Research Paper
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; Florentin Smarandache
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.
Research Paper
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.
Review Paper
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.
Research Paper
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.
Research Paper
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.
Research Paper
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.
Research Paper
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.
