Abstract
The Picture fuzzy linguistic set (PFLS) is an extension of the intuitionistic fuzzy set (IFS) and linguistic variables (LVs), which has been applied successfully in the process of decision making. Considering the lack of closeness of extant PFLS operations and the interrelationship among input attributes do not consider. In this paper, for the sake of addressing those limitations, we firstly redefine some novel operational laws for PFLS by introducing linguistic scale functions and the related properties are studied. Then, a novel score function and accuracy function are also defined to compare PFLSs. Subsequently, in consideration of the superiority of the Muirhead Mean (MM) operator in capturing the interaction relationship between the input parameters, we extend the MM operator to the Picture fuzzy linguistic context and then propose Picture fuzzy linguistic weighted MM operator and its dual form in a new light. After that, these operators have adopted to build two novel models to solve multiple attribute decision-making (MADM) problems. Finally, a practical example for the selection of the innovative “Mobike” sharing bike design is provided to illustrate the practicality and effectiveness of proposed approaches.
Highlights
Decision making (DM) is a common activity in our daily life
Take the multiple attribute decision-making (MADM) problem of the research sexual treatment plan for COVID-19 patients Si et al (2021) as an example, suppose that S = {s0, s1, ..., s6} be a linguistic term set (LTS), H1= s3, 0.3, 0.2, 0.5 and H2= s5, 0.2, 0.4, 0.3 are two Picture fuzzy linguistic set (PFLS), by the operational rules given by Ashraf et al (2018), we can obtain the result of H1 ⊕ H2 is s8, 0.44, 0.08, 0.15, obviously, the linguistic term part beyond the upper bound of redefined S
Committed to solving the above problems, in this article, some Picture fuzzy linguistic variable (PFLV) operating rules are re-improved by introducing linguistic scale functions (LSFs), and a novel score function and accuracy function are proposed
Summary
Decision making (DM) is a common activity in our daily life. Owing to the DM problems are usually uncertain and fuzzy, it is difficult for decision makers (DMs) to depict the attribute values as real numbers. Ashraf et al (2018) proposed the concept of picture fuzzy linguistic set on the basis of PFS and LTs to describe the complex cognitive information, and the corresponding operational laws of PFLS are defined. Take the MADM problem of the research sexual treatment plan for COVID-19 patients Si et al (2021) as an example, suppose that S = {s0, s1, ..., s6} be a LTS, H1= s3, 0.3, 0.2, 0.5 and H2= s5, 0.2, 0.4, 0.3 are two PFLSs, by the operational rules given by Ashraf et al (2018), we can obtain the result of H1 ⊕ H2 is s8, 0.44, 0.08, 0.15 , obviously, the linguistic term part beyond the upper bound of redefined S. Cuong and Kreinovich (2014) defined some basic logical operations of PFN, which are shown as follows:
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