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Generalized Single Valued Triangular Neutrosophic Numbers And Aggregation Operators For Application To Multi Attribute Group Decision Making


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Generalized Single Valued Triangular Neutrosophic Numbers and Aggregation Operators for Application to Multi-attribute Group Decision Making


Generalized Single Valued Triangular Neutrosophic Numbers and Aggregation Operators for Application to Multi-attribute Group Decision Making

Author: Mehmet Şahin

language: en

Publisher: Infinite Study

Release Date:


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In this study we define the generalizing single valued triangular neutrosophic number. In addition, single valued neutrosophic numbers are transformed into single valued triangular neutrosophic numbers according to the values of truth, indeterminacy and falsity. Furthermore, we extended the Hamming distance given for triangular intuitionistic fuzzy numbers to single valued triangular neutrosophic numbers. We have defined new score functions based on the Hamming distance.

Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets


Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets

Author: Florentin Smarandache

language: en

Publisher: MDPI

Release Date: 2019-04-04


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Neutrosophy (1995) is a new branch of philosophy that studies triads of the form (, , ), where is an entity {i.e. element, concept, idea, theory, logical proposition, etc.}, is the opposite of , while is the neutral (or indeterminate) between them, i.e., neither nor . Based on neutrosophy, the neutrosophic triplets were founded, which have a similar form (x, neut(x), anti(x)), that satisfy several axioms, for each element x in a given set. This collective book presents original research papers by many neutrosophic researchers from around the world, that report on the state-of-the-art and recent advancements of neutrosophic triplets, neutrosophic duplets, neutrosophic multisets and their algebraic structures – that have been defined recently in 2016 but have gained interest from world researchers. Connections between classical algebraic structures and neutrosophic triplet / duplet / multiset structures are also studied. And numerous neutrosophic applications in various fields, such as: multi-criteria decision making, image segmentation, medical diagnosis, fault diagnosis, clustering data, neutrosophic probability, human resource management, strategic planning, forecasting model, multi-granulation, supplier selection problems, typhoon disaster evaluation, skin lesson detection, mining algorithm for big data analysis, etc.

Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets, Volume II


Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets, Volume II

Author: Florentin Smarandache

language: en

Publisher: Infinite Study

Release Date:


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Neutrosophy (1995) is a new branch of philosophy that studies triads of the form (, , ), where is an entity (i.e., element, concept, idea, theory, logical proposition, etc.), is the opposite of , while is the neutral (or indeterminate) between them, i.e., neither nor . Based on neutrosophy, the neutrosophic triplets were founded; they have a similar form: (x, neut(x), anti(x), that satisfy some axioms, for each element x in a given set. This book contains the successful invited submissions to a special issue of Symmetry, reporting on state-of-the-art and recent advancements of neutrosophic triplets, neutrosophic duplets, neutrosophic multisets, and their algebraic structures—that have been defined recently in 2016, but have gained interest from world researchers, and several papers have been published in first rank international journals.