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.
Type-2 fuzzy sets and their variants
Ini John Umoeka; Veronica Neekay Akwukwuma
Abstract
The reliability of software product is seen as critical quality factor that cannot be overemphasized. Since real world application is loaded with high amount of uncertainty, such as applicable to software reliability, there should be a technique of dealing with such uncertainty. This paper presents a ...
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The reliability of software product is seen as critical quality factor that cannot be overemphasized. Since real world application is loaded with high amount of uncertainty, such as applicable to software reliability, there should be a technique of dealing with such uncertainty. This paper presents a reliability model to effectively handle uncertainty in software data to enhance reliability prediction of software at the early (requirements and design) stages of Software Development Life Cycle (SDLC). In this paper, a hybrid methodology of Takagi Sugeno Kang (TSK)-based Interval Type-2 Fuzzy Logic System (IT2FLS) with Artificial Neural Network (ANN) learning is employed for the prediction of software reliability. The parameters of the model are optimized using Gradient Descent (GD) back-propagation method. Relevant reliability software requirement and design metrics and software size metrics are utilized as inputs. The proposed approach uses twenty-eight real software project data. The performance of the model is evaluated using five performance metrics and found to provide output values that are very close to the actual output showing better predictive accuracy.
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.
Fuzzy sets and their variants
Pejman Peykani; Mojtaba Nouri; Farzad Eshghi; Mohammad Khamechian; Hamed Farrokhi-Asl
Abstract
Investment Portfolio Optimization (IPO) is one of the most important problems in the financial area. Also, one of the most important features of financial markets is their embedded uncertainty. Thus, it is essential to propose a novel IPO model that can be employed in the presence of uncertain data. ...
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Investment Portfolio Optimization (IPO) is one of the most important problems in the financial area. Also, one of the most important features of financial markets is their embedded uncertainty. Thus, it is essential to propose a novel IPO model that can be employed in the presence of uncertain data. Accordingly, the main goal of this paper is to propose a novel Fuzzy Multi-Period Multi-Objective Portfolio Optimization (FMPMOPO) model that is capable to be used under data ambiguity and practical constraints including budget constraint, cardinality constraint, and bound constraint. It should be noted that three objectives including terminal wealth, risk, and liquidity as well as practical constraints are considered in proposed FMPMOPO model. Also, the alpha-cut method is employed to deal with fuzzy data. Finally, the proposed Fuzzy Multi-Period Wealth-Risk-Liquidity (FMPWRL) model is implemented in real-world case study from Tehran Stock Exchange (TSE). The experimental results show the applicability and efficacy of the proposed FMPWRL model for fuzzy multi-period multi-objective investment portfolio optimization problem under fuzzy environment.
Fuzzy sets and their variants
Ceren Cubukcu; Cem Cantekin
Abstract
Covid-19 pandemic forced all the world to make significant changes in their daily routines. As a result, internet and digital technologies started to be used more actively by individuals and businesses. Due to this digitalization, everyone is more open to digital threats. In order to provide the security ...
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Covid-19 pandemic forced all the world to make significant changes in their daily routines. As a result, internet and digital technologies started to be used more actively by individuals and businesses. Due to this digitalization, everyone is more open to digital threats. In order to provide the security of the network, firewalls should be used. Firewalls act as a barrier between the internal and the external networks. Thus, it is more important than ever to choose the right firewall for each network. In this study, an integrated Fuzzy-Analytic Hierarchy Process (AHP) and TOPSIS model is introduced to find out the most suitable firewall. A survey is designed and used to generate the data of this study. This study distinguishes from other studies by proposing a solution which ranks the firewall alternatives using a combination of fuzzy-AHP and TOPSIS models. As a result, among the five different firewall alternatives, the second one is found out to be the best. A solution proposal ranking the firewall alternatives is new in the literature. This approach is used in many different Multi-Criteria Decision Making (MCDM) problems before but not in firewall selection. Hence, this study can be considered quite innovative in terms of the problem it handles and the model used. It offers a new solution related to a decision making problem that has started to gain more importance with the current digitalization process due to Covid-19 pandemic.
Fuzzy sets and their variants
Alireza Aliahmadi; Hamed Nozari; Javid Ghahremani-Nahr; Agnieszka Szmelter-Jarosz
Abstract
In recent years, the high complexity of the business environment, dynamism and environmental change, uncertainty and concepts such as globalization and increasing competition of organizations in the national and international arena have caused many changes in the equations governing the supply chain. ...
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In recent years, the high complexity of the business environment, dynamism and environmental change, uncertainty and concepts such as globalization and increasing competition of organizations in the national and international arena have caused many changes in the equations governing the supply chain. In this case, supply chain organizations must always be prepared for a variety of challenges and dynamic environmental changes. One of the effective solutions to face these challenges is to create a resilient supply chain. Resilient supply chain is able to overcome uncertainties and disruptions in the business environment. The competitive advantage of this supply chain does not depend only on low costs, high quality, reduced latency and high level of service. Rather, it has the ability of the chain to avoid catastrophes and overcome critical situations, and this is the resilience of the supply chain. AI and IoT technologies and their combination, called AIoT, have played a key role in improving supply chain performance in recent years and can therefore increase supply chain resilience. For this reason, in this study, an attempt was made to better understand the impact of these technologies on equity by examining the dimensions and components of the Artificial Intelligence of Things (AIoT)-based supply chain. Finally, using nonlinear fuzzy decision making method, the most important components of the impact on the resilient smart supply chain are determined. Understanding this assessment can help empower the smart supply chain.
Fuzzy sets and their variants
Ladji Kane; Moctar Diakite; Souleymane Kane; Hawa Bado; Moussa Konate; Koura Traore
Abstract
Transportation problem 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 ...
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Transportation problem 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 fully fuzzy transportation problem involving trapezoidal 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 triangular fuzzy numbers i.e. two interval transportation problems. 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 four application examples are solved. The results show that the proposed method is simpler and computationally more efficient than existing methods in the literature.
Type-2 fuzzy sets and their variants
Uduak Umoh; Imo Eyoh; Etebong Isong; Anietie Ekong; Salvation Peter
Abstract
Several attempts had been made to analyze emotion words in the fields of linguistics, psychology and sociology; with the advent of computers, the analyses of these words have taken a different dimension. Unfortunately, limited attempts have so far been made to using interval type-2 fuzzy logic (IT2FL) ...
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Several attempts had been made to analyze emotion words in the fields of linguistics, psychology and sociology; with the advent of computers, the analyses of these words have taken a different dimension. Unfortunately, limited attempts have so far been made to using interval type-2 fuzzy logic (IT2FL) to analyze these words in native languages. This study used IT2FL to analyze Igbo emotion words. IT2F sets are computed using the interval approach method which is divided into two parts: the data part and the fuzzy set part. The data part preprocessed data and its statistics computed for the interval that survived the preprocessing stages while the fuzzy set part determined the nature of the footprint of uncertainty; the IT2F set mathematical models for each emotion characteristics of each emotion word is also computed. The data used in this work was collected from fifteen subjects who were asked to enter an interval for each of the emotion characteristics: Valence, Activation and Dominance on an interval survey of the thirty Igbo emotion words. With this, the words are being analyzed and can be used for the purposes of translation between vocabularies in consideration to context.
Soft sets and their variants
P G Patil; Vyshakha Elluru; S Shivashankar
Abstract
Many real-world problems face strenuous in making decisions. Many theories have evolved for dealing with such problems. The present paper deals with Fuzzy Binary Soft Sets and their applications to Multi Criteria Decision Making (MCDM) problems. Then introduced an expanded matrix representation of Fuzzy ...
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Many real-world problems face strenuous in making decisions. Many theories have evolved for dealing with such problems. The present paper deals with Fuzzy Binary Soft Sets and their applications to Multi Criteria Decision Making (MCDM) problems. Then introduced an expanded matrix representation of Fuzzy Binary Soft Sets, an extended resultant matrix, and operator, and an algorithm to solve a proposed problem.
Fuzzy sets and their variants
Sunday Adesina Adebisi; Mike Ogiugo; Michael Enioluwafe
Abstract
A group is nilpotent if it has a normal series of a finite length n. By this notion, every finite p-group is nilpotent. The nilpotence property is an hereditary one. Thus, every finite p-group possesses certain remarkable characteristics. In this paper, the explicit formulae is given for the number of ...
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A group is nilpotent if it has a normal series of a finite length n. By this notion, every finite p-group is nilpotent. The nilpotence property is an hereditary one. Thus, every finite p-group possesses certain remarkable characteristics. In this paper, the explicit formulae is given for the number of distinct fuzzy subgroups of the Cartesian product of the dihedral group of order 23 with a cyclic group of order of an m power of two for, which m ≥ 3.
Rough sets and their variants
Mahmut Dirik
Abstract
Fire is a natural disaster that poses a profound existential threat to humanity. It has traditionally been fought with conventional methods, which, unfortunately, are often fraught with limitations and potential environmental damage. Given these limitations, there is an urgent need for research into ...
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Fire is a natural disaster that poses a profound existential threat to humanity. It has traditionally been fought with conventional methods, which, unfortunately, are often fraught with limitations and potential environmental damage. Given these limitations, there is an urgent need for research into novel firefighting methods. Sound wave-based firefighting systems, an emerging solution, show promising potential in this regard.The current study uses an extensive data set derived from numerous experimental trials of sound-wave-based firefighting. Based on this extensive dataset, we have developed a sound wave technology-based fire suppression model that includes five different fuzzy logic methods: Fuzzy Rough Set (FRS), Fuzzy K-Nearest Neighbors (FNN), Fuzzy Ownership K-Nearest Neighbors (FONN), Fuzzy-Rough K-Nearest Neighbors (FRNN), and Vaguely Quantified K-Nearest Neighbors (VQNN).The main objective of these models is to accurately distinguish between the extinguished and non-extinguished states of a flame. This classification is based on a number of intrinsic model parameters, such as the type of fuel, the size of the flame, the decibel level, the frequency, the airflow, and the distance.To evaluate the classification effectiveness of the models, a number of statistical methods were used, including Mean Absolute Error (MAE), Root Mean Square Error (RMSE), Kappa Statistics (KP), and Mean Square Error (MSE).Our analysis yielded promising results, with the models FRS, FNN, FONN, FRNN, and VQNN achieving classification accuracies of 93.12%, 96.66%, 95.56%, 96.35%, and 96.89%, respectively. These results confirm the high accuracy of the proposed model in classifying fire data and underline its practical applicability.
Artificial Intelligence
Mehmet Karahan; Furkan Lacinkaya; Kaan Erdonmez; Eren Deniz Eminagaoglu; Cosku Kasnakoglu
Abstract
In recent years, development of the machine learning algorithms has led to the creation of intelligent surveillance systems. Thanks to the machine learning, it is possible to perform intelligent surveillance by recognizing people's facial features, classifying their age and gender, and detecting objects ...
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In recent years, development of the machine learning algorithms has led to the creation of intelligent surveillance systems. Thanks to the machine learning, it is possible to perform intelligent surveillance by recognizing people's facial features, classifying their age and gender, and detecting objects around instead of ordinary surveillance. In this study, a novel algorithm has been developed that classifies people's age and gender with a high accuracy rate. In addition, a novel object recognition algorithm has been developed that detects objects quickly and with high accuracy. In this study, age and gender classification was made based on the facial features of people using Convolutional Neural Network (CNN) architecture. Secondly, object detection was performed using different machine learning algorithms and the performance of the different machine learning algorithms was compared in terms of median average precision and inference time. The accuracy of the age and gender classification algorithm was tested using the Adience dataset and the results were graphed. The experimental results show that age and gender classification algorithms successfully classify people's age and gender. Then, the performances of object detection algorithms were tested using the COCO dataset and the results were presented in graphics. The experimental results stress that machine learning algorithms can successfully detect objects.
Linguistic term sets and their variants
Mohammad Ebrahim Sadeghi; Hamed Nozari; Hadi Khajezadeh Dezfoli; Mehdi Khajezadeh Dezfoli
Abstract
Examining the trend of the global economy shows that global trade is moving towards high-tech products. Given that these products generate very high added value, countries that can produce and export these products will have high growth in the industrial sector. The importance of investing in advanced ...
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Examining the trend of the global economy shows that global trade is moving towards high-tech products. Given that these products generate very high added value, countries that can produce and export these products will have high growth in the industrial sector. The importance of investing in advanced technologies for economic and social growth and development is so great that it is mentioned as one of the strong levers to achieve development. It should be noted that the policy of developing advanced technologies requires consideration of various performance aspects, risks and future risks in the investment phase. Risk related to high-tech investment projects has a meaning other than financial concepts only. In recent years, researchers have focused on identifying, analyzing, and prioritizing risk. There are two important components in measuring investment risk in high-tech industries, which include identifying the characteristics and criteria for measuring system risk and how to measure them. This study tries to evaluate and rank the investment risks in advanced industries using fuzzy TOPSIS technique based on verbal variables.
Fuzzy sets and their variants
Satya Kumar Das
Abstract
In this paper, we have developed the multi-item inventory model in the fuzzy environment. Here we considered the demand rate is constant and production cost is dependent on the demand rate. Set-up- cost is dependent on average inventory level as well as demand. Lead time crashing cost is considered the ...
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In this paper, we have developed the multi-item inventory model in the fuzzy environment. Here we considered the demand rate is constant and production cost is dependent on the demand rate. Set-up- cost is dependent on average inventory level as well as demand. Lead time crashing cost is considered the continuous function of leading time. Limitation is considered on storage of space. Due to uncertainty all cost parameters of the proposed model are taken as generalized trapezoidal fuzzy numbers. Therefore this model is very real. The formulated multi objective inventory problem has been solved by various techniques like as Geometric Programming (GP) approach, Fuzzy Programming Technique with Hyperbolic Membership Function (FPTHMF), Fuzzy Nonlinear Programming (FNLP) technique and Fuzzy Additive Goal Programming (FAGP) technique. An example is given to illustrate the model. Sensitivity analysis and graphical representation have been shown to test the parameters of the model.
Q-rung orthopair fuzzy sets and their variants
Mujahid Abbas; Muhammad Waseem Asghar; Yanhui Guo
Abstract
The q-Rung Orthopair Fuzzy Soft Set (q-ROFSS) theory is a significant extension of Pythagorean fuzzy soft set and intuitionistic fuzzy soft set theories for dealing with the imprecision and uncertainty in data. The purpose of this study is to improve and apply this theory in decision-making. To achieve ...
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The q-Rung Orthopair Fuzzy Soft Set (q-ROFSS) theory is a significant extension of Pythagorean fuzzy soft set and intuitionistic fuzzy soft set theories for dealing with the imprecision and uncertainty in data. The purpose of this study is to improve and apply this theory in decision-making. To achieve this purpose, we firstly propose some Bonferroni Mean (BM) and Weighted Bonferroni Mean (WBM) aggregation operators for aggregating the data. Some desired properties are presented in detail and the existing aggregation operators are used as distinct cases of our proposed operators. Further, a decision-making analysis is presented based on our proposed operations and applied to decision-making in COVID-19 diagnosis. The preferred way is discussed to protect maximum human lives from COVID-19. A numerical example is given to support the claim. The experimental results demonstrate the proposed operators have an ability to make a precise decision with imprecision and uncertain information which will find a broad application in the decision-making area.
Q-rung orthopair fuzzy sets and their variants
Mahalakshmi Pethaperumal; Vimala Jeyakumar; Jeevitha Kannan; Ashma Banu
Abstract
The q-Rung Orthopair Fuzzy set (qROF-set) environment is a contemporary tool for handling uncertainty and vagueness in decision-making scenarios. In this paper, we delve into the algebraic examination of q-rung orthopair Multi-Fuzzy Sets (MFSs) and explore their operational laws. The novel q-Rung Orthopair ...
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The q-Rung Orthopair Fuzzy set (qROF-set) environment is a contemporary tool for handling uncertainty and vagueness in decision-making scenarios. In this paper, we delve into the algebraic examination of q-rung orthopair Multi-Fuzzy Sets (MFSs) and explore their operational laws. The novel q-Rung Orthopair Multi-Fuzzy subgroup (qROMF-subgroup) is the extension of Intuitionistic Multi-Fuzzy Subgroup (IMF-subgroup) to encompass the domain of groups. The properties of the proposed fuzzy subgroup are examined in detail, and the paper concludes by defining two additional concepts: qROMF-coset and qROMF-normal subgroup. Finally, we present a comparison of the newly introduced model with existing approaches to validate its superior performance.
Intuitionistic fuzzy sets and their variants
Ivanosca Andrade Da Silva; Berta Bedregal; Benjamin Bedregal; Regivan Hugo Nunes Santiago
Abstract
In this paper we extend the notion of interval representation for interval-valued Atanassov’s intuitionistic representations, in short Lx-representations, and use this notion to obtain the best possible one, of the Weighted Average (WA) and Ordered Weighted Average (OWA) operators. A main characteristic ...
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In this paper we extend the notion of interval representation for interval-valued Atanassov’s intuitionistic representations, in short Lx-representations, and use this notion to obtain the best possible one, of the Weighted Average (WA) and Ordered Weighted Average (OWA) operators. A main characteristic of this extension is that when applied to diagonal elements, i.e. fuzzy degrees, they provide the same results as the WA and OWA operators, respectively. Moreover, they preserve the main algebraic properties of the WA and OWA operators. A new total order for interval-valued Atanassov’s intuitionistic fuzzy degrees is also introduced in this paper which is used jointly with the best Lx-representation of the WA and OWA, in a method for multi-attribute group decision making where the assesses of the experts, in order to take in consideration uncertainty and hesitation, are interval-valued Atanassov’s intuitionistic fuzzy degrees. A characteristic of this method is that it works with interval-valued Atanassov’s intuitionistic fuzzy values in every moments, and therefore considers the uncertainty on the membership and non-membership in all steps of the decision making. We apply this method in two illustrative examples and compare our result with other methods.
Spherical fuzzy sets
Princy Rayappan; Mohana Krishnaswamy
Abstract
Similarity measure is an important tool in multiple criteria decision-making problems, which can be used to measure the difference between the alternatives. In this paper, some new similarity measures of Spherical Fuzzy Sets (SFS) are defined based on the Euclidean distance measure and the proposed similarity ...
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Similarity measure is an important tool in multiple criteria decision-making problems, which can be used to measure the difference between the alternatives. In this paper, some new similarity measures of Spherical Fuzzy Sets (SFS) are defined based on the Euclidean distance measure and the proposed similarity measures satisfy the axiom of the similarity measure. Furthermore, we apply the proposed similarity measures to medical diagnosis decision making problem; the numerical example is used to illustrate the feasibility and effectiveness of the proposed similarity measures of SFS, which are then compared to other existing similarity measures.
Complex Fuzzy Sets and their variants
Rubeena Khaliq; Pervaiz Iqbal; Shahid Ahmad Bhat; Ram Singh; Shilpi Jain; Praveen Agarwal
Abstract
In this present study, the tumor growth model using the Gompertz equation with the Allee effect is developed under a fuzzy environment using the Generalized Hukuhara Derivative (GHD) approach. To capture the tumor growth patterns with the Allee threshold, the parameters present in the model vary ...
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In this present study, the tumor growth model using the Gompertz equation with the Allee effect is developed under a fuzzy environment using the Generalized Hukuhara Derivative (GHD) approach. To capture the tumor growth patterns with the Allee threshold, the parameters present in the model vary from time to time, and in real life, it is very difficult to estimate the exact cell count. In this vague situation, the initial condition, coefficient, and both together are taken as the fuzzy number. In this paper, the GHD approach is used to solve the fuzzy tumor growth model in which four different cases are considered with respect to (i)-gH differentiability and (ii)-gH differentiability concept. The main objective of this study is to present a significant reduction in uncertainty while modeling the tumor growth in a fuzzy environment with the Allee effect. Finally, the proposed model and technique are illustrated by numerical simulation and analysis of tumor growth is conducted.
Complex Fuzzy Sets and their variants
Orhan Engin; Meral İşler
Abstract
This paper deals with the Fuzzy Hybrid Flow Shop (FHFS) scheduling inspired by a real apparel process. A Parallel Greedy (PG) algorithm is proposed to solve the FHFS problems with Setup Time (ST) and Lot Size (LS). The fuzzy model is used to define the uncertain setup and Processing Time (PT) and Due ...
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This paper deals with the Fuzzy Hybrid Flow Shop (FHFS) scheduling inspired by a real apparel process. A Parallel Greedy (PG) algorithm is proposed to solve the FHFS problems with Setup Time (ST) and Lot Size (LS). The fuzzy model is used to define the uncertain setup and Processing Time (PT) and Due Dates (DDs). The setup and PTs are defined by a Triangular Fuzzy Number (TAFN). Also, the Fuzzy Due Date (FDD) is denoted by a doublet. The tardiness, the tardy jobs, the setup and Idle Time (IT), and the Total Flow (TF) time are minimized by the proposed PG algorithm. The effectiveness of the proposed PG algorithm is demonstrated by comparing it with the Genetic Algorithm (GeA) in the literature. A real-world application in an apparel process is done. According to the results, the proposed PG algorithm is an efficient method for FHFS scheduling problems with ST and LS in real-world applications.
Fuzzy sets and their variants
Eshetu Dadi Gurmu; Tagay Takele Fikadu
Abstract
In this study, we discussed a fuzzy programming approach to bi-level linear programming problems and their application. Bi-level linear programming is characterized as mathematical programming to solve decentralized problems with two decision-makers in the hierarchal organization. They become more important ...
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In this study, we discussed a fuzzy programming approach to bi-level linear programming problems and their application. Bi-level linear programming is characterized as mathematical programming to solve decentralized problems with two decision-makers in the hierarchal organization. They become more important for the contemporary decentralized organization where each unit seeks to optimize its own objective. In addition to this, we have considered Bi-Level Linear Programming (BLPP) and applied the Fuzzy Mathematical Programming (FMP) approach to get the solution of the system. We have suggested the FMP method for the minimization of the objectives in terms of the linear membership functions. FMP is a supervised search procedure (supervised by the upper Decision Maker (DM)). The upper-level decision-maker provides the preferred values of decision variables under his control (to enable the lower level DM to search for his optimum in a wider feasible space) and the bounds of his objective function (to direct the lower level DM to search for his solutions in the right direction).
Neutrosophic sets and their variants
Sulima Ahmed Mohammed Zubair
Abstract
This study introduces an approach for Multiple Attribute Decision-Making (MADM) that deals with the complexity of Single-Valued Neutrosophic Uncertain Linguistic Variables (SVNULVs). This method is engineered to grasp the interconnectedness of multiple inputs and to meet the diverse requirements for ...
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This study introduces an approach for Multiple Attribute Decision-Making (MADM) that deals with the complexity of Single-Valued Neutrosophic Uncertain Linguistic Variables (SVNULVs). This method is engineered to grasp the interconnectedness of multiple inputs and to meet the diverse requirements for semantic transformations. Due to the shortcomings of existing operational rules in terms of closeness and flexibility, this paper proposes a novel set of operational rules and a ranking process for SVNULVs, integrating the concept of a Linguistic Scale Function (LSF). We propose an innovative operator along with its weighted counterpart to amalgamate SVNULVs, thereby characterizing the dynamics among various inputs through these new operations. Concurrently, we scrutinize and discuss the unique cases and favorable properties of these proposed operators. Building upon this new operator, the paper also unveils a fresh MADM methodology leveraging SVNULVs. To validate the effectiveness of this proposed methodology, an illustrative example is employed, demonstrating the precision of the method and its advantages over existing MADM techniques.
Neutrosophic sets and their variants
Volkan Duran; Selcuk Topal; Florentin Smarandache
Abstract
The main concept of neutrosophy is that any idea has not only a certain degree of truth but also a degree of falsity and indeterminacy in its own right. Although there are many applications of neutrosophy in different disciplines, the incorporation of its logic in education and psychology is rather scarce ...
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The main concept of neutrosophy is that any idea has not only a certain degree of truth but also a degree of falsity and indeterminacy in its own right. Although there are many applications of neutrosophy in different disciplines, the incorporation of its logic in education and psychology is rather scarce compared to other fields. In this study, the Satisfaction with Life Scale was converted into the neutrosophic form and the results were compared in terms of confirmatory analysis by convolutional neural networks. To sum up, two different formulas are proposed at the end of the study to determine the validity of any scale in terms of neutrosophy. While the Lawshe methodology concentrates on the dominating opinions of experts limited by a one-dimensional data space analysis, it should be advocated that the options can be placed in three-dimensional data space in the neutrosophic analysis . The effect may be negligible for a small number of items and participants, but it may create enormous changes for a large number of items and participants. Secondly, the degree of freedom of Lawshe technique is only 1 in 3D space, whereas the degree of freedom of neutrosophical scale is 3, so researchers have to employ three separate parameters of 3D space in neutrosophical scale while a resarcher is restricted in a 1D space in Lawshe technique in 3D space. The third distinction relates to the analysis of statistics. The Lawhe technical approach focuses on the experts' ratio of choices, whereas the importance and correlation level of each item for the analysis in neutrosophical logic are analysed. The fourth relates to the opinion of experts. The Lawshe technique is focused on expert opinions, yet in many ways the word expert is not defined. In a neutrosophical scale, however, researchers primarily address actual participants in order to understand whether the item is comprehended or opposed to or is imprecise. In this research, an alternative technique is presented to construct a valid scale in which the scale first is transformed into a neutrosophical one before being compared using neural networks. It may be concluded that each measuring scale is used for the desired aim to evaluate how suitable and representative the measurements obtained are so that its content validity can be evaluated.
Linguistic term sets and their variants
Somaieh Alavi; Masoomeh Zeinalnezhad; Emad Mousavi
Abstract
Green Project Management (GPM) involves a set of management actions to identify and evaluate the impact of activities on the environment and to control and improve performance. Accordingly, the concepts of lean, agility and resilience have a special place as driving forces because they can play an important ...
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Green Project Management (GPM) involves a set of management actions to identify and evaluate the impact of activities on the environment and to control and improve performance. Accordingly, the concepts of lean, agility and resilience have a special place as driving forces because they can play an important role in improving the environment. Therefore, the present study is conducted with the aim of identifying and prioritizing GPM activities. They are introduced based on the principles of project management knowledge set and considering the concept of green. Then, by considering the concepts of resilience, agility and purity as research criteria using Fuzzy Analytic Hierarchy Process (FAHP), activities are prioritized. This study has a pairwise comparison questionnaire that data are collected from construction industry experts. The incompatibility rate index is used to determine the reliability of the questionnaire. The results show that the five activities of GPM are identifying a team that can align the project with environmental policies. Development, documentation of the project charter, setting goals in the project charter, quality control, cost, planning, safety of environmental activities, and preparation of GPM programs, respectively, should be given more attention.
Intuitionistic fuzzy sets and their variants
Nour Abed Alhaleem; Abd Ghafur Ahmad
Abstract
In this paper, the (α,β)-level sets where α and β are elements in the interval [0,1] is introduced. Several related properties for (α,β)-cut of intuitionistic fuzzy normed ideals in a normed ring (NR) will be studied and proven. Further, for any two normed rings NR,NR^' ...
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In this paper, the (α,β)-level sets where α and β are elements in the interval [0,1] is introduced. Several related properties for (α,β)-cut of intuitionistic fuzzy normed ideals in a normed ring (NR) will be studied and proven. Further, for any two normed rings NR,NR^' with a mapping f:NR → NR^', a relation between the intuitionistic fuzzy normed ideal I of NR and the intuitionistic fuzzy normed ideal f(I) (the image of I) of NR^' will been obtained with the support of their (α,β)-level subsets.
