An MAGDM approach with q‐rung orthopair trapezoidal fuzzy information for waste disposal site selection problem

Abstract

This paper extends q ‐rung orthopair fuzzy numbers into q ‐rung orthopair trapezoidal fuzzy numbers to solve a multiattribute group decision‐making problem. The decision‐makers (DMs) provide some of their assessments in hesitant form, along with hesitancy weights. The basic operations laws, Hamming distance, weighted similarity measure, value and ambiguity indexes, weighted average aggregation operator, and weighted geometric aggregation operator, with their properties, are discussed for these extended fuzzy numbers. The value and ambiguity indexes are used in the Shannon entropy to evaluate the weights of the DMs and attributes'. These weights are then used to aggregate the DMs' assessments in the TOPSIS approach to obtain a weighted similarity measure from both the alternatives' positive and negative ideal solutions. The proposed approach's effectiveness is demonstrated by solving a waste disposal site selection problem. The approach is further validated through the basic properties of multiattribute decision making, comparative analyses, and comparing simulation results with an existing approach.

Development of q-Rung Orthopair Trapezoidal Fuzzy Einstein Aggregation Operators and Their Application in MCGDM Problems

“…It is worth noting that operational regulations play a crucial role in data integration. Gupta et al (2021) proposed the basic operations laws and defined WA and WG AOs for q-ROTrFNs and moreover developed a TOPSIS approach for solving the MAGDM problem. As an alternative to algebraic sum and product, Einstein-based t-norm and t-conorm provide the best approximation for sum and product of q-ROTrFNs.…”

“…Several basic principles that will be used throughout the article are briefly reviewed in this section. In order to better understand this paper, we will introduce some basic and useful concepts of q-ROFSs (Yager, 2016), q-ROTrFN (Gupta et al, 2021), and Einstein operations (Klement et al, 2004) in this section.…”

“…If the alternative's uncertainty is expressed as an interval, TrFN is the best choice for representing it. Gupta et al (2021) presented the notion of q-rung orthopair TrFNs (q-ROTrFNs), which was inspired by the ideas of q-ROFS (Yager, 2016) and TrFN (Jianqiang & Zhong, 2009). For q-ROTrFNs, established a novel ranking algorithm and Hamming distance measure.…”

New entropy propositions for interval‐valued spherical fuzzy sets and their usage in an extension of ARAS (ARAS‐IVSFS)

“…After him, fuzzy sets have been expanded into various environments possessing different properties: rough sets (Pawlak, 1982), intuitionistic fuzzy sets (Atanassov, 1986), soft sets (Molodtsov, 1999), bipolar valued fuzzy sets (Lee, 2000), bipolar soft sets (Mahmood, 2020), and linear diophantine fuzzy sets (Riaz & Hashmi, 2019), etc. Since all the mentioned set definitions have significant advantages and potentials, they are currently found suitable for being considered as a mathematical tool in the quantitative decision‐making field, such as Akram et al (2021), Atef et al (2021), Jeevaraj (2021), Gupta et al (2021), Riaz et al (2021), Zhang et al (2021), and so on. Intuitionistic, q ‐rung orthopair fuzzy sets and neutrosophic sets may be grouped in a family called three‐dimensional (3D) fuzzy sets because they are able to demonstrate the vagueness more extensively via involving three independent fuzziness degrees: membership, non‐membership, and hesitancy.…”

“…considered as a mathematical tool in the quantitative decision-making field, such as Akram et al (2021), Atef et al (2021), Jeevaraj (2021), Gupta et al (2021), Riaz et al (2021), Zhang et al (2021), and so on. Intuitionistic, q-rung orthopair fuzzy sets and neutrosophic sets may be grouped in a family called three-dimensional (3D) fuzzy sets because they are able to demonstrate the vagueness more extensively via involving three independent fuzziness degrees: membership, non-membership, and hesitancy.…”