Pythagorean fuzzy full implication multiple I method and corresponding applications

2021 ◽  
pp. 1-15
Author(s):  
TaiBen Nan ◽  
Haidong Zhang ◽  
Yanping He
Keyword(s):  
Decision Making ◽  
Modus Ponens ◽  
Pythagorean Fuzzy Set ◽  
Implication Operator ◽  
Continuity Properties ◽  
Fuzzy Implication ◽  
Decision Making Problem ◽  
Fuzzy Implication Operator ◽  
Degree Of Similarity ◽  
Fuzzy Modus Ponens

The overwhelming majority of existing decision-making methods combined with the Pythagorean fuzzy set (PFS) are based on aggregation operators, and their logical foundation is imperfect. Therefore, we attempt to establish two decision-making methods based on the Pythagorean fuzzy multiple I method. This paper is devoted to the discussion of the full implication multiple I method based on the PFS. We first propose the concepts of Pythagorean t-norm, Pythagorean t-conorm, residual Pythagorean fuzzy implication operator (RPFIO), Pythagorean fuzzy biresiduum, and the degree of similarity between PFSs based on the Pythagorean fuzzy biresiduum. In addition, the full implication multiple I method for Pythagorean fuzzy modus ponens (PFMP) is established, and the reversibility and continuity properties of the full implication multiple I method of PFMP are analyzed. Finally, a practical problem is discussed to demonstrate the effectiveness of the Pythagorean fuzzy full implication multiple I method in a decision-making problem. The advantages of the new method over existing methods are also explained. Overall, the proposed methods are based on logical reasoning, so they can more accurately and completely express decision information.

scholarly journals Influence of the fuzzy implication operator on the method-of-cases inference rule

1990 ◽  
Vol 4 (4) ◽  
pp. 307-318 ◽  
Author(s):  
Ruan Da ◽  
E.E. Kerre ◽  
G. De Cooman ◽  
B. Cappelle ◽  
F. Vanmassenhove
Keyword(s):  
Inference Rule ◽  
Implication Operator ◽  
Fuzzy Implication ◽  
Fuzzy Implication Operator ◽  
Method Of Cases

scholarly journals MOORA under Pythagorean Fuzzy Set for Multiple Criteria Decision Making

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Luis Pérez-Domínguez ◽  
Luis Alberto Rodríguez-Picón ◽  
Alejandro Alvarado-Iniesta ◽  
David Luviano Cruz ◽  
Zeshui Xu
Keyword(s):  
Decision Making ◽  
Multiobjective Optimization ◽  
Fuzzy Set ◽  
Multiple Criteria Decision Making ◽  
Multiple Criteria ◽  
Decision Makers ◽  
Ratio Analysis ◽  
Pythagorean Fuzzy Set ◽  
Decision Making Problem ◽  
Moora Method

The multiobjective optimization on the basis of ratio analysis (MOORA) method captures diverse features such as the criteria and alternatives of appraising a multiple criteria decision-making (MCDM) problem. At the same time, the multiple criteria problem includes a set of decision makers with diverse expertise and preferences. In fact, the literature lists numerous approaches to aid in this problematic task of choosing the best alternative. Nevertheless, in the MCDM field, there is a challenge regarding intangible information which is commonly involved in multiple criteria decision-making problem; hence, it is substantial in order to advance beyond the research related to this field. Thus, the objective of this paper is to present a fused method between multiobjective optimization on the basis of ratio analysis and Pythagorean fuzzy sets for the choice of an alternative. Besides, multiobjective optimization on the basis of ratio analysis is utilized to choose the best alternatives. Finally, two decision-making problems are applied to illustrate the feasibility and practicality of the proposed method.

PYTHAGOREAN FUZZY MULTI SET AND ITS APPLICATIONS IN FISH FEED FOR INDIAN MAJOR CARP

2020 ◽  
Vol 9 (11) ◽  
pp. 9803-9811
Author(s):  
R. Sophia Porchelvi ◽  
V. Jayapriya
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Fish Feed ◽  
Uncertain Environments ◽  
Pythagorean Fuzzy Set ◽  
Indian Major Carp ◽  
Set Operations ◽  
Basic Set ◽  
Decision Making Problem ◽  
Exponential Distance

Pythagorean fuzzy set is an extension of Intutionistic fuzzy set, which is more capable of expressing and handling the uncertainty under uncertain environments, so that it was broadly applied in various fields. In this paper, we explored the concept of Pythagorean fuzzy multi set (PFMS). We describe some basic set operations of Pythagorean fuzzy multi set and also, we proposed sine exponential distance function. Finally, through an illustrative example it is shown how the proposed distance works in decision-making problem.

scholarly journals Pythagorean Fuzzy (R,S)-Norm Information Measure for Multicriteria Decision-Making Problem

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Abhishek Guleria ◽  
Rakesh Kumar Bajaj
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Multicriteria Decision Making ◽  
Information Measure ◽  
Present Communication ◽  
Pythagorean Fuzzy Set ◽  
Numerical Examples ◽  
Multicriteria Decision ◽  
Decision Making Problem ◽  
Future Work

In the present communication, a parametric (R, S)-norm information measure for the Pythagorean fuzzy set has been proposed with the proof of its validity. The monotonic behavior and maximality feature of the proposed information measure have been studied and presented. Further, an algorithm for solving the multicriteria decision-making problem with the help of the proposed information measure has been provided keeping in view of the different cases for weight criteria, when weights are unknown and other when weights are partially known. Numerical examples for each of the case have been successfully illustrated. Finally, the work has been concluded by providing the scope for future work.

scholarly journals Lukasiewicz Fuzzy Implication Operator on Pythagorean Fuzzy Tautological Matrices

2021 ◽  
Vol 9 (6) ◽  
pp. 01-05
Author(s):  
Venkatesan Dhanan
Keyword(s):  
Implication Operator ◽  
Fuzzy Implication ◽  
Fuzzy Implication Operator

In this paper, introduced Pythagorean fuzzy tautologial matrices and Pythagorean fuzzy cotautological matrices and some properties of Lukasiwicz implication operator over Pythagorean fuzzy tautologial matrices and Pythagorean fuzzy cotautological matrices are discussed. Also discussed the relation between implication with Lukasiewicz disjunction and conjunction operations of PFCMs and PFCTMs.

scholarly journals Una comparación entre el método MOORA y CODAS bajo ambiente de Conjunto Pitagoreano Difuso

2019 ◽  
pp. 9-19
Author(s):  
Abbi Azalia Flores-Ruvalcaba ◽  
Luis Pérez-Domínguez ◽  
Luz Angélica García-Villalba ◽  
Sara Almeraz-Durán
Keyword(s):  
Decision Making ◽  
Fuzzy Logic ◽  
Comparative Analysis ◽  
Illustrative Case ◽  
Multi Criteria Decision Making ◽  
Qualitative Information ◽  
Pythagorean Fuzzy Set ◽  
Decision Making Capacity ◽  
Decision Making Problem ◽  
Selection Of

Multi-criteria decision-making methods (MCDM) have accelerated in recent years. Many authors have made remarkable manipulation of the uncertainty involved in MCDM problems as a constant to make the most appropriate decision among the alternatives proposed. For this reason, fuzzy logic has been integrated into the MCDM, achieving new hybrid methodologies. These have managed to increase decision-making capacity, allowing us to manipulate nonfuzzy (quantitative) and fuzzy (qualitative) information. The main of this paper presents the comparative analysis of the Pythagorean Fuzzy CODAS method in order to examine the advantages and differences in comparison to MOORA Pythagorean Fuzzy Set method. The analysis, in this sense, aims to present a new scenario for the selection of the best decision-making problem, taking its advantages and thus achieve a greater benefit in real problems applications. An illustrative case will be presented with the MOORA-PFS methodology, to see the results obtained with Pythagorean Fuzzy CODAS. Besides, this comparative study to academics to choose more operative methods for solve MCDM problems.

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