Research Paper
Fuzzy sets and their variants
Gia Sirbiladze
Abstract
The Ordered Weighted Averaging (OWA) operator was introduced by Yager [58] to provide a method for aggregating inputs that lie between the max and min operators. In this article several variants of the generalizations of the fuzzy-probabilistic OWA operator - POWA (introduced by Merigo [27] and ...
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The Ordered Weighted Averaging (OWA) operator was introduced by Yager [58] to provide a method for aggregating inputs that lie between the max and min operators. In this article several variants of the generalizations of the fuzzy-probabilistic OWA operator - POWA (introduced by Merigo [27] and [28]) are presented in the environment of fuzzy uncertainty, where different monotone measures (fuzzy measure) are used as an uncertainty measure. The considered monotone measures are: possibility measure, Sugeno additive measure, monotone measure associated with Belief Structure and capacity of order two. New aggregation operators are introduced: AsPOWA and SA-AsPOWA. Some properties of new aggregation operators are proved. Concrete faces of new operators are presented with respect to different monotone measures and mean operators. Concrete operators are induced by the Monotone Expectation (Choquet integral) or Fuzzy Expected Value (Sugeno integral) and the Associated Probability Class (APC) of a monotone measure. For the new operators the information measures–Orness, Entropy, Divergence and Balance are introduced as some extensions of the definitions presented in [28].
Research Paper
Fuzzy sets and their variants
Gia Sirbiladze
Abstract
The Ordered Weighted Averaging (OWA) operator was introduced by R.R. Yager [34] to provide a method for aggregating inputs that lie between the max and min operators. In this article we continue to present some extensions of OWA-type aggregation operators. Several variants of the generalizations of the ...
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The Ordered Weighted Averaging (OWA) operator was introduced by R.R. Yager [34] to provide a method for aggregating inputs that lie between the max and min operators. In this article we continue to present some extensions of OWA-type aggregation operators. Several variants of the generalizations of the fuzzy-probabilistic OWA operator - FPOWA (introduced by J.M. Merigo [13,14]) are presented in the environment of fuzzy uncertainty, where different monotone measures (fuzzy measure) are used as uncertainty measures. The considered monotone measures are: possibility measure, Sugeno additive measure, monotone measure associated with Belief Structure and Choquet capacity of order two. New aggregation operators are introduced: AsFPOWA and SA-AsFPOWA. Some properties of new aggregation operators and their information measures are proved. Concrete faces of new operators are presented with respect to different monotone measures and mean operators. Concrete operators are induced by the Monotone Expectation (Choquet integral) or Fuzzy Expected Value (Sugeno integral) and the Associated Probability Class (APC) of a monotone measure. New aggregation operators belong to the Information Structure I6 (see Part I, section 3). For the illustration of new constructions of AsFPOWA and SA-AsFPOWA operators an example of a fuzzy decision-making problem regarding the political management with possibility uncertainty is considered. Several aggregation operators (“classic” and new operators) are used for the comparing of the results of decision making.
Research Paper
Neutrosophic sets and their variants
Athanase Polymenis
Abstract
Neutrosophic statistics are used when one is dealing with imprecise and indeterminate data or parameters. In the present paper we propose a method for performing a neutrosophic Student’s t –type of statistical test that concerns the population mean when data arise from an autoregressive process ...
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Neutrosophic statistics are used when one is dealing with imprecise and indeterminate data or parameters. In the present paper we propose a method for performing a neutrosophic Student’s t –type of statistical test that concerns the population mean when data arise from an autoregressive process of order 1 (AR(1)). In classical statistics data obtained through this process are not independent when the autocorrelation coefficient of the process is not equal to 0, and hence the usual Student’s t distribution is inadequate for inferring about the population mean; however a result obtained in earlier literature states that a Student’s t –type of statistic, which is asymptotically normally distributed, can be used instead. Our method is based on the neutrosophic version of this result and it is implemented using simulated data.
Research Paper
Spherical fuzzy sets
PRINCY R; K Mohana
Abstract
In this paper, we investigate the multiple attribute decision making problems with spherical fuzzy information. The advantage of spherical fuzzy set is easily reflecting the ambiguous nature of subjective judgments because the spherical fuzzy sets are suitable for capturing imprecise, uncertain and inconsistent ...
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In this paper, we investigate the multiple attribute decision making problems with spherical fuzzy information. The advantage of spherical fuzzy set is easily reflecting the ambiguous nature of subjective judgments because the spherical fuzzy sets are suitable for capturing imprecise, uncertain and inconsistent information in the multiple attribute decision making analysis. Thus, the cross- entropy of spherical fuzzy sets called, spherical fuzzy cross-entropy, is proposed as an extension of the cross-entropy of fuzzy sets. Then, a multiple attribute decision making method based on the proposed spherical fuzzy cross entropy is established in which attribute values for alternatives are spherical fuzzy numbers. In decision making process, we utilize the spherical fuzzy weighted cross entropy between the ideal alternative and an alternative to rank the alternatives corresponding to the cross entropy values and to select the most desirable one(s). Finally, a practical example for enterprise resource planning system selection is given to verify the developed approach and to demonstrate its practicality and effectiveness.
Research Paper
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.
Research Paper
Intuitionistic fuzzy sets and their variants
Jaydip Bhattacharya
Abstract
An operator is a special symbol for performing a specific function. Several operators like modal operators, topological operators, level operators, etc. have been defined over intuitionistic fuzzy sets. At the same time, so many operations were introduced and studied. The key objective of this paper ...
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An operator is a special symbol for performing a specific function. Several operators like modal operators, topological operators, level operators, etc. have been defined over intuitionistic fuzzy sets. At the same time, so many operations were introduced and studied. The key objective of this paper is to study those operations over intuitionistic fuzzy sets and to investigate their properties. Some new results are obtained and proved.
Research Paper
Plithogenic sets and their variants
Nivetha Martin; Florentin Smarandache; R Priya
Abstract
The theory of Plithogeny is gaining momentum in recent times as it generalizes the concepts of fuzzy, intuitionistic, neutrosophy and other extended representations of fuzzy sets. The relativity of the comprehensive and accommodative nature of plithogenic sets in dealing with attributes shall be applied ...
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The theory of Plithogeny is gaining momentum in recent times as it generalizes the concepts of fuzzy, intuitionistic, neutrosophy and other extended representations of fuzzy sets. The relativity of the comprehensive and accommodative nature of plithogenic sets in dealing with attributes shall be applied to handle the decision–making problems in the field of sociology. This paper introduces the concepts of Plithogenic Sociogram (PS) and Plithogenic Number (PN) where the former is the integration of plithogeny to the sociometric technique of sociogram and the latter is the generalization of fuzzy, intuitionistic and neutrosophic numbers that shall be used in representations of preferences in group dynamics. This research work outlines the conceptual development of these two newly proposed concepts and discusses the merits of the existing theory of similar kind with suitable substantiation. The plithogenic sociogram model encompassing the attributive preferences with plithogenic number representation is also developed to explicate how it can be materialized in the real social field. A conjectural illustration is put forth to analyze the efficiency and the feasibility of the proposed plithogenic sociogram model and its function in decision-making. This paper also throws light on generalized plithogenic number, dominant attribute constrained plithogenic number and combined dominant attribute constrained plithogenic number together with its operations and suitable illustrations.
Review Paper
Soft sets and their variants
Mujahid Abbas; Yanhui Guo; Ghulam Murtaza
Abstract
The aim of this paper is to investigate different definitions of soft points in the existing literature on soft set theory and its extensions in different directions. Then limitations of these definitions are illustrated with the help of examples. Moreover, the definition of soft point in the setup of ...
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The aim of this paper is to investigate different definitions of soft points in the existing literature on soft set theory and its extensions in different directions. Then limitations of these definitions are illustrated with the help of examples. Moreover, the definition of soft point in the setup of fuzzy soft set, intervalvalued fuzzy soft set, hesitant fuzzy soft set and intuitionistic soft set are also discussed. We also suggest an approach to unify the definitions of soft point which is more applicable than the existing notions.
Research Paper
Fuzzy sets and their variants
Shaveta Arora; Renu Vadhera; Bharti Chugh
Abstract
COVID-19, an epidemic disease, has challenged human lives all over the world. Governments and scientific communities are trying their level best to help the masses. This disease which is caused by corona virus majorly attacks the upper respiratory system rendering the human immunity incapacitated and, ...
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COVID-19, an epidemic disease, has challenged human lives all over the world. Governments and scientific communities are trying their level best to help the masses. This disease which is caused by corona virus majorly attacks the upper respiratory system rendering the human immunity incapacitated and, in some cases, proving fatal. Therefore, it is very much important to identify the infected people quickly and accurately, so that it can be prevented from spread. Early addressal of the symptoms can help to prevent the disease to become severe for all mankind. This calls for the development of a decision-making system to help the medical fraternity for the timely action. This proposed fuzzy based system predicts Covid-19 based on individuals’ symptoms and parameters. It receives input parameters as fever, cough, breathing difficulty, muscle ache, sore throat, travel history, age, medical history in the form of different membership functions and generates one output that predicts the likelihood of a person being infected with COVID-19 using Mamdani fuzzy inference system. The timely prognosis of the disease at home isolation or at the security checks can help the patient to seek the medical treatment as early as possible. Patient case studies, real time observations, cluster cases were studied to create the rule base for FDMS. The results are validated by using real-time individuals test cases on the proposed system which yields 97.2% accuracy, 100% sensitivity and 96.2% specificity.
Research Paper
Hesitant fuzzy sets and their variants
Majid Darehmiraki; Madineh Farnam
Abstract
For the three last decades, the multi-objective fractional programming problem has attracted the attention of many researchers due to various applications in production planning, financial field, and inventory management, and so on. The main aim of this study is to introduce a new application of hesitant ...
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For the three last decades, the multi-objective fractional programming problem has attracted the attention of many researchers due to various applications in production planning, financial field, and inventory management, and so on. The main aim of this study is to introduce a new application of hesitant fuzzy sets in real-life modeling. We intend to model multi-objective linear fractional programming problems under a hesitant fuzzy environment and present a procedure to solve them. the increasing applications of multi-objective linear fractional programming problems and the lack of research papers in this field under a hesitant fuzzy environment are the main motivations of this study. In a hesitant fuzzy set, the membership degree of an element belongs to the set can be represented by several possible values in [0,1]. These values can be chosen by different experts that cannot reach a single opinion in determining a membership degree. so, in our model several evaluations for each of goals established by decision makers based on their attitudes. The generalization of the fuzzy decision-making principle and some new concepts provide an effective solution procedure for the problem. Finally, a practical example is extended to illustrate the applicability of the proposed method.
Research Paper
Pythagorean fuzzy sets and their variants
J Marynirmala
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-rings using homomorphism.
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-rings using homomorphism.
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-rings using homomorphism.
Review Paper
Fuzzy sets and their variants
Satya kumar Das
Abstract
In this article, we have developed a deteriorated multi-item inventory model in a fuzzy environment. Here the demand rate is constant. Production cost and set-up cost are the most vital issue in the inventory system of the market world. Here production cost and set-up- cost are continuous functions of ...
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In this article, we have developed a deteriorated multi-item inventory model in a fuzzy environment. Here the demand rate is constant. Production cost and set-up cost are the most vital issue in the inventory system of the market world. Here production cost and set-up- cost are continuous functions of demand. Set-up-cost is also dependent on average inventory level. Deterioration cost is the most challenging issue in the business world. So here deterioration cost is dependent on inventory level and demand. Lead time crashing cost is considered the continuous function of leading time. In the real world all cost are not fixed. Due to uncertainty all cost parameters of the proposed model are taken as generalized triangular fuzzy number (GTFN). The formulated multi objective inventory problem has been solved by various techniques like as geometric programming (GP) technique, Fuzzy programming technique with hyperbolic membership function (FPTHMF), Fuzzy non-linear programming technique (FNLP). Numerical example is taken to illustrate the model. Sensitivity analysis and graphical representation have been shown to test the parameters of the model.
