Abstract
The linear Diophantine fuzzy set (LDFS) has been proved to be an efficient tool in expressing decision maker (DM) evaluation values in multicriteria decision-making (MCDM) procedure. To more effectively represent DMs’ evaluation information in complicated MCDM process, this paper proposes a MCDM method based on proposed novel aggregation operators (AOs) under linear Diophantine fuzzy set (LDFS). A q -Rung orthopair fuzzy set ( q -ROFS), Pythagorean fuzzy set (PFS), and intuitionistic fuzzy set (IFS) are rudimentary concepts in computational intelligence, which have diverse applications in modeling uncertainty and MCDM. Unfortunately, these theories have their own limitations related to the membership and nonmembership grades. The linear Diophantine fuzzy set (LDFS) is a new approach towards uncertainty which has the ability to relax the strict constraints of IFS, PFS, and q –ROFS by considering reference/control parameters. LDFS provides an appropriate way to the decision experts (DEs) in order to deal with vague and uncertain information in a comprehensive way. Under these environments, we introduce several AOs named as linear Diophantine fuzzy Einstein weighted averaging (LDFEWA) operator, linear Diophantine fuzzy Einstein ordered weighted averaging (LDFEOWA) operator, linear Diophantine fuzzy Einstein weighted geometric (LDFEWG) operator, and linear Diophantine fuzzy Einstein ordered weighted geometric (LDFEOWG) operator. We investigate certain characteristics and operational laws with some illustrations. Ultimately, an innovative approach for MCDM under the linear Diophantine fuzzy information is examined by implementing suggested aggregation operators. A useful example related to a country’s national health administration (NHA) to create a fully developed postacute care (PAC) model network for the health recovery of patients suffering from cerebrovascular diseases (CVDs) is exhibited to specify the practicability and efficacy of the intended approach.
Highlights
Introduction and LiteratureReview e problem of vague and misleading information has become a major issue for decades
linear Diophantine fuzzy set (LDFS) is a new approach towards uncertainty and vagueness which is superior to existing approaches of intuitionistic fuzzy sets (IFSs), Pythagorean fuzzy set (PFS), and q-rung orthopair fuzzy set (q-ROFS). e eminent characteristic of LDFS is that against each satisfaction and dissatisfaction degrees, there exists a pair of reference or control parameters, so the valuation area of theoretical knowledge they can describe is superior
Multi-criteria decision-making (MCDM) is an important real decision problem, and its most basic and most important research direction is how to express these uncertain information. e IFSs, PFSs, and q-ROFSs are all a good way to deal with fuzzy information
Summary
We recall certain rudiments of LDFSs, some of its operations, and score functions. roughout the study, we utilize Q as a universal set. Where σD(⌣η), ρD(⌣η), αD(⌣η), βD(⌣η) ∈ [0, 1] are the membership grade (MG), the nonmembership grade (NMG), and the corresponding reference parameters, respectively, which satisfy the basic conditions:. αΛ , βΛ satisfying the following conditions: (1) σΛ , ρΛ , αΛ , βΛ ∈ [0, 1] (2) 0 ≤ αΛ + βΛ ≤ 1 (3) 0 ≤ αΛ σΛ + βΛ ρΛ ≤ 1 It considers membership grades (MGs), but it does not consider nonmembership grades (NMGs). Sum of product of satisfaction and dissatisfaction grades with their corresponding reference parameters equal to one Figure 1: Comparison view of IFNs, PFFNs, q-ROFNs, and LDFNs. Example 1 (reimbursement cases for medical treatment). Let Λ σΛ , ρΛ , αΛ , βΛ be a LDFN; we denote the score function of LDFN as I(Λ ), and we define it by. (i) ∪ i∈ΔΛ i (supi∈Δσi, inf i∈Δρi, supi∈Δαi, inf i∈Δβi) (ii) ∩ i∈ΔΛ i (inf i∈Δσi, supi∈Δρi, inf i∈Δαi, supi∈Δβi)
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