Abstract
This paper aims to utilize the core structure of linear programming technique for multidimensional analysis of preference (LINMAP) to propose a parametric LINMAP methodology for addressing multiple criteria group decision-making problems based on Pythagorean fuzzy sets. To compare Pythagorean membership grades, this paper presents a Hamming distance-based approach for identifying closeness-based order relations based on Pythagorean fuzzy closeness indices. The concept of comprehensive closeness measures is introduced to measure individual order consistency and inconsistency between subjective preference relations and objective order relations. In the spirit of LINMAP, this paper determines individual goodness of fit and poorness of fit and further constructs a novel parametric LINMAP model. The applicability of the developed approach is explored by a practical application of railway project investment. Some comparative analyses are conducted to demonstrate the usefulness and advantages of the proposed methodology.
Highlights
The linear programming technique for multidimensional analysis of preference (LINMAP), initiated by Srinivasan and Shocker [1], is a well-known compromising model in the decision-making field [2], [3]
The optimal weight wj of each criterion cj ∈ C and the optimal individual degree of violation Ziki for each ordered pair (i, i ) ∈ k provided by the decision maker ek can be obtained by solving the parametric Pythagorean fuzzy (PF) LINMAP model using the Simplex method
This paper has presented the PF closeness index to identify the PF closeness-based order relation between PF evaluative ratings
Summary
The linear programming technique for multidimensional analysis of preference (LINMAP), initiated by Srinivasan and Shocker [1], is a well-known compromising model in the decision-making field [2], [3]. The purpose of this paper is to utilize PF closeness-based order relations via a recently developed Hamming distance measure and construct a novel parametric PF LINMAP model to address multiple criteria GDM problems. This paper introduces the concept of comprehensive closeness measures to acquire synthetic effects over all evaluative criteria and specify objective order relations These comprehensive measures and relations can be used to identify individual indices of order consistency and order inconsistency between the preorders of the alternatives in the preference set for each decision maker. This paper makes use of PF sets to model inherent fuzziness and subjectivity within uncertain environments and resolve situations where decision makers hesitate in assessing alternatives under complex uncertainty.
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