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.

Interaction aggregation operators to solve multi criteria decision making problem under pythagorean fuzzy soft environment

2021 ◽  
pp. 1-21
Author(s):  
Rana Muhammad Zulqarnain ◽  
Xiao Long Xin ◽  
Harish Garg ◽  
Rifaqat Ali
Keyword(s):  
Decision Making ◽  
Weighted Average ◽  
Aggregation Operators ◽  
Soft Set ◽  
Multi Criteria Decision Making ◽  
Fuzzy Soft Set ◽  
Pythagorean Fuzzy Set ◽  
Operational Laws ◽  
Decision Making Problem ◽  
Soft Interaction

In this article, we investigate the multi-criteria decision-making complications under Pythagorean fuzzy soft information. The Pythagorean fuzzy soft set (PFSS) is a proper extension of the Pythagorean fuzzy set (PFS) which discusses the parametrization of the attributes of alternatives. It is also a generalization of the intuitionistic fuzzy soft set (IFSS). The PFSS is used to precisely evaluate the deficiencies, anxiety, and hesitation in decision-making (DM). The most essential determination of the current study is to advance some operational laws along with aggregation operators (AOs) within the Pythagorean fuzzy soft environs such as Pythagorean fuzzy soft interaction weighted average (PFSIWA) and Pythagorean fuzzy soft interaction weighted geometric (PFSIWG) operators with their desirable features. Furthermore, a DM technique has been established based on the developed operators to solve multi-criteria decision-making (MCDM) problems. Moreover, an application of the projected method is presented for the selection of an effective hand sanitizer during the COVID-19 pandemic. A comparative analysis with the merits, effectivity, tractability, along with some available research deduces the effectiveness of this approach.

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