Pythagorean fuzzy sets and their variants
SUBHANKAR JANA; Anjali Patel; Juthika Mahanta
Abstract
The fuzzy set is generally used to identify the topological relationship between two vague spatial objects. Indeterminacy can arise at any point in the modelling process, and the fuzzy model is unable to deal with this. Given that the Pythagorean fuzzy is better equipped to deal with such indeterminacies ...
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The fuzzy set is generally used to identify the topological relationship between two vague spatial objects. Indeterminacy can arise at any point in the modelling process, and the fuzzy model is unable to deal with this. Given that the Pythagorean fuzzy is better equipped to deal with such indeterminacies than the fuzzy set, we advocated for the use of Pythagorean fuzzy modelling to determine the topological relation between two spatial objects. This paper contributes to the expanding study of Pythagorean fuzzy topological spaces by introducing core, fringe, outer, regular open set, regular closed set, double connectedness and homeomorphism in Pythagorean fuzzy environment. Using these definitions, the paper proposes an algebraic model, namely the Pythagorean fuzzy 9-intersection matrix, to find topological relations between any two Pythagorean fuzzy sets in a Pythagorean topological space. The inbuilt capability of Pythagorean fuzzy set to handle indeterminacy establishes the proposed model as the potential tool to find topological relations between two indeterminate spatial objects. Ample instances are discussed to nourish the existence of indeterminate spatial objects. Finally, a simple Pythagorean fuzzy region is defined and all possible relations between such two Pythagorean fuzzy regions are examined.
Fermatean fuzzy sets and their variants
Vishnu Narayan Mishra; Tarun Kumar; Mukesh Kumar Sharma; Laxmi Rathour
Abstract
This paper aims to study Pythagorean and Fermatean Fuzzy Subgroups (FFSG) in the context of -norm and -conorm functions. The paper examines the extensions of fuzzy subgroups, specifically "Pythagorean Fuzzy Subgroups (PFSG)" and "FFSG", along with their properties. In the existing literature ...
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This paper aims to study Pythagorean and Fermatean Fuzzy Subgroups (FFSG) in the context of -norm and -conorm functions. The paper examines the extensions of fuzzy subgroups, specifically "Pythagorean Fuzzy Subgroups (PFSG)" and "FFSG", along with their properties. In the existing literature on Pythagorean and FFSG, the standard properties for membership and non-membership functions are based on the "min" and "max" operations, respectively. However, in this work, we develop a theory that utilizes the -norm for "min" and the -conorm for "max", providing definitions of Pythagorean and FFSG with these functions, along with relevant examples. By incorporating this approach, we introduce multiple options for selecting the minimum and maximum values. Additionally, we prove several results related to Pythagorean and FFSG using the -norm and -conorm, and discuss important properties associated with them.
Pythagorean fuzzy sets and their variants
Amal Kumar Adak; Gaurikant Kumar
Abstract
Multiple Criteria Decision Analysis (MCDA) has been widely investigated and successfully applied to many fields,owing to its great capability of modeling the process of actual decision-making problems and establishing proper evaluation and assessment mechanisms. With the development of management and ...
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Multiple Criteria Decision Analysis (MCDA) has been widely investigated and successfully applied to many fields,owing to its great capability of modeling the process of actual decision-making problems and establishing proper evaluation and assessment mechanisms. With the development of management and economics, real-world decision-making problem are becoming diversified and complicated to an increasing extent, especially within a changeable and unpredictable enviroment. Multi-criteria is a decision-making technique that explicitly evaluates numerous contradictory criteria. TOPSIS is a well-known multi-criteria decision-making process. The goal of this research is to use TOPSIS to solve MCDM problems in a Pythagorean fuzzy environment. The distance between two Pythagorean fuzzy numbers is utilized to create the model using the spherical distance measure. To construct a ranking order of alternatives and determine the best one,the revised index approach is utilized. Finally, we look at a set of MCDM problems to show how the proposed method and approach work in practice. In addition, it shows comparative data from the relative closeness and updated index methods.
Pythagorean fuzzy sets and their variants
Tutku Tuncalı Yaman; Gonca Reyhan Akkartal
Abstract
In the decision theory, there are many useful tools for operations in logistics and Supply Chain Management (SCM). One of the vital trivets of logistics operations is warehouse management which is also one of the parts of a supply chain. Deciding on the location of a warehouse has a critical issue especially ...
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In the decision theory, there are many useful tools for operations in logistics and Supply Chain Management (SCM). One of the vital trivets of logistics operations is warehouse management which is also one of the parts of a supply chain. Deciding on the location of a warehouse has a critical issue especially during an outbreak. In this study, we aimed that to figure out differences between the perceived importance of the considered criteria in the decision process regarding warehouse location in the medical sector in terms of the changing dynamics after the Covid-19 pandemic. Pursuing this goal, the results of a preliminary study which was resulted from the gathered data of a decision-making group including industry professionals before the pandemic outbreak were accepted as an anchor to obtain a comparison with the current state. To construct a proper representation of the post-Covid state, a similar methodology was used, and similar decision-makers data were collected with the preliminary study in the identification of the importance figures and causal relationships between criteria. According to comparative results of pre-and post-Covid studies, it is found that there are significant changes in the perceived role of adjacency to target markets and customs criteria in medical warehouse location decisions. It is obvious that the results will shed light on medical sector professionals’ decision process while adapting to the current pandemic conditions.
Neutrosophic sets and their variants
R. Radha; A. Stanis Arul Mary
Abstract
A Quadripartitioned Neutrosophic Pythagorean (QNP) set is a powerful general format framework that generalizes the concept of Quadripartitioned Neutrosophic Sets and Neutrosophic Pythagorean Sets. In this paper, we apply the notion of quadripartitioned Neutrosophic Pythagorean sets to Lie algebras. We ...
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A Quadripartitioned Neutrosophic Pythagorean (QNP) set is a powerful general format framework that generalizes the concept of Quadripartitioned Neutrosophic Sets and Neutrosophic Pythagorean Sets. In this paper, we apply the notion of quadripartitioned Neutrosophic Pythagorean sets to Lie algebras. We develop the concept of QNP Lie subalgebras and QNP Lie ideals. We describe some interesting results of QNP Lie ideals.
Pythagorean fuzzy sets and their variants
J Marynirmala; D. Sivakumar
Abstract
We present the notion of Pythagorean Fuzzy Weak Bi-Ideals (PFWBI) and interval valued Pythagorean fuzzy weak bi-ideals of Γ-near-rings and studies some of its properties. We present the notion of interval valued Pythagorean fuzzy weak bi-ideal and establish some of its properties. We study interval ...
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We present the notion of Pythagorean Fuzzy Weak Bi-Ideals (PFWBI) and interval valued Pythagorean fuzzy weak bi-ideals of Γ-near-rings and studies some of its properties. We present the notion of interval valued Pythagorean fuzzy weak bi-ideal and establish some of its properties. We study interval valued Pythagorean fuzzy weak bi-ideals of Γ-near-ring using homomorphism.
Pythagorean fuzzy sets and their variants
Veerappan Chinnadurai; Arul Selvam
Abstract
In this paper, we define the new notion of interval-valued Pythagorean fuzzy ideals in semigroups and established the properties of its with suitable examples. Also, we introduce the concept of interval valued Pythagorean fuzzy sub-semigroup, interval valued Pythagorean fuzzy left (resp. right) ideal, ...
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In this paper, we define the new notion of interval-valued Pythagorean fuzzy ideals in semigroups and established the properties of its with suitable examples. Also, we introduce the concept of interval valued Pythagorean fuzzy sub-semigroup, interval valued Pythagorean fuzzy left (resp. right) ideal, interval valued Pythagorean fuzzy bi-ideal, interval valued Pythagorean fuzzy interior ideal and homomorphism of an interval valued Pythagorean fuzzy ideal in semigroups with suitable illustration. We show that every interval valued Pythagorean fuzzy left (resp. right) ideal is an interval valued Pythagorean fuzzy bi-ideal.
Pythagorean fuzzy sets and their variants
V. S. Subha; P. Dhanalakshmi
Abstract
In this paper, we expose cosine, jaccard and dice similarity measures and rough interval Pythagorean mean operator. Some of the important properties of the defined similarity measures have been established. Then the proposed methods are applied for solving multi attribute decision making problems. Finally, ...
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In this paper, we expose cosine, jaccard and dice similarity measures and rough interval Pythagorean mean operator. Some of the important properties of the defined similarity measures have been established. Then the proposed methods are applied for solving multi attribute decision making problems. Finally, a numerical example is solved to show the feasibility, applicability and effectiveness of the proposed strategies.
