The Characteristic Objects Method: A New Distance‐based Approach to Multicriteria Decision‐making Problems

Abstract

Multicriteria decision-making (MCDM) methods are concerned with the ranking of alternatives based on expert judgements made using a number of criteria. In the MCDM field, the distance-based approach is one popular method for obtaining a final ranking. The technique for order preference by similarity to the ideal solution (TOPSIS) is a commonly used example of this kind of MCDM method. The TOPSIS ranks the alternatives with respect to their geometric distance from the positive and negative ideal solutions. Unfortunately, two reference points are often insufficient, especially for nonlinear problems. As a consequence of this situation, the final result ranking is prone to errors, including the rank reversals phenomenon.This study proposes a new distance-based MCDM method: the characteristic objects method. In this approach, the preferences of each alternative are obtained on the basis of the distance from the nearest characteristic objects and their values. For this purpose, we have determined the domain and Fuzzy number set for all the considered criteria. The characteristic objects are obtained as the combination of the crisp values of all the Fuzzy numbers. The preference values of all the characteristic object are determined on the basis of the tournament method and the principle of indifference. Finally, the Fuzzy model is constructed and is used to calculate preference values of the alternatives, making it a multicriteria model that is free of rank reversal. The numerical example is used to illustrate the efficiency of the proposed method with respect to results from the TOPSIS method. The characteristic objects method results are more realistic than the TOPSIS results.

Sustainable Decision-Making using the COMET Method: An Empirical Study of the Ammonium Nitrate Transport Management

“…In the previous works, the accuracy of the COMET method was verified [71]. The formal notation of the COMET method should be briefly recalled [65], [66], [67].…”

“…Modeling with the usage of the fuzzy sets has proven to be an effective way to formulate the multi-criteria decision problems [62], [63], [64]. The basic notions and concepts of the Fuzzy Set Theory are defined below [65], [66], [67]: The characteristic function µ A of a crisp set A ⊆ X assigns a value of either 0 or 1 to each member of X, as well as the crisp sets only allow a full membership (µ A (x) = 1) or no membership at all (µ A (x) = 0). This function can be generalized to a function µÃ so that the value assigned to the element of the universal set X falls within a specified range, i.e., µÃ : X → [0, 1].…”

Group Decision-Making for Hesitant Fuzzy Sets Based on Characteristic Objects Method

“…To assign the approximate value of preference to each CO, we use the same MATLAB code as used by Salabun in [45]. As a result, we get a vertical vector P, where the α-th component of P represents the approximate value of preference for CO α .…”

The Interval Cognitive Network Process for Multi-Attribute Decision-Making

“…In recent years, various methods, such as utility additive method (UTA) [2], robust ordinal regression (ROR) [3], analytic hierarchy process (AHP) [4], analytic network process (ANP) [5], primitive cognitive network process (P-CNP) [6], step-wise weight assessment ratio analysis (SWARA) [7,8], weighted aggregated sum product assessment (WASPAS) [9], factor relationship (FARE) method [10], the visekriterijumska optimizacija i kompromisno resenje (VIKOR) method [11], the characteristic objects method (COMET) [12], and COMET with hesitant fuzzy sets (HFS COMET) [13,14] have been proposed to handle MADM problems. Among these methods, AHP has been increasingly studied by plenty of researchers and applied in various applications due to its simplicity and practicability [15][16][17][18].…”