Pythagorean Picture Fuzzy Sets, Part 1- basic notions

Cường, Bùi Công

doi:10.15625/1813-9663/35/4/13898

Cited by 10 publications

(10 citation statements)

References 24 publications

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“…To deal with ambiguity or inconsistency, the IFS frame seems to be a narrow version, for instance, when an expert delivers data in the form of yes, abstain, and no. Cuong [14] proposed the concept of a picture fuzzy set (PFS), which deals with three-dimensional information utilizing a degree of abstention, as well as membership and non-membership degrees, in order to survive in such a scenario. For these degrees, the well-known PFS has a severe requirement: the total must be less than or equal to 1.…”

Section: Introductionmentioning

confidence: 99%

A novel multi-criteria group decision-making method based on Aczel–Alsina spherical fuzzy aggregation operators: Application to evaluation of solar energy cells

Naeem

Ali

2022

Phys. Scr.

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Keeping in view the significance of spherical fuzzy set (SFS), this research focuses on innovative multi-criteria group decision-making (MCGDM) technique for coping with spherical fuzzy scenarios. To serve this purpose, we explore Aczel–Alsina spherical fuzzy operational laws and their desirable characteristics. Based on these new operational laws, we expound various aggregation operators, namely Aszel-Alsina spherical fuzzy weighted averaging (AASFWA) operator, Aczel–Alsina spherical fuzzy ordered weighted averaging (AASFOWA) operator, Aczel–Alsina spherical fuzzy hybrid averaging (AASFHA) operator, Aczel-Alsina spherical fuzzy weighted geometric (AASFWG) operator, Aczel–Alsina spherical fuzzy ordered weighted geometric (AAS-FOWG) operator, and Aczel–Alsina spherical fuzzy hybrid geometric (AASFHG) operator. Besides, some fundamental results of the newly devised aggregation operators are outlined and verified. In reliance on the propound operators, a step-wise MCGDM method is endowed, and then a case study is given to illustrate the practicality of the presented approach. Additionally, detailed parameter analysis and a systematic comparative study are carried out to verify the stability and validity of the explored works.

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Section: Introductionmentioning

confidence: 99%

A novel multi-criteria group decision-making method based on Aczel–Alsina spherical fuzzy aggregation operators: Application to evaluation of solar energy cells

Naeem

Ali

2022

Phys. Scr.

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“…Definition 1.2. [17,19] A Pythagorean picture fuzzy set (PPFS) A on a universe U is an object of the form A = {(u, x 1A (u), x 2A (u), x 3A (u)) |u ∈ U } , where x 1A (u), x 2A (u), x 3A (u) are respectively called the degree of positive membership, the degree of neutral membership, the degree of negative membership of u in A, and the following conditions are satisfied 0…”

Section: Pythagorean Picture Fuzzy Setsmentioning

confidence: 99%

“…Picture fuzzy t-norms are direct extensions of the fuzzy t-norms in [2,5,6] and of the intuitionistic fuzzy t-norms in [4]. Some simple t-norms and t-conorms were firstly given in [17].…”

Section: Picture T-norms and T-conorms On Ppfsmentioning

confidence: 99%

“…The basic notions of the picture fuzzy sets theory were given in [9-11, 34, 35]. The connectives in picture fuzzy logic were also presented in [8] that supported to new computing procedures in computational intelligence and in other applications (see [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]).…”

Section: Introductionmentioning

confidence: 99%

“…

Pythagorean picture fuzzy set (PPFS) is a combination of Picture Fuzzy Set and the Yager's Pythagorean Fuzzy Set [12][13][14]. In the first part of the paper [17] we introduced some basic notions namely the set operators on PPFS. The missing part in our previous work is defining the extension of such the operators on the Spherical Fuzzy Sets toward applications of multiattribute group decision making problems.

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confidence: 99%

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Pythagorean Picture Fuzzy Sets(ppfs), Part 2- Some Main Picture Logic Operators on PPFS and Some Picture Inference Processes in PPF Systems

Cường

2022

JCC

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Pythagorean picture fuzzy set (PPFS) - is a combination of Picture fuzzy set with the Yager’s Pythagorean fuzzy set [12-14]. In the first part of the paper [17] we considered basic notions on PPFS as set operators of PPFS. Unfortunately, we have not papers [18,19, 20] about spherical fuzzy sets with the same definition with some operators and applications to multi attribute group decision making problems. Now in the second part, we will present some main operators in picture fuzzy logic on PPFS: picture negation operator, picture t-norm, picture t-conorm, picture implication operators on PPFS. Last, the compositional rule of inference in PPFS setting should be presented and an numerical example was given.

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Pythagorean Fuzzy Set for Enhancement of Low Contrast Mammogram Images

Chaira,

Sarkar

2024

Int J Imaging Syst Tech

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Breast masses are often one of the primary signs of breast cancer, and precise segmentation of these masses is essential for accurate diagnosis and treatment planning. Diagnosis may be complex depending on the size and visibility of the mass. When the mass is not visible clearly, precise segmentation becomes very difficult and in that case enhancement is essential. Inadequate compression, patient movement, or paddle/breast movement during the exposure process might cause hazy mammogram images. Without enhancement, accurate segmentation and detection cannot be done. As there exists uncertainties in different regions, reducing uncertainty is still a main problem and so fuzzy methods may deal these uncertainties in a better way. Though there are many fuzzy and advanced fuzzy methods, we consider Pythagorean fuzzy set as one of the fuzzy sets that may be powerful to deal with uncertainty. This research proposes a new Pythagorean fuzzy methodology for mammography image enhancement. The image is first transformed into a fuzzy image, and the nonmembership function is then calculated using a newly created Pythagorean fuzzy generator. Membership function of Pythagorean fuzzy image is computed from nonmembership function. The plot between the membership value and the hesitation degree is used to calculate a constant term in the membership function. Next, an enhanced image is obtained by applying fuzzy intensification operator to the Pythagorean fuzzy image. The proposed method is compared qualitatively and quantitatively with those of non‐fuzzy, intuitionistic fuzzy, Type 2 fuzzy, and Pythagorean fuzzy methods, it is found that the suggested method outperforms the other methods. To show the usefulness of the proposed enhanced method, segmentation is carried out on the enhanced images.

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Pythagorean Picture Fuzzy Sets, Part 1- basic notions

Cited by 10 publications

References 24 publications

A novel multi-criteria group decision-making method based on Aczel–Alsina spherical fuzzy aggregation operators: Application to evaluation of solar energy cells

A novel multi-criteria group decision-making method based on Aczel–Alsina spherical fuzzy aggregation operators: Application to evaluation of solar energy cells

Pythagorean Picture Fuzzy Sets(ppfs), Part 2- Some Main Picture Logic Operators on PPFS and Some Picture Inference Processes in PPF Systems

Pythagorean Fuzzy Set for Enhancement of Low Contrast Mammogram Images

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