An Extended VIKOR Method Based on q-Rung Orthopair Shadowed Set and Its Application to Multi-Attribute Decision Making

Abstract

In the multi-attribute decision making (MADM) process, the attribute values are sometimes provided by experts or the public in the form of words. To model the linguistic evaluation more accurately, this paper proposes the q-rung orthopair shadowed set (q-ROSS) to represent attribute values and extends the VIKOR (VIsekriterijumska optimizacija i KOmpromisno Resenje) method to solve MADM problems in the q-ROSS context. First, we propose the q-ROSS to express evaluation information. Some basic operation rules and distance measures are investigated accordingly. When the amount of data is large, the left and right endpoints of the collected interval numbers will obey symmetric normal distribution. Secondly, based on the normal distribution assumption, the collected data intervals are mapped to shadowed sets through a data processing approach. Furthermore, we extend the VIKOR model to tackle the MADM problem where the evaluation values are expressed by q-rung orthopair shadowed numbers. A location selection problem verifies the practicability of our method, and the effectiveness and superiority of the presented approach are reflected through comparative analysis.

A Novel MADM Framework under q-Rung Orthopair Fuzzy Bipolar Soft Sets

“…Keeping in view the shortcomings of the existing systems, we offer a new direction for the research in the emerging era of decision-making techniques. For other useful terminologies the readers are suggested to [31][32][33][34][35][36].…”

Integration of fuzzy-weighted zero-inconsistency and fuzzy decision by opinion score methods under a q-rung orthopair environment: A distribution case study of COVID-19 vaccine doses

“…In several cases, decision makers (DMs) have difficulty in expressing a specific preference and precise evaluation values accurately when case studies rely on unreliable, ambiguous or incomplete information [41] , [42] , [43] , [44] , [45] , [46] , [47] , [48] , [49] . Presuming that the preferences of alternatives to qualities articulated by DMs or experts are precise is unrealistic because of the complications of objectivity and vagueness of human reasoning [50] [94-101]. Hence, conducting an optimal decision process is an extremely difficult task for DMs.…”

“…The concept of IFSs takes into account the expression of membership (µ) and non-membership (υ) degrees, and thus the selection of support the MCDM problems are involved. However, this fuzzy set has disadvantages in the context of decision-making information description, and these disadvantages impose restrictions on the representation of membership and non-membership grades, making the sum of the two parameters lower than or equal to 1 [50] . Owing to the limitations of IFSs, researchers have developed a more comprehensive fuzzy set, called the PFS.…”

“…When q=2, the q-ROFS becomes PFSs ( Figure 1 concludes the relationship amongst IFSs, PFSs and q-ROFS).

Figure 1 Concept Relationship between IFSs, PFSs and q-ROFS [50]

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“…Accordingly [63] measured the q-rung orthopair hesitant fuzzy sets)q-ROHFSs(and the properties related to the distance and similarity measures of q-ROHFSs, and the axiomatised definition and formula for the entropy of q-ROHFSs. Moreover, a q-rung orthopair shadowed set was suggested to represent attribute values and extends the vlsekriterijumska optimizcija i kaompromisno resenje (VIKOR) [50] . The authors in [64] introduced the hybrid concept of q-rung orthopair m-polar fuzzy set (qROmPFS) and developed a robust MCDM approach where several uncertainties are measured by the proposed concept.…”