No abstract

The spherical fuzzy set (SFS) concept and its interval-valued version (IVSFS) are among the recent developments aiming at handling the hesitancy representation issue in multiple attribute decision-making problems. In SFS, decision-makers can assign independent membership, non-membership, and hesitancy degrees. IVSFS extends this feature by assigning intervals to these three degrees. In this manner, the uncertainty, vagueness, and ambiguity hidden in human judgements can be quantified and processed more comprehensively. In multiple attribute decision-making problems, the attribute weights are not commonly known. To determine these weights, there are two families of methods: subjective and objective ones. While subjective methods need expert judgements in weighting, objective methods can reveal the weights from the current dataset. Entropy-based weighting technique is one of the well-known objective methods. In the study, two IVSFS entropy expressions are introduced, and their practicality is presented in obtaining objective weights. Then, an IVSFS extension of Additive Ratio Assessment Method is proposed and integrated with the entropy-based weighting schema. The proposition is applied in solving a 3D printer selection problem and a comparative analysis is conducted to check its robustness and validity.

In the present study, we define new 2-Fibonacci polynomials by using terms of a new family of Fibonacci numbers given in [4]. We show that there is a relationship between the coefficient of the 2-Fibonacci polynomials and Pascal's triangle. We give some identities of the 2-Fibonacci polynomials. Afterwards, we compare the polynomials with known Fibonacci polynomials. We also express 2-Fibonacci polynomials by the Fibonacci polynomials. Furthermore, we prove some theorems related to the polynomials. Also, we introduce the derivative of the 2-Fibonacci polynomials.

The literature of multiple attribute decision making (MADM) is fruitful since there are various and successful applications of different fuzzy set extensions such as intuitionistic, Pythagorean and q-Rung orthopair fuzzy sets (IFS, PFS and q-ROFS).Besides their powerful aspects, some definitional limitations are known. In order to eradicate these boundaries regarding the definitions of membership and nonmembership degrees, linear Diophantine fuzzy set (LDFS) concept has been recently emerged. By considering two parameters, LDFS extends the representation area of the previous fuzzy set definitions and provides more extensive human judgement coverage field. In this study, the first distance and entropy measures in the literature have been developed for LDFSs. Their axiomatic definitions are given, and the proofs are shown. Also, thanks to our extensive literature review, we became aware that there is no MADM extension dedicatedly proposed for LDFS. So, the first MADM method extension for LDFS environment has also been developed in this study. A very well-known MADM approach, TOPSIS, has been extended into LDFS environment for the first time in the literature. The applicability is shown in a healthcare management decision problem and the validity is checked and approved by comparing the alternative rankings LDF-TOPSIS and the aggregation operators that were obtained from the literature produced.

From the perspective of multiple attribute decision analysis, the evaluation of decision alternatives should be based on the performance scores determined with respect to more than one attribute. Fuzzy logic concepts can equip the evaluation process with different scales of linguistic terms to let the decision-makers point out their ideas and preferences. A more recent one of fuzzy sets is the picture fuzzy set which covers three separately allocable elements: positive, neutral, and negative membership degrees. The novel and distinctive element included by a picture fuzzy set is the refusal degree which is equal to the difference between 1 and the sum of the other three. In this study, we aim to contribute to the literature of the picture fuzzy sets by (i) proposing two novel entropy measures that can be used in objective attribute weighting and (ii) developing a novel picture fuzzy version of CODAS (COmbinative Distance-based ASsessment) method which is empowered with entropy-based attribute weighting. The applicability of the method is shown in a green supplier selection problem. To clarify the differences of the proposed method, a comparative analysis is provided by considering traditional CODAS, spherical fuzzy CODAS, and spherical fuzzy TOPSIS with different entropy-based scenarios.