D- numbers and their variants
Payam Shafi Salimi
Abstract
Success in supply begins with the right choice of suppliers and in the long run is directly related to how suppliers are managed, because suppliers have a significant impact on the success or failure of a company. Multi-criteria decisions are approaches that deal with ranking and selecting one or more ...
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Success in supply begins with the right choice of suppliers and in the long run is directly related to how suppliers are managed, because suppliers have a significant impact on the success or failure of a company. Multi-criteria decisions are approaches that deal with ranking and selecting one or more suppliers from a set of suppliers. Multi-criteria decisions provide an effective framework for comparing suppliers based on the evaluation of different criteria. The present research is applied based on the purpose and descriptive-survey based on the nature and method of the research. In the present study, two library and field methods have been used to collect information. According to the objectives of this study, suppliers will be evaluated using two methods of fuzzy hierarchical analysis with D-numbers. In order to better understand these two methods, a case study is presented in which suppliers are ranked using two methods and then the results are compared with each other. For manufacturing companies, 4 categories of parts were considered and based on the classification, the suppliers of the manufacturing company were evaluated and analyzed. In the results of suppliers of type A and B components in hierarchical analysis, D and fuzzy methods have many differences in the evaluation and ranking of suppliers, and this shows the lack of expectations of experts in D and fuzzy analysis. On the other hand, in type C and D components, the classification and ranking of suppliers have been matched in two ways and shows that the opinions in the evaluation of these suppliers are the same.
Plithogenic sets and their variants
Nivetha Martin; R. Priya
Abstract
The escalation of COVID-19 curves is high and the researchers worldwide are working on diagnostic models, in the way this article proposes COVID-19 diagnostic model using Plithogenic cognitive maps. This paper introduces the new concept of Plithogenic sub cognitive maps including the mediating effects ...
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The escalation of COVID-19 curves is high and the researchers worldwide are working on diagnostic models, in the way this article proposes COVID-19 diagnostic model using Plithogenic cognitive maps. This paper introduces the new concept of Plithogenic sub cognitive maps including the mediating effects of the factors. The thirteen study factors are categorized as grouping factors, parametric factors, risks factors and output factor. The effect of one factor over another is measured directly based on neutrosophic triangular representation of expert’s opinion and indirectly by computing the mediating factor’s effects. This new approach is more realistic in nature as it takes the mediating effects into consideration together with contradiction degree of the factors. The possibility of children, adult and old age with risk factors and parametric factors being infected by corona virus is determined by this diagnostic model. The escalation of COVID-19 curves is high and the researchers worldwide are working on diagnostic models, in the way this article proposes COVID-19 diagnostic model using Plithogenic cognitive maps. This paper introduces the new concept of Plithogenic sub cognitive maps including the mediating effects of the factors. The thirteen study factors are categorized as grouping factors, parametric factors, risks factors and output factor. The effect of one factor over another is measured directly based on neutrosophic triangular representation of expert’s opinion and indirectly by computing the mediating factor’s effects. This new approach is more realistic in nature as it takes the mediating effects into consideration together with contradiction degree of the factors. The possibility of children, adult and old age with risk factors and parametric factors being infected by corona virus is determined by this diagnostic model.
Intuitionistic fuzzy sets and their variants
Suresh Mohan; Arun Prakash Kannusamy; Vengataasalam Samiappan
Abstract
The concept of an intuitionistic fuzzy number (I F N) is of importance for representing an ill-known quantity. Ranking fuzzy numbers plays a very important role in the decision process, data analysis and applications. The concept of an intuitionistic fuzzy number (IFN) is of importance for quantifying ...
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The concept of an intuitionistic fuzzy number (I F N) is of importance for representing an ill-known quantity. Ranking fuzzy numbers plays a very important role in the decision process, data analysis and applications. The concept of an intuitionistic fuzzy number (IFN) is of importance for quantifying an ill-known quantity. Ranking of intuitionistic fuzzy numbers plays a vital role in decision making and linear programming problems. Also, ranking of intuitionistic fuzzy numbers is a very difficult problem. In this paper, a new method for ranking intuitionistic fuzzy number is developed by means of magnitude for different forms of intuitionistic fuzzy numbers. In Particular ranking is done for trapezoidal intuitionistic fuzzy numbers, triangular intuitionistic fuzzy numbers, symmetric trapezoidal intuitionistic fuzzy numbers, and symmetric triangular intuitionistic fuzzy numbers. Numerical examples are illustrated for all the defined different forms of intuitionistic fuzzy numbers. Finally some comparative numerical examples are illustrated to express the advantage of the proposed method.
Neutrosophic sets and their variants
Mohammad Abobala
Abstract
If R is a ring, then Rn(I) is called a refined neutrosophic ring. Every AH-subset of Rn(I) has the form P = ∑ni=0 p i Ii= {a0+a1I+⋯+anIn: ai∈p i}, where p i are subsets of the classical ring R. The objective of this paper is to determine the necessary and sufficient conditions on p i which ...
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If R is a ring, then Rn(I) is called a refined neutrosophic ring. Every AH-subset of Rn(I) has the form P = ∑ni=0 p i Ii= {a0+a1I+⋯+anIn: ai∈p i}, where p i are subsets of the classical ring R. The objective of this paper is to determine the necessary and sufficient conditions on p i which make P be an ideal of Rn(I). Also, this work introduces a full description of the algebraic structure and form for AH-maximal and minimal ideals in Rn(I).
Neutrosophic sets and their variants
Mamoni Dhar
Abstract
In real life situations, there are many issues in which we face uncertainties, vagueness, complexities and unpredictability. Neutrosophic sets are a mathematical tool to address some issues which cannot be met using the existing methods. Neutrosophic soft matrices play a crucial role in handling indeterminant ...
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In real life situations, there are many issues in which we face uncertainties, vagueness, complexities and unpredictability. Neutrosophic sets are a mathematical tool to address some issues which cannot be met using the existing methods. Neutrosophic soft matrices play a crucial role in handling indeterminant and inconsistent information during decision making process. The main focus of this article is to discuss the concept of neutrosophic sets, neutrosophic soft sets and neutrosophic soft matrices theory which are very useful and applicable in various situations involving uncertainties and imprecisions. Thereafter our intention is to find a new method for constructing a decision matrix using neutrosophic soft matrices as an application of the theory. A neutrosophic soft matrix based algorithm is considered to solve some problems in the diagnosis of a disease from the occurrence of various symptoms in patients. This article deals with patient-symptoms and symptoms-disease neutrosophic soft matrices. To come to a decision, a score matrix is defined where multiplication based on max-min operation and complementation of neutrosophic soft matrices are taken into considerations.
Neutrosophic sets and their variants
Sapan Kumar Das
Abstract
The paper talks about the pentagonal Neutrosophic sets and its operational law. The paper presents the cut of single valued pentagonal Neutrosophic numbers and additionally introduced the arithmetic operation of single-valued pentagonal Neutrosophic numbers. Here, we consider a transportation problem ...
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The paper talks about the pentagonal Neutrosophic sets and its operational law. The paper presents the cut of single valued pentagonal Neutrosophic numbers and additionally introduced the arithmetic operation of single-valued pentagonal Neutrosophic numbers. Here, we consider a transportation problem with pentagonal Neutrosophic numbers where the supply, demand and transportation cost is uncertain. Taking the benefits of the properties of ranking functions, our model can be changed into a relating deterministic form, which can be illuminated by any method. Our strategy is easy to assess the issue and can rank different sort of pentagonal Neutrosophic numbers. To legitimize the proposed technique, some numerical tests are given to show the adequacy of the new model.
Neutrosophic sets and their variants
Somen Debnath
Abstract
Statistics mainly concerned with data that may be qualitative or quantitative. Earlier we have used the notion of statistics in the classical sense where we assign values that are crisp. But in reality, we find some areas where the crisp concept is not sufficient to solve the problem. So, it seems difficult ...
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Statistics mainly concerned with data that may be qualitative or quantitative. Earlier we have used the notion of statistics in the classical sense where we assign values that are crisp. But in reality, we find some areas where the crisp concept is not sufficient to solve the problem. So, it seems difficult to assign a definite value for each parameter. For this, fuzzy sets and logic have been introduced to give the flexibility to analyze and classify statistical data. Moreover, we may come across such parameters that are indeterminate, uncertain, imprecise, incomplete, unknown, unsure, approximate, and even completely unknown. Intuitionistic fuzzy set explain uncertainty at some extent. But itis not sufficient to study all sorts of uncertainty present in real-life. It means that there exists data which are neutrosophic in nature. So, neutrosophic data plays a significant role to study the concept of indeterminacy present in a data without any restriction. The main objective of preparing this article is to highlighting the importance of neutrosophication of statistical data in a study to assess the symptoms related to Reproductive Tract Infections (RTIs) or Sexually Transmitted Infections (STIs) among women by sampling estimation.
Type-2 fuzzy sets and their variants
Uduak Umoh; Samuel Udoh; Abdultaofeek Abayomi; Alimot Abdulzeez
Abstract
Interval Type-2 Fuzzy Logic Systems (IT2 FLSs) have shown popularity, superiority, and more accuracy in performance in a number of applications in the last decade. This is due to its ability to cope with uncertainty and precisions adequately when compared with its type-1 counterpart. In this paper, an ...
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Interval Type-2 Fuzzy Logic Systems (IT2 FLSs) have shown popularity, superiority, and more accuracy in performance in a number of applications in the last decade. This is due to its ability to cope with uncertainty and precisions adequately when compared with its type-1 counterpart. In this paper, an Interval Type-2 Fuzzy Logic System (IT2FLS) is employed for remote vital signs monitoring and predicting of shock level in cardiac patients. Also, the conventional, Type-1 Fuzzy Logic System (T1FLS) is applied to the prediction problems for comparison purpose. The cardiac patients’ health datasets were used to perform empirical comparison on the developed system. The result of study indicated that IT2FLS could coped with more information and handled more uncertainties in health data than T1FLS. The statistical evaluation using performance metrices indicated a minimal error with IT2FLS compared to its counterpart, T1FLS. It was generally observed that the shock level prediction experiment for cardiac patients showed the superiority of IT2FLS paradigm over T1FLS.
Fuzzy sets and their variants
Alireza Marzband
Abstract
In recent years, management and, consequently, supply chain performance measurement, has attracted the attention of a large number of managers and researchers in the field of production and operations management. In parallel with the evolution of organizations from a single approach to a network and ...
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In recent years, management and, consequently, supply chain performance measurement, has attracted the attention of a large number of managers and researchers in the field of production and operations management. In parallel with the evolution of organizations from a single approach to a network and supply chain approach, performance measurement systems have also changed and moved towards network and supply chain performance measurement. Therefore, in order to face the storm of great change and transformation and not give in to the wave of competitive aggression, organizations have long had one thing in common, and that is to focus approaches and focus efforts towards achieving results. Results that lead to a competitive advantage and are more effective and decisive in the performance indicators of the organization, including earning more. In this study, in order to identify and prioritize the factors affecting the supply chain in manufacturing companies, using indicators such as cost, timely delivery and procurement time to evaluate the supply chain efficiency is considered. And performance evaluation was performed at the manufacturer level. Therefore, in order to evaluate the performance of the supply chain using the AHP integration approach and the DEA method approach in the fuzzy environment, the suppliers and suppliers of the manufacturing company were evaluated and ranked in terms of performance.
Interval Arithmetic
Hossein Jafari; Mohammad Ehsanifar
Abstract
The VIKOR method was developed for Multi-Criteria Decision Making (MCDM). It determines the compromise ranking list and the compromise solution obtained with the initial weights. This method focuses on ranking and selecting from a set of alternatives in the presence of conflicting criteria. It introduces ...
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The VIKOR method was developed for Multi-Criteria Decision Making (MCDM). It determines the compromise ranking list and the compromise solution obtained with the initial weights. This method focuses on ranking and selecting from a set of alternatives in the presence of conflicting criteria. It introduces the multi-criteria ranking index based on the particular measure of ‘‘closeness” to the “Ideal” solution. The aim of this paper is to extend the VIKOR method for decision making problems with interval number. The extended VIKOR method’s ranking is obtained through comparison of interval numbers and for doing the comparisons between intervals. In the end, a numerical example illustrates and clarifies the main results developed in this paper.
Fuzzy sets and their variants
Mohsen Imeni
Abstract
Many areas of accounting have highly ambiguous due to undefined and inaccurate terms. Many ambiguities are generated by the human mind. In the field of accounting, these ambiguities lead to the creation of uncertain information. Many of the targets and concepts of accounting with binary classification ...
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Many areas of accounting have highly ambiguous due to undefined and inaccurate terms. Many ambiguities are generated by the human mind. In the field of accounting, these ambiguities lead to the creation of uncertain information. Many of the targets and concepts of accounting with binary classification are not consistent. Similarly, the discussion of the materiality or reliability of accounting is not a two-part concept. Because there are degrees of materiality or reliability. Therefore, these ambiguities lead to the presentation information that is not suitable for decision making. Lack of attention to the issue of ambiguity in management accounting techniques, auditing procedures, and financial reporting may lead to a reduced role of accounting information in decision-making processes. Because information plays an important role in economic decision-making, and no doubt, the quality of their, including accuracy in providing it to a wide range of users, can be useful for decision-making. One of the features of the fuzzy set is that it reduces the need for accurate data in decision making. Hence this information can be useful for users.
Fuzzy sets and their variants
Mohammad Ghasempoor Anaraki; Dmitriy S. Vladislav; Mahdi Karbasian; Natalja Osintsev; Victoria Nozick
Abstract
One of the most important issues concerning the designing a supply chain is selecting the supplier. Selecting proper suppliers is one of the most crucial activities of an organization towards the gradual improvement and a promotion in performance. This intricacy is because suppliers fulfil a part of ...
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One of the most important issues concerning the designing a supply chain is selecting the supplier. Selecting proper suppliers is one of the most crucial activities of an organization towards the gradual improvement and a promotion in performance. This intricacy is because suppliers fulfil a part of customer’s expectancy and selecting among them is multi-criteria decision, which needs a systematic and organized approach without which this decision may lead to failure. The purpose of this research is proposing a new method for assessment and rating the suppliers. We have identified several evaluation criteria and attributes; the selection among them was by the Simple Multi-Attribute Rating Technique (SMART) method, then we have specified the connection and the influence of the criteria on each other by DEMATEL method. After that, suppliers were graded by using the Fuzzy Analytical Network Process (FANP) approach and the most efficient one was selected. The innovation of this research is combining the SMART method, DEMATEL method, and Analytical Network Process in Fuzzy state which lead to more exact and efficient results which is proposed for the first time by the researchers of this study.
Other
Abbasali Monzeli; Behrouz Daneshian; Gasem Tohidi; Masud Sanei; Shabnam Razavian
Abstract
Data Envelopment Analysis (DEA) is one of the well-known methods for calculating efficiency, determining efficient boundaries and evaluating efficiency that is used in specific input and output conditions. Traditional models of DEA do not try to reduce undesirable outputs and increase undesirable inputs. ...
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Data Envelopment Analysis (DEA) is one of the well-known methods for calculating efficiency, determining efficient boundaries and evaluating efficiency that is used in specific input and output conditions. Traditional models of DEA do not try to reduce undesirable outputs and increase undesirable inputs. Therefore, in this study, in addition to determining the efficiency of Decision-Making Units (DMU) with the presence of some undesirable input and output components, its effect has also been investigated on the efficiency limit. To do this, we first defined the appropriate production possibility set according to the problem assumptions, and then we presented a new method to determine the unfavorable performance of some input and output components in decision-making units. And we determined the impact of unfavorable inputs and outputs on the efficient boundary. We also showed the model result by providing examples for both unfavorable input and output states and solving them and determining the efficiency score and driving them to the efficient boundary by plotting those boundaries.
Neutrosophic sets and their variants
Florentin Smarandache
Abstract
In this paper we present the development from paradoxism to neutrosophy, which gave birth to neutrosophic set and logic and especially to NeutroAlgebraic Structures (or NeutroAlgebras) and AntiAlgebraic Structures (or AntiAlgebras) that are generalizations and alternatives of the classical algebraic ...
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In this paper we present the development from paradoxism to neutrosophy, which gave birth to neutrosophic set and logic and especially to NeutroAlgebraic Structures (or NeutroAlgebras) and AntiAlgebraic Structures (or AntiAlgebras) that are generalizations and alternatives of the classical algebraic structures.
Fuzzy sets and their variants
Iman Ghasemian Sahebi; Alireza Arab; Seyed Pendar Toufighi
Abstract
The crucial role of bureaucracy in the economic, political, socio-cultural and political structures, and its impact in achieving the goals of organization is so important that in order to achieve the development, change directions consists of purifying and modernization of the administrative system in ...
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The crucial role of bureaucracy in the economic, political, socio-cultural and political structures, and its impact in achieving the goals of organization is so important that in order to achieve the development, change directions consists of purifying and modernization of the administrative system in Iran also seems necessary. An important part of the transportation industry in each country, is the airports. So, dealing with the bureaucracy airports to implement better practices and removing unnecessary processes is the most issues. Hence, it can be stated that the aim of this study is to identify barriers of transformation in the organization administrative and then prioritizing these barriers in Mehrabad airport. For this purpose, the grounded theory and fuzzy SWARA methods was used to identifying the barriers and prioritizing them. Grounded theory results showed that cognitive barriers, structural barriers, participation barriers, economic and income barriers, legal barriers, strategic barriers, and management barriers are the barriers of the transformation in the Mehrabad airport administrative system. The fuzzy SWARA method used to prioritize these barriers, which according to the results, the structural barriers were the important barriers. Then cognitive and legal barriers were placed in the next rank. At the end, some solutions have been presented for overcoming these barriers in the Mehrabad airport.
Fuzzy sets and their variants
Ladji Kane; Hamala Sidibe; Souleymane Kane; Hawa Bado; Moussa Konate; Daouda Diawara; Lassina Diabate
Abstract
Transportation Problem (TP) is an important network structured linear programming problem that arises in several contexts and has deservedly received a great deal of attention in the literature. The central concept in this problem is to find the least total transportation cost of a commodity in order ...
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Transportation Problem (TP) is an important network structured linear programming problem that arises in several contexts and has deservedly received a great deal of attention in the literature. The central concept in this problem is to find the least total transportation cost of a commodity in order to satisfy demands at destinations using available supplies at origins in a crisp environment. In real life situations, the decision maker may not be sure about the precise values of the coefficients belonging to the transportation problem. The aim of this paper is to introduce a formulation of TP involving Triangular fuzzy numbers for the transportation costs and values of supplies and demands. We propose a two-step method for solving fuzzy transportation problem where all of the parameters are represented by non-negative triangular fuzzy numbers i.e., an Interval Transportation Problems (TPIn) and a Classical Transport Problem (TP). Since the proposed approach is based on classical approach it is very easy to understand and to apply on real life transportation problems for the decision makers. To illustrate the proposed approach two application examples are solved. The results show that the proposed method is simpler and computationally more efficient than existing methods in the literature.
Fuzzy sets and their variants
Muhammad Naveed Jafar; Faizullah Khan; Amir Naveed
Abstract
We lived in uncertain word and prediction in this uncertain word is a major issue. Prediction in cricket is very complex because there are many factors which are effecting on results. Weather, pitch, Conditions, Home grounds are some of these factors. In this article it is aimed to predict the results ...
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We lived in uncertain word and prediction in this uncertain word is a major issue. Prediction in cricket is very complex because there are many factors which are effecting on results. Weather, pitch, Conditions, Home grounds are some of these factors. In this article it is aimed to predict the results of PSL-2020 by using TOPSIS and Fuzzy TOPSIS methods. It will be interesting because first time in PSL history it is going to be held in Pakistan. But we use some serious factor to predict the winner of PSL-2020.
Fuzzy sets and their variants
Meysam Kaviani; Seyed Fakhreddin Fakhrehosseini
Abstract
Over the past decades, financial researchers have proposed different methods in portfolio selection, so that, Markwotiz [1] introduced risk and return criteria for a portfolio selection. Since it is difficult how to select an adequate stock portfolio, fuzzy models have been able to help researchers by ...
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Over the past decades, financial researchers have proposed different methods in portfolio selection, so that, Markwotiz [1] introduced risk and return criteria for a portfolio selection. Since it is difficult how to select an adequate stock portfolio, fuzzy models have been able to help researchers by considering uncertainty. In this research, we surveyed a portfolio management by reviewing the relevant literature of fuzzy model in financial management. The results showed that a fuzzy model can to determine an optimal portfolio.
Soft sets and their variants
Renukadevi Vellapandi; Sangeetha Gunasekaran
Abstract
We introduce a new concept of certainty and coverage of a parameter of the soft set and present a new decision making approach for the soft set over the universe using the certainty of a parameter. Also, we point out the drawbacks of the reduct definition by pointing out the delusion of Proposition 14 ...
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We introduce a new concept of certainty and coverage of a parameter of the soft set and present a new decision making approach for the soft set over the universe using the certainty of a parameter. Also, we point out the drawbacks of the reduct definition by pointing out the delusion of Proposition 14 given by Herawan et al. [20] and provide the revised definition of the reduct of the multi soft set.
Intuitionistic fuzzy sets and their variants
Paul Augustine Ejegwa; Idoko Charles Onyeke
Abstract
The concept of correlation coefficient of intuitionistic fuzzy sets is a reliable tool in information theory with numerous applications in diverse areas. Correlation coefficients of intuitionistic fuzzy sets have been studied through two-way approach by many researchers. This approach inappropriately ...
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The concept of correlation coefficient of intuitionistic fuzzy sets is a reliable tool in information theory with numerous applications in diverse areas. Correlation coefficients of intuitionistic fuzzy sets have been studied through two-way approach by many researchers. This approach inappropriately discarded the hesitation margins of the concerned intuitionistic fuzzy sets, which makes the results of such experiments unreliable. In this paper, we modified the correlation coefficient of intuitionistic fuzzy sets of Thao et al. [36] in a three-way approach by including the hesitation margins in the computational process to enhance reliable output through an algorithmic method. We show that the modified correlation coefficient of intuitionistic fuzzy sets is more reasonable with precise outputs than correlation coefficient method. In terms of application, we demonstrate an analysis of medical diagnosis on some selected patients via an algorithm of the novel approach coded with JAVA programming language.
Fuzzy sets and their variants
Tim Chen; Ilnar Karimov; Jcy Chen; Alexandv Constantinovitc
Abstract
Clays have a tendency to this article first introduces the basic concepts of fuzzy theory, including comparisons between fuzzy sets and traditional explicit sets, fuzzy sets basic operations such as the membership function of the set and the colloquial variable, the intersection and union of the fuzzy ...
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Clays have a tendency to this article first introduces the basic concepts of fuzzy theory, including comparisons between fuzzy sets and traditional explicit sets, fuzzy sets basic operations such as the membership function of the set and the colloquial variable, the intersection and union of the fuzzy set, and use the above concepts to guide into the four basic reasoning mechanisms of fuzzy mode and introduce several common types of fuzzy application examples such as fuzzy washing machine and fuzzy control of incinerator plant in China illustrate the application of fuzzy theory in real society.
Picture fuzzy sets and their variants
Ngan Thi Roan; Salvador Coll; Marina Alonso; Juan Miguel Martínez Rubio; Pedro López; Fran Andujar; Son Hoang Le; Manh Van Vu
Abstract
In order to solve the complex decision-making problems, there are many approaches and systems based on the fuzzy theory were proposed. In 1998, Smarandache introduced the concept of single-valued neutrosophic set as a complete development of fuzzy theory. In this paper, we research on the distance measure ...
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In order to solve the complex decision-making problems, there are many approaches and systems based on the fuzzy theory were proposed. In 1998, Smarandache introduced the concept of single-valued neutrosophic set as a complete development of fuzzy theory. In this paper, we research on the distance measure between single-valued neutrosophic sets based on the H-max measure of Ngan et al. [8]. The proposed measure is also a distance measure between picture fuzzy sets which was introduced by Cuong in 2013 [15]. Based on the proposed measure, an Adaptive Neuro Picture Fuzzy Inference System (ANPFIS) is built and applied to the decision making for the link states in interconnection networks. In experimental evaluation on the real datasets taken from the UPV (Universitat Politècnica de València) university, the performance of the proposed model is better than that of the related fuzzy methods.
Neutrosophic sets and their variants
Veerappan Chinnadurai; Mayandi Pandaram Sindhu
Abstract
The neutro-fine topological space is a space that contains a combination of neutrosophic and fine sets. In this study, the various types of open sets such as generalized open and semi-open sets are defined in such space. The concept of interior and closure on semi-open sets are defined and some of their ...
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The neutro-fine topological space is a space that contains a combination of neutrosophic and fine sets. In this study, the various types of open sets such as generalized open and semi-open sets are defined in such space. The concept of interior and closure on semi-open sets are defined and some of their basic properties are stated. These definitions extend the concept to generalized semi-open sets. Moreover, the minimal and maximal open sets are defined and some of their properties are studied in this space. As well as, discussed the complement of all these sets as its closed sets. The basic properties of the union and intersection of these open sets are stated in some theorems. Only a few sets satisfy this postulates, and others are disproved as shown in the counterexamples. The converse of some theorems is proved in probable examples.
Fuzzy sets and their variants
Mehrdad Rasoulzadeh; Mohammad Fallah
Abstract
A combination of projects, assets, programs, and other components put together in a set is called a portfolio. Arranging these components helps to facilitate the efficient management of the set and subsequently leads to achieving the strategic goals. Generally, the components of the portfolio are quantifiable ...
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A combination of projects, assets, programs, and other components put together in a set is called a portfolio. Arranging these components helps to facilitate the efficient management of the set and subsequently leads to achieving the strategic goals. Generally, the components of the portfolio are quantifiable and measurable which makes it possible for management to manage, prioritize, and measure different portfolios. In recent years, the portfolio in various sectors of economics, management, industry, and especially project management has been widely applied and numerous researches have been done based on mathematical models to choose the best portfolio. Among the various mathematical models, the application of data envelopment analysis models due to the unique features as well as the capability of ranking and evaluating performances has been taken by some researchers into account. In this regard, several articles have been written on selecting the best portfolio in various fields, including selecting the best stocks portfolio, selecting the best projects, portfolio of manufactured products, portfolio of patents, selecting the portfolio of assets and liabilities, etc. After presenting the Markowitz mean-variance model for portfolio optimization, these pieces of research have witnessed significant changes. Moreover, after the presentation of the fuzzy set theory by Professor Lotfizadeh, despite the ambiguities in the selection of multiple portfolios, a wide range of applications in portfolio optimization was created by combining mathematical models of portfolio optimization.
Fuzzy sets and their variants
Michael Voskoglou
Abstract
The present work focuses on two directions. First, a new fuzzy method using triangular / trapezoidal fuzzy numbers as tools is developed for evaluating a group’s mean performance, when qualitative grades instead of numerical scores are used for assessing its members’ individual performance. ...
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The present work focuses on two directions. First, a new fuzzy method using triangular / trapezoidal fuzzy numbers as tools is developed for evaluating a group’s mean performance, when qualitative grades instead of numerical scores are used for assessing its members’ individual performance. Second, a new technique is applied for solving Linear Programming problems with fuzzy coefficients. Examples are presented on student and basket-ball player assessment and on real life problems involving Linear Programming under fuzzy conditions to illustrate the applicability of our results in practice. A discussion follows on the perspectives of future research on the subject and the article closes with the general conclusions.
