Efficient Multiple Attribute Group Decision Making Models with Correlation Coefficient of Vague Sets

Abstract

A new approach for multiple attribute group decision making (MAGDM) problems where the attribute weights and the expert weights are real numbers and the attribute values take the form of vague values, is presented in this paper. Since families of ordered weighted averaging (OWA) operators are available in the literature, and only a few available for vague sets, the vague ordered weighted averaging (VOWA) operator and the induced vague ordered weighted averaging (IVOWA) operator are introduced in this paper and utilized for aggregating the vague information. The correlation coefficient for vague sets is used for ranking the alternatives and a new MAGDM model is developed based on the IVOWA operator and the vague weighted averaging (VWA) operator. In addition to the proposed model, two different models are proposed based on Linguistic Quantifiers for the situation when the expert weights are completely unknown. An illustrative example is given and a comparison is made between the models to demonstrate the applicability of the proposed approach of MAGDM.

A Novel Mixed Integer Programming Formulation for Selecting the Best Renewable Energies to Invest

“…First group is the classical MCDM problems which the ratings and the weights of criteria are measured in crisp numbers. Second group is the fuzzy multiple criteria decision-making (FMCDM) problems which the ratings and the weights of criteria evaluated on imprecision and vagueness are usually expressed by linguistic terms, fuzzy numbers or intuition fuzzy numbers (Robinson & Amirtharaj, 2014).…”

Research on Vague multi-attribute group decision-making method based on evidence theory

“…Elzarka(2017) first calculated the weight of each expert according to the mutual score among experts, and then calculated the weight value of each attribute according to the weight matrix given by experts and expert weights. Robinson (2014) proposed two methods to solve the expert weights based on RIM Linguistic Quantifiers or Gaussian distribution. At present, most of the methods to solve the expert weight or attribute weight will give the relevant information first, and there is less research on not giving the information related to the weight at all.…”

“…Wang (2005) ， Zhou(2016) ， Gao(2017) used TOPSIS method to calculate the distance between each alternative and the ideal solution to sort the alternatives. In the research of aggregation of expert evaluation information, scholars have defined the the product algorithm of Vague values and real values (Elzarka 2017), the product algorithm between Vague values (Robinson 2014), and the union and intersection algorithm between Vague values (Lin 2019) to aggregate the evaluation information of each alternative and obtain the final evaluation value of each alternative. However, because these algorithms do not consider the reasonable allocation of the unknown degree of Vague sets, the synthetic results can not reasonably express the information contained in the original evaluation values.…”

Intuitionistic Trapezoidal Fuzzy MAGDM Problems with Sumudu Transform in Numerical Methods

“…Zeng &Li,(2007)andParketal.,(2009investigatedthecorrelationcoefficientofIFSandproposedthe correlation coefficient of interval valued intuitionistic fuzzy sets. Robinson, (2016) Robinson & Amirtharaj,(2011a,2011b,2012a,2012b,2013,2014c,definedcorrelation coefficient for different higher order intuitionistic fuzzy sets and utilized in MAGDM problems. Robinson & Jeeva, (2017), Jeeva & Robinson, (2018) proposed several methods of determining decisionmakerweightingvectorthroughJacobianandSORiterationprocessandSumudutransform whichareutilizedinMAGDMproblemsunderintuitionisticfuzzysets.Robinson&Jeeva(2016) proposednewmethodforMiningTrapezoidalIntuitionisticFuzzyCorrelationRulesforEigenValued MAGDM Problems.…”