Fermatean fuzzy sets

In this paper, we propose the concept of Fermatean fuzzy linguistic term sets based on linguistic term sets and Fermatean fuzzy sets. The basic operational laws, the score function, and the accuracy function of Fermatean fuzzy linguistic numbers are provided. Then we propose the Fermatean fuzzy linguistic weighted aggregation operator, the Fermatean fuzzy linguistic weighted geometric operator, and the Fermatean fuzzy linguistic distance measures. Furthermore, we extend the TOPSIS method to the proposed distance measures, and the ranking of alternatives is obtained under a Fermatean fuzzy linguistic environment. An example is provided to illustrate the feasibility and effectiveness of the proposed method, and a comparison with the existing method is also analyzed. Finally, the sensitivity analysis of the parameter λ in the proposed distance measure is also discussed.

“…The main advantage of FFS is that it can describe more uncertainties than IFS and PFS, which can be applied in many decision‐making problems. The relevant research can be referred to …”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fermatean fuzzy linguistic set and its application in multicriteria decision making

Liu

Chen

2018

“…The concept of Fermatean fuzzy set (FFS)

F = {⟨ x_{j}, μ_{F} (x_{j}), ν_{F} (x_{j}) ⟩ ∣ x_{j} \in X}

X = {x_{1}, x_{2}, …, x_{n}}

was first proposed by Senapati and Yager, where the membership degree

μ_{F} (x_{j})

and nonmembership degree

ν_{F} (x_{j})

are both single values between zero and one, satisfied with

0 \leq {(μ_{F} (x_{j}))}^{3} + {(ν_{F} (x_{j}))}^{3} \leq 1

. The FFS has been widely applied in many multiple‐criteria decision‐making problems due to its effectiveness and efficiency in expressing incomplete information under uncertain circumstances . The main motivation for proposing the FFS is that it can describe more uncertainty in decision‐making problems than the intuitionistic fuzzy set (IFS)

I = {⟨ x_{j}, μ_{I} (x_{j}), ν_{I} (x_{j}) ⟩ ∣ x_{j} \in X}

(

0 \leq μ_{I} (x_{j}) + ν_{I} (x_{j}) \leq 1

) and the Pythagorean fuzzy set (PFS)

P = {⟨ x_{j}, μ_{P} (x_{j}), ν_{P} (x_{j}) ⟩ ∣ x_{j} \in X}

(

0 \leq {(μ_{P} (x_{j}))}^{2} + {(ν_{P} (x_{j}))}^{2} \leq 1

).…”

Section: Introductionmentioning

confidence: 99%

Distance measure for Fermatean fuzzy linguistic term sets based on linguistic scale function: An illustration of the TODIM and TOPSIS methods

Liu

Wang

2019

In this paper, we propose the Fermatean fuzzy linguistic term set (FFLTS) based on the linguistic scale function. A new similarity measure between FFLTSs is constructed, which not only includes the linguistic scale function but also combines the cosine similarity measure and Euclidean distance measure, and then the related properties of the similarity measure are proven. A corresponding distance measure is obtained according to the relationship between the distance measure and similarity measure. Furthermore, we extend the Tomada de Decisão Interativa Multicritério (TODIM) method and the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method to the corresponding distance measure under the Fermatean fuzzy linguistic environment. The main advantages of the proposed methods are that they can not only transform linguistic information effectively in different decision environments but also improve the adaptability of FFLTS in decision-making problems.Finally, a numerical example is provided to illustrate the effectiveness and feasibility of the proposed methods, which are also compared with other existing methods. The sensitivity analysis of the parameters and the influence of linguistic scale function on the ranking results are also discussed.

“…Uncertainty is very important in many fields, which has attracted many researchers' attention . There are various models to handle uncertainty, including fuzzy sets, rough sets, Z numbers, D numbers, R numbers, intuitionistic evidence sets (IES), Two Dimension Belief Function (TDBF) and Dempster‐Shafer (D‐S) evidence theory and so on . D‐S evidence theory attract more and more attention due to it needs weaker condition than the Bayesian probability .…”

Section: Introductionmentioning

confidence: 99%

Quantum model of mass function

Gao

Deng

2019

Dempster-Shafer (D-S) evidence theory has been used in many fields due to the flexibility and effectiveness in modelling uncertainties, which is the extension of classical probability. Uncertainty principle is one of the most important principles in quantum theory, which has been used in many fields. How to set the connection between quantum theory and D-S evidence theory is also an open issue. Hence, the paper proposed the quantum model of mass function to consider the quantum theory and D-S evidence theory. In the proposed quantum method, quantum mass function uses euler formula to represent. The paper also discusses some operations based on the quantum model of the mass function. Moreover, the paper also discusses the relationship between quantum mass function and classical mass function by using some numerical examples. Classical mass function is a special case when there is no interference in quantum mass function. Similar to the other quantum models, this study provides a more wide application in quantum information. K E Y W O R D S basic probability assignment, belief function, Dempster-Shafer evidence theory, mass function, quantum theory