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.
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.
