168 research outputs found
Circular Pythagorean fuzzy sets and applications to multi-criteria decision making
In this paper, we introduce the concept of circular Pythagorean fuzzy set
(value) (C-PFS(V)) as a new generalization of both circular intuitionistic
fuzzy sets (C-IFSs) proposed by Atannassov and Pythagorean fuzzy sets (PFSs)
proposed by Yager. A circular Pythagorean fuzzy set is represented by a circle
that represents the membership degree and the non-membership degree and whose
center consists of non-negative real numbers and with the condition
. A C-PFS models the fuzziness of the uncertain information
more properly thanks to its structure that allows modelling the information
with points of a circle of a certain center and a radius. Therefore, a C-PFS
lets decision makers to evaluate objects in a larger and more flexible region
and thus more sensitive decisions can be made. After defining the concept of
C-PFS we define some fundamental set operations between C-PFSs and propose some
algebraic operations between C-PFVs via general -norms and -conorms. By
utilizing these algebraic operations, we introduce some weighted aggregation
operators to transform input values represented by C-PFVs to a single output
value. Then to determine the degree of similarity between C-PFVs we define a
cosine similarity measure based on radius. Furthermore, we develop a method to
transform a collection of Pythagorean fuzzy values to a PFS. Finally, a method
is given to solve multi-criteria decision making problems in circular
Pythagorean fuzzy environment and the proposed method is practiced to a problem
about selecting the best photovoltaic cell from the literature. We also study
the comparison analysis and time complexity of the proposed method
Similarity measure between Pythagorean fuzzy sets based on lower, upper and middle fuzzy sets with applications to pattern recognition and multicriteria decision making with PF-TODIM
The choice of similarity measure (SM) plays an important role in distinguishing between objects. Similarity measure of
Pythagorean fuzzy sets (PFSs) is very useful and effective in discriminating between different Pythagorean fuzzy sets. Therefore,
in this paper, we suggest a new similarity measure for PFSs based on converting the PFSs into their lower, upper and middle
fuzzy sets (FSs) to calculate their degree of similarity. We construct an axiomatic definition for a new SM of PFSs. Furthermore,
we put forward a new way to express the similarity measure of PFSs to show its competency, reliability and applicability. For
establishing reasonability and usefulness of the proposed methods, we present several practical examples related to pattern
recognition and multicriteria decision making problems. Finally, we construct an algorithm for Portuguese of interactive and
multiple attributes decision making (TODIM) method based on the proposed similarity measures, for handling complex
multicriteria decision making problems related to day to day life. Our final results show that the suggested method is reasonable,
reliable and useful in managing different complex decision making problems in the context of Pythagorean fuzzy sets as the
domain
Pythagorean 2-tuple linguistic power aggregation operators in multiple attribute decision making
In this paper, we investigate the multiple attribute decision making
problems with Pythagorean 2-tuple linguistic information.
Then, we utilize power average and power geometric operations
to develop some Pythagorean 2-tuple linguistic power aggregation
operators: Pythagorean 2-tuple linguistic power weighted
average (P2TLPWA) operator, Pythagorean 2-tuple linguistic power
weighted geometric (P2TLPWG) operator, Pythagorean 2-tuple linguistic
power ordered weighted average (P2TLPOWA) operator,
Pythagorean 2-tuple linguistic power ordered weighted geometric
(P2TLPOWG) operator, Pythagorean 2-tuple linguistic power
hybrid average (P2TLPHA) operator and Pythagorean 2-tuple linguistic
power hybrid geometric (P2TLPHG) operator. The prominent
characteristic of these proposed operators are studied. Then,
we have utilized these operators to develop some approaches to
solve the Pythagorean 2-tuple linguistic multiple attribute decision
making problems. Finally, a practical example for enterprise
resource planning (ERP) system selection is given to verify the
developed approach and to demonstrate its practicality and
effectiveness
A new outranking method for multicriteria decision making with complex Pythagorean fuzzy information
[EN]This article contributes to the advancement and evolution of outranking decision-making methodologies, with a novel essay on the ELimination and Choice Translating REality (ELECTRE) family of methods. Its primary target is to unfold the constituents and expound the implementation of the ELECTRE II method for group decision making in complex Pythagorean fuzzy framework. This results in the complex Pythagorean fuzzy ELECTRE II method. By inception, it is intrinsically superior to models using one-dimensional data. It is designed to perform the pairwise comparisons of the alternatives using the core notions of concordance, discordance and indifferent sets, which is then followed by the construction of complex Pythagorean fuzzy concordance and discordance matrices. Further, the strong and weak outranking relations are developed by the comparison of concordance and discordance indices with the concordance and discordance levels. Later, the forward, reverse and average rankings of the alternatives are computed by the dint of strong and weak outranking graphs. This methodology is supported by a case study for the selection of wastewater treatment process, and by a numerical example for the selection of the best cloud solution for a big data project. Its consistency is confirmed by an effectiveness test and comparison analysis with the Pythagorean fuzzy ELECTRE II and complex Pythagorean fuzzy ELECTRE I methodsPublicación en abierto financiada por el Consorcio de Bibliotecas Universitarias de Castilla y León (BUCLE), con cargo al Programa Operativo 2014ES16RFOP009 FEDER 2014-2020 DE CASTILLA Y LEÓN, Actuación:20007-CL - Apoyo Consorcio BUCL
Rough cubic Pythagorean fuzzy sets in semigroup
In this paper, we intend the concept of rough cubic Pythagorean fuzzy ideals in the semigroup. By using this notion, we discuss lower approximation and upper approximation of cubic Pythagorean fuzzy left (right) ideals, bi-ideals, interior ideals, and study some of their related properties in detail.Publisher's Versio
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