Weight determination and ranking priority in interval group MCDM

Abstract

In this study, we propose a method to determine the weight of decision makers (DMs) in group multiple criteria decision making (GMCDM) problems with interval data . Here, we obtain an interval weight for each DM and then the relative closeness of each decision from the negative ideal solution (NIS) and the positive ideal solution (PIS) is then computed. In the proposed method, after weighting the decision matrix of each DM, the alternatives are ranked using interval arithmetic. A comparative example along with a real world problem on air quality assessment is given to illustrate our method. Technique (SMART) method [12] which asks for direct ratings on a scale from 0 to 100 and the Measuring Attractiveness by a Categorical Based Evaluation Technique (MACBETH) method [13] which requires pairwise comparisons on an interval. The other method is ELimination Et Choix Traduisant la REalité (ELECTRE) which has different types. It is worthy to mention that the study of Govindan and Jespen [14] is a comprehensive source of ELECTRE and ELECTRE-based methods. Their study considers different types of ELECTRE methods and compares, modifies and defines the area of applications of each method. Recently, Ishizaka and Siraj [15] evaluated AHP, SMART and MAGBETH for a real MCDM problem. The authors investigate whether these three methods really help the DMs or not. The assessment of public transport satisfaction investigated by Nassereddine and Eskandari [16]. For this purpose, the authors employ an integrated MCDM technique. Their method is a combination of Delphi, group AHP (GAHP) and Preference Ranking Organization METHod for Enrichment of Evaluations (PROMETHEE). A method based on TOPSIS and entropy proposed by Abdollahi et al. [17] to rank multifarious Demand Response Resources (DRRs). To be noted that the MCDM models are widely used in systems engineering [18-22].Frankly speaking, most of the above mentioned methods include one DM while real life problems have different managerial, engineering, social and etc. aspects and they usually deal with a group of DMs. Papers such as [23-29] have presented methods to solve GMCDM problems. These methods have considered the cases that data are exact and have crisp values. But, in most real world problems the decision information are expressed as interval or fuzzy numbers [30]. Nowadays, the Fuzzy MCDM (FMCDM) problems play an important role in industrial and system engineering. An extension of fuzzy VIKOR to solve Supplier Selection Problem (SSP) was presented by Mahmoudi et al. [31]. In their method a fuzzy distance measure is proposed to rank the suppliers. Besides, they consider unequal weights for DMs and the performance of each supplier under each criteria is represented by a linguistic variable. Finally the alternatives are ranked using preference ration method. An MCDM problem with stochastic and intuitionistic data was proposed by Hu et al. [32]. The problem of dam site selection was considered as a Group FMCDM (GFMCDM) by Minatour et al. [33]. To solve the problem an integrati...

Relative agreement method for multiple criteria decision making problems with interval numbers

“…In this section, some interval definitions and interval operation are presented, these preliminaries will be used in the next section [20][21][22].   is a real number, then: [ , ]…”

Sistema de evaluación y priorización de inversiones públicas

“…Posteriormente, esta metodología se ha adaptado a II (Yue, 2011b(Yue, , 2012c(Yue, , 2012b y IFI (Yue, 2014), que se han utilizado en otros estudios Zarook et al, 2015). Otros autores han ampliado el trabajo de Yue modificando los datos de entrada para OFI (Kacprzak, 2019), PFI (Biswas & Sarkar, 2019), MGLI o IFI con distancia de Hamming , proponiendo nuevos coeficientes de cercanía (Dorfeshan & Mousavi, 2019;Gitinavard et al, 2016;Saffarzadeh et al, 2019) o utilizando enfoques de teoría de conjuntos difusos en lugar del promedio aritmético (Yang et al, 2017) para la solución ideal.…”