardinality

Linguistic neutrosophic numbers (LNNs) are a powerful tool for describing fuzzy information with three independent linguistic variables (LVs), which express the degrees of truth, uncertainty, and falsity, respectively. However, existing LNNs cannot depict the hesitancy of the decision-maker (DM). To solve this issue, this paper first defines a hesitant linguistic neutrosophic number (HLNN), which consists of a few LNNs regarding an evaluated object due to DMs’ hesitancy to represent their hesitant and uncertain information in the decision-making process. Then, based on the least common multiple cardinality (LCMC), we present generalized distance and similarity measures of HLNNs, and then develop a similarity measure-based multiple-attribute decision-making (MADM) method to handle the MADM problem in the HLNN setting. Finally, the feasibility of the proposed approach is verified by an investment decision case

La comprensión de conceptos estadísticos en la educación secundaria

The skills derived from traditional mathematics, such as statistics, have gained an important prominence in recent years. The fundamental objective of this article is to analyse whether the student is able to understand statistical concepts in secondary education. For the investigation, the problem was approached from a quantitative focus of descriptive cut, through the application of a questionnaire to a sample composed by 83students of the secondary level of commercial schools of the city of Pereira. The final results showed that 42.2% of the students have problems understanding concepts related to dispersion measures, while 54.2% have problems calculating probabilities. The Chi-Square statistic allows us to conclude that the level ofdomain is related to the school in which it is studied (X2 =33.065; p=0.00).Las competencias derivadas de las matemáticas tradicionales como la estadística, han cobrado un importante protagonismo los años recientes. El objetivo fundamental del presente artículo es analizar si el estudiante logra comprender los conceptos estadísticos en la formación secundaria. Para la investigación, se abordó el problema desde un enfoque cuantitativo de corte descriptivo, mediante la aplicación de uncuestionario a una muestra compuesta por 83 estudiantes del nivel secundario de colegios comerciales de la ciudad de Pereira. Los resultados finales, permitieron conocer que el 42,2% de los estudiantes tienen problemas para comprender conceptos relacionados con las medidas de dispersión, mientras que 54,2%tiene problemas con el cálculo de probabilidades. El estadístico Chi Cuadrado permite concluir que el nivel de dominio guarda relación con el colegio en el que se estudie (X2 =33,065; p=0,00)

La comprensión de conceptos estadísticos en la educación secundaria

The skills derived from traditional mathematics, such as statistics, have gained an important prominence in recent years. The fundamental objective of this article is to analyse whether the student is able to understand statistical concepts in secondary education. For the investigation, the problem was approached from a quantitative focus of descriptive cut, through the application of a questionnaire to a sample composed by 83students of the secondary level of commercial schools of the city of Pereira. The final results showed that 42.2% of the students have problems understanding concepts related to dispersion measures, while 54.2% have problems calculating probabilities. The Chi-Square statistic allows us to conclude that the level ofdomain is related to the school in which it is studied (X2 =33.065; p=0.00).Las competencias derivadas de las matemáticas tradicionales como la estadística, han cobrado un importante protagonismo los años recientes. El objetivo fundamental del presente artículo es analizar si el estudiante logra comprender los conceptos estadísticos en la formación secundaria. Para la investigación, se abordó el problema desde un enfoque cuantitativo de corte descriptivo, mediante la aplicación de uncuestionario a una muestra compuesta por 83 estudiantes del nivel secundario de colegios comerciales de la ciudad de Pereira. Los resultados finales, permitieron conocer que el 42,2% de los estudiantes tienen problemas para comprender conceptos relacionados con las medidas de dispersión, mientras que 54,2%tiene problemas con el cálculo de probabilidades. El estadístico Chi Cuadrado permite concluir que el nivel de dominio guarda relación con el colegio en el que se estudie (X2 =33,065; p=0,00)

Interval-valued 2-tuple hesitant fuzzy linguistic term set and its application in multiple attribute decision making

[EN] The hesitant fuzzy linguistic term sets can retain the completeness of linguistic information elicitation by assigning a set of possible linguistic terms to a qualitative variable. However, sometimes experts cannot make sure that the objects attain these possible linguistic terms but only provide the degrees of confidence to express their hesitant cognition. Given that the interval numbers can denote the possible membership degrees that an object belongs to a set, it is suitable and convenient to provide an interval-valued index to measure the degree of a linguistic variable to a given hesitant fuzzy linguistic term set. Inspired by this idea, we introduce the concept of interval-valued 2-tuple hesitant fuzzy linguistic term set (IV2THFLTS) based on the interval number and the hesitant fuzzy linguistic term set. Then, we define some interval-valued 2-tuple hesitant fuzzy linguistic aggregation operators. Afterwards, to overcome the instability of subjective weights, we propose a method to compute the weights of attributes. For the convenience of application, a method is given to solve the multiple attribute decision making problems with IV2THFLTSs. Finally, a case study is carried out to validate the proposed method, and some comparisons with other methods are given to show the advantages of the proposed method.The work was supported in part by the National Natural Science Foundation of China (Nos. 71501135, 71771156), the China Postdoctoral Science Foundation (2016T90863, 2016M602698), the Fundamental Research Funds for the central Universities (No. YJ201535), and the Scientific Research Foundation for Excellent Young Scholars at Sichuan University (No. 2016SCU04A23).Si, G.; Liao, H.; Yu, D.; Llopis Albert, C. (2018). Interval-valued 2-tuple hesitant fuzzy linguistic term set and its application in multiple attribute decision making. Journal of Intelligent & Fuzzy Systems. 34(6):4225-4236. https://doi.org/10.3233/JIFS-171967S4225423634

Hesitant Fuzzy Linguistic Analytic Hierarchical Process With Prioritization, Consistency Checking, and Inconsistency Repairing

Analytic hierarchy process (AHP), as one of the most important methods to tackle multiple criteria decision-making problems, has achieved much success over the past several decades. Given that linguistic expressions are much closer than numerical values or single linguistic terms to a human way of thinking and cognition, this paper investigates the AHP with comparative linguistic expressions. After providing the snapshot of classical AHP and its fuzzy extensions, we propose the framework of hesitant fuzzy linguistic AHP, which shows how to yield a decision for qualitative decision-making problems with complex linguistic expressions. First, the comparative linguistic expressions over criteria or alternatives are transformed into hesitant fuzzy linguistic elements and then the hesitant fuzzy linguistic preference relations (HFLPRs) are constructed. Considering that HFLPRs may be inconsistent, we conduct consistency checking and improving processes after obtaining priorities from the HFLPRs based on a linear programming method. Regarding the consistency-improving process, we develop a new way to establish a perfectly consistent HFLPR. The procedure of the hesitant fuzzy linguistic AHP is given in stepwise. Finally, a numerical example concerning the used-car management in a lemon market is given to illustrate the ef ciency of the proposed hesitant fuzzy linguistic AHP method.This work was supported in part by the National Natural Science Foundation of China under Grant 71771156, in part by the 2019 Sichuan Planning Project of Social Science under Grant SC18A007, in part by the 2019 Soft Science Project of Sichuan Science and Technology Department under Grant 2019JDR0141, and in part by the Project of Innovation at Sichuan University under Grant 2018hhs-43

Qualitative decision making with correlation coefficients of hesitant fuzzy linguistic term sets

Artículo de publicación ISIThe hesitant fuzzy linguistic term set (HFLTS) is a new and flexible tool in representing hesitant qualitative information in decision making. Correlation measures and correlation coefficients have been applied widely in many research domains and practical fields. This paper focuses on the correlation measures and correlation coefficients of HFLTSs. To start the investigation, the definition of HFLTS is improved and the concept of hesitant fuzzy linguistic element (HFLE) is introduced. Motivated by the idea of traditional correlation coefficients of fuzzy sets, intuitionistic fuzzy sets and hesitant fuzzy sets, several different types of correlation coefficients for HFLTSs are proposed. The prominent properties of these correlation coefficients are then investigated. In addition, considering that different HFLEs may have different weights, the weighted correlation coefficients and ordered weighted correlation coefficients are further investigated. Finally, an application example concerning the traditional Chinese medical diagnosis is given to illustrate the applicability and validation of the proposed correlation coefficients of HFLTSs in the process of qualitative decision making.National Natural Science Foundation of China 61273209 Excellent Ph.D. Thesis Foundation of Shanghai Jiao Tong University 20131216 Scholarship from China Scholarship Council 20130623004

Selection third-party logistics service providers in supply chain finance by a hesitant fuzzy linguistic combined compromise solution method

In supply chain finance, the multiple criteria decision making (MCDM) problem of selecting a suitable third-party logistics (3PL) service supplier is of great significance to financial institutions. A suitable 3PL service supplier can not only help financial institutions carry out the supply chain finance business, but also can replace financial institutions to supervise the operation of a target financing supply chain, thus reducing the operational risks of financial institutions. As a useful MCDM method, the combined compromise solution (CoCoSo) method mainly combines a compromise decision algorithm with an aggregation strategy to obtain a compromise solution. This study extends the CoCoSo method to hesitant fuzzy linguistic environment to solve the multi-expert MCDM problem of the 3PL service supplier selection. Target criteria whose values are in linguistic forms are considered in the process of normalizing the decision matrix. A new integration approach with respect to subordinate compromise scores is introduced, and the subjective and objective weights of criteria are considered simultaneously in this extended process to avoid one-sidedness of criterion weights. A case study about the 3PL service supplier selection is given, in which the sensitivity analysis and comparative analysis are provided to highlight the advantages of the proposed method