Trapezoidal neutrosophic set and its application to multiple attribute decision-making PDF Download

Author: Jun Ye
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 11

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Book Description
Based on the combination of trapezoidal fuzzy numbers and a single-valued neutrosophic set, this paper proposes a trapezoidal neutrosophic set, some operational rules, score and accuracy functions for trapezoidal neutrosophic numbers.

Author: Hai-Long Yang
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 23

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Book Description
Neutrosophic set (NS) was originally proposed by Smarandache to handle indeterminate and inconsistent information. It is a generalization of fuzzy sets and intuitionistic fuzzy sets. Wang and Smarandache proposed interval neutrosophic sets (INS) which is a special case of NSs and would be extensively applied to resolve practical issues. In this paper, we put forward generalized interval neutrosophic rough sets based on interval neutrosophic relations by combining interval neutrosophic sets with rough sets. We explore the hybrid model through constructive approach as well as axiomatic approach. On one hand, we define generalized interval neutrosophic lower and upper approximation operators through constructive approach. Moreover, we investigate the relevance between generalized interval neutrosophic lower (upper) approximation operators and particular interval neutrosophic relations. On the other hand, we study axiomatic characterizations of generalized interval neutrosophic approximation operators, and also show that different axiom sets of theoretical interval neutrosophic operators make sure the existence of different classes of INRs that yield the same interval neutrosophic approximation operators. Finally, we introduce generalized interval neutrosophic rough sets on two universes and a universal algorithm of multi-attribute decision making based on generalized interval neutrosophic rough sets on two universes. Besides, an example is given to demonstrate the validity of the new rough set model.

Author: Pranab Biswas
Publisher: Infinite Study
ISBN:
Category :
Languages : en
Pages : 11

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Book Description
Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is a popular strategy for Multi-Attribute Decision Making (MADM). In this paper, we extend the TOPSIS strategy of MADM problems in trapezoidal neutrosophic number environment.

Author: Huiling Xue
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 17

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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.

Author: Pranab Biswas
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 11

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Book Description
Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is a popular strategy for Multi-Attribute Decision Making (MADM). In this paper, we extend the TOPSIS strategy of MADM problems in trapezoidal neutrosophic number environment.

Author: Florentin Smarandache
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 596

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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. Some articles in this issue: Neutrosophic Soft Fixed Points, Selection of Alternative under the Framework of Single-Valued Neutrosophic Sets, Application of Single Valued Trapezoidal Neutrosophic Numbers in Transportation Problem.

Author: Florentin Smarandache
Publisher: MDPI
ISBN: 3038972886
Category : Mathematics
Languages : en
Pages : 207

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Book Description
This book is a printed edition of the Special Issue "Neutrosophic Multi-Criteria Decision Making" that was published in Axioms

Author: Surapati Pramanik
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 13

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Book Description
VIseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) is a popular strategy for multi- attribute decision making (MADM). We extend the VIKOR strategy for MAGDM problems in trapezoidal neutrosophic number environment. In decision making situation, single-valued trapezoidal neutrosophic numbers are employed to express the attribute values. Then we develop an extended VIKOR strategy to deal with MAGDM in single-valued trapezoidal neutrosophic number environment. The influence of decision-making mechanism coefficient is presented. To illustrate and validate the proposed VIKOR strategy, an illustrative numerical example of MAGDM problem is solved in trapezoidal neutrosophic number environment.

Author: Irfan Deli
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 20

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Book Description
In this paper, we first introduce single valued trapezoidal neutrosophic (SVTN) numbers with their properties. We then define some operations and distances of the SVTN-numbers. Based on these new operations, we also define some aggregation operators, including SVTN-ordered weighted geometric operator, SVTN-hybrid geometric operator, SVTN-ordered weighted arithmetic operator and SVTN-hybrid arithmetic operator. We then examine the properties of these SVTN-information aggregation operators. By using the SVTN-weighted geometric operator and SVTN-hybrid geometric operator, we also define a multi attribute group decision making method, called SVTN-group decision making method. We finally give an illustrative example and comparative analysis to verify the developed method and to demonstrate its practicality and effectiveness.

Author: Wen Jiang
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 13

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Book Description
Multi-attribute decision-making refers to the decision-making problem of selecting the optimal alternative or sorting the scheme when considering multiple attributes, which is widely used in engineering design, economy, management and military, etc. But in real application, the attribute information of many objects is often inaccurate or uncertain, so it is very important for us to find a useful and efficient method to solve the problem. Neutrosophic set is proposed from philosophical point of view to handle inaccurate information efficiently, and a single-valued neutrosophic set (SVNS) is a special case of neutrosophic set, which is widely used in actual application fields. In this paper, a new method based on single-valued neutrosophic sets aggregation to solve multi-attribute decision making problem is proposed. Firstly, the neutrosophic decision matrix is obtained by expert assessment, a score function of single-valued neutrosophic sets (SVNSs) is defined to obtain the positive ideal solution (PIS) and the negative ideal solution (NIS). Then all alternatives are aggregated based on TOPSIS method to make decision. Finally numerical examples are given to verify the feasibility and rationality of the method.