A New Group Decision-Making Technique under Picture Fuzzy Soft Expert Information

Abstract

As an extension of intuitionistic fuzzy sets, the theory of picture fuzzy sets not only deals with the degrees of rejection and acceptance but also considers the degree of refusal during a decision-making process; therefore, by incorporating this competency of picture fuzzy sets, the goal of this study is to propose a novel hybrid model called picture fuzzy soft expert sets by combining picture fuzzy sets with soft expert sets for dealing with uncertainties in different real-world group decision-making problems. The proposed hybrid model is a more generalized form of intuitionistic fuzzy soft expert sets. Some novel desirable properties of the proposed model, namely, subset, equality, complement, union and intersection, are investigated together with their corresponding examples. Two well-known operations AND and OR are also studied for the developed model. Further, a decision-making method supporting by an algorithmic format under the proposed approach is presented. Moreover, an illustrative application is provided for its better demonstration, which is subjected to the selection of a suitable company of virtual reality devices. Finally, a comparison of the initiated method is explored with some existing models, including intuitionistic fuzzy soft expert sets.

A Cross-Sectional Study on Mental Health of School Students during the COVID-19 Pandemic in India

“…Unlike IFS, PFS indicates the degree of refusal and brings about better accuracy and granularity in the analysis, which involves a considerable amount of subjectivity and impreciseness in the available information [41]. Due to its potential for superior analysis under uncertainty, PFS has been utilized by various researchers (e.g., [42][43][44][45][46][47][48]) in distinct situations, for multi-criteria decision making (MCDM) related problems. In the following section, we mention some of the basic definitions, operations and properties of PFS [49,50].…”

Certain Operations on Complex Picture Fuzzy Graphs

“…Shao et al [19] studied some properties of vague graph. Gulzar et al [7]- [10] worked on fuzzy group. Jana et al [11] studied picture fuzzy Dombi aggregation operators.…”

Extended Transportation Models Based on Picture Fuzzy Sets

“…Ali and Ansari [44] presented Fermatean fuzzy bipolar soft set (FFBSS) model and studied its basic properties. Tchier et al [45] combined PFSs and soft expert sets and introduced a hybrid model which is used to analyze DMPs. Das [46] defined score function to get IBFS and solved neutrosophic TPs.…”

“…x 12 � [(15,35,45, 60, 75, 95, 110, 200); (0.92, 0.02, 0.01)], 􏽥 x 11 � χ 11 , δ 11 , ϵ 11 , η 11 , κ 11 , ϑ 11 , ω 11 , ζ 11 􏼁; α 11 , β 11 , c 11 􏼁 􏼂 􏼃, 􏽥 x 12 � χ 12 , δ 12 , ϵ 12 , η 12 , κ 12 , ϑ 12 , ω 12 , ζ 12 􏼁; α 12 , β 12 , c 12 􏼁 􏼂 􏼃, 􏽥 x 13 � χ 13 , δ 13 , ϵ 13 , η 13 , κ 13 , ϑ 13 , ω 13 , ζ 13 􏼁; α 13 , β 13 , c 13 􏼁 􏼂 􏼃, 􏽥 x 21 � χ 21 , δ 21 , ϵ 21 , η 21 , κ 21 , ϑ 21 , ω 21 , ζ 21 􏼁; α 21 , β 21 , c 21 􏼁 􏼂 􏼃, 􏽥 x 22 � χ 22 , δ 22 , ϵ 22 , η 22 , κ 22 , ϑ 22 , ω 22 , ζ 22 􏼁; α 22 , β 22 , c 22 􏼁 􏼂 􏼃, 􏽥 x 23 � χ 23 , δ 23 , ϵ 23 , η 23 , κ 23 , ϑ 23 , ω 23 , ζ 23 􏼁; α 23 , β 23 , c 23 􏼁 􏼂 􏼃, 􏽥 x 31 � χ 31 , δ 31 , ϵ 31 , η 31 , κ 31 , ϑ 31 , ω 31 , ζ 31 􏼁; α 31 , β 31 , c 31 􏼁 􏼂 􏼃, 􏽥 x 32 � χ 32 , δ 32 , ϵ 32 , η 32 , κ 32 , ϑ 32 , ω 32 , ζ 32 􏼁; α 32 , β 32 , c 32 􏼁 􏼂 􏼃, 􏽥 x 33 � χ 33 , δ 33 , ϵ 33 , η 33 , κ 33 , ϑ 33 , ω 33 , ζ 33 􏼁; α 33 , β 33 , c 33 􏼁 Input data for FPFTP. χ 11 , δ 11 , ϵ 11 , η 11 , κ 11 , ϑ 11 , ω 11 , ζ 11 􏼁; α 11 , β 11 , c 11 􏼁 􏼂 􏼃⊕ [(130, 180, 220, 250, 290, 340, 370, 410); (0.8, 0.1, 0.1)] ⊗ χ 12 , δ 12 , ϵ 12 , η 12 , κ 12 , ϑ 12 , ω 12 , ζ 12 􏼁; α 12 , β 12 , c 12 􏼁 􏼂 􏼃⊕ ⊗ χ 13 , δ 13 , ϵ 13 , η 13 , κ 13 , ϑ 13 , ω 13 , ζ 13 􏼁; α 13 , β 13 , c 13 􏼁 􏼂 􏼃⊕ 21 , δ 21 , ϵ 21 , η 21 , κ 21 , ϑ 21 , ω 21 , ζ 21 􏼁; α 21 , β 21 , c 21 􏼁 􏼂 􏼃⊕ 22 , δ 22 , ϵ 22 , η 22 , κ 22 , ϑ 22 , ω 22 , ζ 22 􏼁; α 22 , β 22 , c 22 􏼁 􏼂 􏼃⊕ ⊗ χ 23 , δ 23 , ϵ 23 , η 23 , κ 23 , ϑ 23 , ω 23 , ζ 23 􏼁; α 23 , β 23 , c 23 􏼁 􏼂 􏼃⊕ ⊗ χ 31 , δ 31 , ϵ 31 , η 31 , κ 31 , ϑ 31 , ω 31 , ζ 31 􏼁; α 31 , β 31 , c 31 􏼁 􏼂 􏼃⊕ ⊗ χ 32 , δ 32 , ϵ 32 , η 32 , κ 32 , ϑ 32 , ω 32 , ζ 32 􏼁; α 32 , β 32 , c 32 􏼁 􏼂 􏼃⊕ ⊗ χ 33 , δ 33 , ϵ 33 , η 33 , κ 33 , ϑ 33 , ω 33 , ζ 33 􏼁; α 33 , β 33 , c 33 􏼁 􏼂 􏼃 ⎛…”

“…15,35,45, 60, 75, 95, 110, 200); (0.92, 0.02, 0.01)] χ 21 + χ 22 + χ 23 , δ 21 + δ 22 + δ 23 , ϵ 21 + ϵ 22 + ϵ 23 , η 21 + η 22 + η 23 , κ 21 + κ 22 + κ 23 , ϑ 21 + ϑ 22 + ϑ 23 , ω 21 + ω 22 + ω 23 , ζ 21 + ζ 22 + ζ 23 􏼠 􏼡; α 21 + α 22 − α 21 α 22 +α 23 − α 21 α 23 − α 22 α 23 +α 21 α 22 α 23 , β 21 β 22 β 23 , c 21 c 22 c 23…”