**Author**: Jun Ye

**Publisher:**Infinite Study

**ISBN:**

**Category :**

**Languages :**en

**Pages :**11

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## Linguistic Neutrosophic Cubic Numbers and Their Multiple Attribute Decision-Making Method

**Author**: Jun Ye

**Publisher:** Infinite Study

**ISBN:**

**Category : **

**Languages : **en

**Pages : **11

**Book Description**

To describe both certain linguistic neutrosophic information and uncertain linguistic neutrosophic information simultaneously in the real world, this paper originally proposes the concept of a linguistic neutrosophic cubic number(LNCN), including an internal LNCN and external LNCN.

## Linguistic Neutrosophic Cubic Numbers and Their Multiple Attribute Decision-Making Method

**Author**: Jun Ye

**Publisher:** Infinite Study

**ISBN:**

**Category : **

**Languages : **en

**Pages : **11

**Book Description**

To describe both certain linguistic neutrosophic information and uncertain linguistic neutrosophic information simultaneously in the real world, this paper originally proposes the concept of a linguistic neutrosophic cubic number(LNCN), including an internal LNCN and external LNCN.

## Multiple Attribute Decision-Making Method Using Linguistic Cubic Hesitant Variables

**Author**: Jun Ye

**Publisher:** Infinite Study

**ISBN:**

**Category : **Mathematics

**Languages : **en

**Pages : **13

**Book Description**

Linguistic decision making (DM) is an important research topic in DM theory and methods since using linguistic terms for the assessment of the objective world is very fitting for human thinking and expressing habits. However, there is both uncertainty and hesitancy in linguistic arguments in human thinking and judgments of an evaluated object. Nonetheless, the hybrid information regarding both uncertain linguistic arguments and hesitant linguistic arguments cannot be expressed through the various existing linguistic concepts.

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

**Author**: Florentin Smarandache

**Publisher:** MDPI

**ISBN:** 3038974757

**Category : **Mathematics

**Languages : **en

**Pages : **450

**Book Description**

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

**Author**: Florentin Smarandache

**Publisher:** Infinite Study

**ISBN:** 3038974765

**Category : **Mathematics

**Languages : **en

**Pages : **450

**Book Description**

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.

## Decision Making Methods with Linguistic Neutrosophic Information: A Review

**Author**: Minna Xu

**Publisher:** Infinite Study

**ISBN:**

**Category : **Mathematics

**Languages : **en

**Pages : **12

**Book Description**

Linguistic neutrosophic information and its extension have been long recognized as a useful tool in decision-making problems in many areas. This paper briefly describes the development process of linguistic neutrosophic information expressions, and gives in-depth studies on seven different concepts and tools. At the same time, a brief evaluation and summary of the decision-making methods of its various measures and aggregation operators are also made. A comparative analysis of different linguistic neutrosophic sets is made with examples to illustrate the effectiveness and practicability of decision making methods based on multiple aggregation operators and measures. Finally, according to the analysis of the current situation of linguistic neutrosophic information, the related trends of its future development are discussed.

## Possibility Neutrosophic Cubic Sets and Their Application to Multiple Attribute Decision Making

**Author**: Huiling Xue

**Publisher:** Infinite Study

**ISBN:**

**Category : **Mathematics

**Languages : **en

**Pages : **17

**Book Description**

The neutrosophic cubic sets are an extension of the neutrosophic sets on the cubic sets. It contains three variables, which respectively represent the membership degree, non-membership degree and uncertainty of the element to the set. The score function is an important indicator in the multi-attribute decision-making problem. In this paper, we consider the possibility that an element belongs to a set and put forward the definition of possibility neutrosophic cubic sets. On this basis, we introduce some related concepts and give the binary operation of possibility neutrosophic cubic sets and use specific examples to supplement the corresponding definition. Meanwhile, a decision-making method based on the score function of possibility neutrosophic cubic sets is proposed and a numerical example is given to illustrate the effectiveness of the proposed method.

## Dombi Aggregation Operators of Neutrosophic Cubic Sets for Multiple Attribute Decision-Making

**Author**: Lilian Shi

**Publisher:** Infinite Study

**ISBN:**

**Category : **Mathematics

**Languages : **en

**Pages : **15

**Book Description**

The neutrosophic cubic set can describe complex decision-making problems with its single-valued neutrosophic numbers and interval neutrosophic numbers simultaneously. The Dombi operations have the advantage of good flexibility with the operational parameter. In order to solve decision-making problems with flexible operational parameter under neutrosophic cubic environments, the paper extends the Dombi operations to neutrosophic cubic sets and proposes a neutrosophic cubic Dombi weighted arithmetic average (NCDWAA) operator and a neutrosophic cubic Dombi weighted geometric average (NCDWGA) operator. Then, we propose a multiple attribute decision-making (MADM) method based on the NCDWAA and NCDWGA operators. Finally, we provide two illustrative examples of MADM to demonstrate the application and effectiveness of the established method.

## Neutrosophic Sets and Systems, Vol. 38, 2020

**Author**: Florentin Smarandache

**Publisher:** Infinite Study

**ISBN:**

**Category : **Mathematics

**Languages : **en

**Pages : **662

**Book Description**

“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc.

## Cosine Measures of Linguistic Neutrosophic Numbers and Their Application in Multiple Attribute Group Decision-Making

**Author**: Lilian Shi

**Publisher:** Infinite Study

**ISBN:**

**Category : **

**Languages : **en

**Pages : **

**Book Description**

The linguistic neutrosophic numbers (LNNs) can express the truth, indeterminacy, and falsity degrees independently by three linguistic variables. Hence, they are an effective tool for describing indeterminate linguistic information under linguistic decision-making environments. Similarity measures are usual tools in decision-making problems.

## NC-TODIM-Based MAGDM under a Neutrosophic Cubic Set Environment

**Author**: Surapati Pramanik

**Publisher:** Infinite Study

**ISBN:**

**Category : **

**Languages : **en

**Pages : **31

**Book Description**

A neutrosophic cubic set is the hybridization of the concept of a neutrosophic set and an interva lneutrosophic set.

Book PDF Download Digital Journal

To describe both certain linguistic neutrosophic information and uncertain linguistic neutrosophic information simultaneously in the real world, this paper originally proposes the concept of a linguistic neutrosophic cubic number(LNCN), including an internal LNCN and external LNCN.

To describe both certain linguistic neutrosophic information and uncertain linguistic neutrosophic information simultaneously in the real world, this paper originally proposes the concept of a linguistic neutrosophic cubic number(LNCN), including an internal LNCN and external LNCN.

Linguistic decision making (DM) is an important research topic in DM theory and methods since using linguistic terms for the assessment of the objective world is very fitting for human thinking and expressing habits. However, there is both uncertainty and hesitancy in linguistic arguments in human thinking and judgments of an evaluated object. Nonetheless, the hybrid information regarding both uncertain linguistic arguments and hesitant linguistic arguments cannot be expressed through the various existing linguistic concepts.

Neutrosophy (1995) is a new branch of philosophy that studies triads of the form (,

Neutrosophy (1995) is a new branch of philosophy that studies triads of the form (,

Linguistic neutrosophic information and its extension have been long recognized as a useful tool in decision-making problems in many areas. This paper briefly describes the development process of linguistic neutrosophic information expressions, and gives in-depth studies on seven different concepts and tools. At the same time, a brief evaluation and summary of the decision-making methods of its various measures and aggregation operators are also made. A comparative analysis of different linguistic neutrosophic sets is made with examples to illustrate the effectiveness and practicability of decision making methods based on multiple aggregation operators and measures. Finally, according to the analysis of the current situation of linguistic neutrosophic information, the related trends of its future development are discussed.

The neutrosophic cubic sets are an extension of the neutrosophic sets on the cubic sets. It contains three variables, which respectively represent the membership degree, non-membership degree and uncertainty of the element to the set. The score function is an important indicator in the multi-attribute decision-making problem. In this paper, we consider the possibility that an element belongs to a set and put forward the definition of possibility neutrosophic cubic sets. On this basis, we introduce some related concepts and give the binary operation of possibility neutrosophic cubic sets and use specific examples to supplement the corresponding definition. Meanwhile, a decision-making method based on the score function of possibility neutrosophic cubic sets is proposed and a numerical example is given to illustrate the effectiveness of the proposed method.

The neutrosophic cubic set can describe complex decision-making problems with its single-valued neutrosophic numbers and interval neutrosophic numbers simultaneously. The Dombi operations have the advantage of good flexibility with the operational parameter. In order to solve decision-making problems with flexible operational parameter under neutrosophic cubic environments, the paper extends the Dombi operations to neutrosophic cubic sets and proposes a neutrosophic cubic Dombi weighted arithmetic average (NCDWAA) operator and a neutrosophic cubic Dombi weighted geometric average (NCDWGA) operator. Then, we propose a multiple attribute decision-making (MADM) method based on the NCDWAA and NCDWGA operators. Finally, we provide two illustrative examples of MADM to demonstrate the application and effectiveness of the established method.

“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc.

The linguistic neutrosophic numbers (LNNs) can express the truth, indeterminacy, and falsity degrees independently by three linguistic variables. Hence, they are an effective tool for describing indeterminate linguistic information under linguistic decision-making environments. Similarity measures are usual tools in decision-making problems.

A neutrosophic cubic set is the hybridization of the concept of a neutrosophic set and an interva lneutrosophic set.