Neutrosophic soft matrices and NSM-decision making

Deli̇, İrfan; Broumi, Said

doi:10.3233/ifs-141505

Cited by 119 publications

(63 citation statements)

References 30 publications

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“…Furthermore, for 2-dimensional uncertain linguistic information, we proposed the 2-Dimensional Uncertain Linguistic Normalized Weighted Geometric Bonferroni Mean (2DULNWGBM) and the 2-Dimensional Uncertain Linguistic Generalized Normalized Weighted Geometric Bonferroni Mean (2DULGNWGBM), and some desirable properties and special cases of 2DUL-NWGBM and 2DULGNWGBM were investigated in detail; also, a multi-criteria decision making method with 2DULVs was developed based on these operators. In further research, it is important to apply these operators in other domains such as fuzzy cluster analysis, pattern recognition, uncertain programming, etc., or extend the proposed operators and methods to other uncertain information such as interval neutrosophic uncertain linguistic variables or neutrosophic soft sets [51,52].…”

Section: Discussionmentioning

confidence: 99%

2-Dimension Uncertain Linguistic Generalized Normalized Weighted Geometric Bonferroni Mean and Its Application in Multiple Attribute Decision Making

Лю

2017

Scientia Iranica

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KEYWORDS Aggregation operators;Multiple-attribute decision making; Bonferroni mean; 2-dimensional uncertain linguistic variables.Abstract. 2-Dimensional Uncertain Linguistic Variables (2DULVs) are powerful tools to express the fuzzy or uncertain information, and the weighted Bonferroni mean can not only take the attribute importance into account, but also capture the interrelationship between the attributes. However, the traditional Bonferroni mean can only deal with the crisp numbers. In this paper, Bonferroni mean was extended to process the 2DULVs. Firstly, we proposed the Normalized Weighted Geometric Bonferroni Mean (NWGBM) operator and the Generalized Normalized Weighted Geometric Bonferroni Mean (GNWGBM) operator, which had the characteristic of reducibility and considered the interrelationships between two attributes. Then, we introduced the computation rules, characteristics, the expected value, and comparison method of the 2DULVs. Further, we developed the 2-Dimensional Uncertain Linguistic Normalized Weighted Geometric Bonferroni Mean (2DULNWGBM) and the 2-Dimensional Uncertain Linguistic Generalized Normalized Weighted Geometric Bonferroni Mean (2DULGNWGBM), and explored some properties and discussed some special cases of them. Finally, we developed a new decision making method based on these operators. An example is given to compare the method with the existing methods.

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Section: Discussionmentioning

confidence: 99%

2-Dimension Uncertain Linguistic Generalized Normalized Weighted Geometric Bonferroni Mean and Its Application in Multiple Attribute Decision Making

Лю

2017

Scientia Iranica

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“…NS is very appropriate for handling inconsistent, indeterminate, and incomplete information in real applications. Recently, many studies have been done on NSS [17][18][19][20][21][22][23][24], the most recent being on vague soft sets [25], neutrosophic vague soft expert sets [26], n-valued refined neutrosophic Each element in (Γ Q , A) represents the degree of attractiveness of each cell phone with a specific color based on each parameter. For example, element [(u 1 , s), 0.6, 0.2, 0.2] under parameter e 3 represents the degree of true, indeterminacy, and falsity attractiveness of device specification of cell phone u 1 with a black color, and they are 0.6, 0.2, and 0.2, respectively.…”

Section: Introductionmentioning

confidence: 99%

An Approach toward a Q-Neutrosophic Soft Set and Its Application in Decision Making

Qamar

Hassan

2019

Symmetry

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A neutrosophic set was proposed as an approach to study neutral uncertain information. It is characterized through three memberships, T, I and F, such that these independent functions stand for the truth, indeterminate, and false-membership degrees of an object. The neutrosophic set presents a symmetric form since truth enrolment T is symmetric to its opposite false enrolment F with respect to indeterminacy enrolment I that acts as an axis of symmetry. The neutrosophic set was further extended to a Q-neutrosophic soft set, which is a hybrid model that keeps the features of the neutrosophic soft set in dealing with uncertainty, and the features of a Q-fuzzy soft set that handles two-dimensional information. In this study, we discuss some operations of Q-neutrosophic soft sets, such as subset, equality, complement, intersection, union, AND operation, and OR operation. We also define the necessity and possibility operations of a Q-neutrosophic soft set. Several properties and illustrative examples are discussed. Then, we define the Q-neutrosophic-set aggregation operator and use it to develop an algorithm for using a Q-neutrosophic soft set in decision-making issues that have indeterminate and uncertain data, followed by an illustrative real-life example. soft sets [27], complex neutrosophic soft expert sets [28,29] and time-neutrosophic soft sets [30]. Many researchers [23,[31][32][33][34][35][36] have constructed several aggregation operators, such as simplified neutrosophic prioritized aggregation operators, single-valued neutrosophic Dombi weighted aggregation operators, simplified neutrosophic weighted aggregation operators, interval neutrosophic exponential weighted aggregation operators, and used them in decision-making issues. Aggregation operators perform a vital role in multicriteria decision making (MCDM) issues whose principle target is to aggregate a collection of inputs to a single number. Thus, aggregation operators give us effective tools to handle neutrosophic data in the decision process.For a two-dimensional universal set, Adam and Hassan [37,38] introduced the Q-fuzzy soft set (Q-FSS) and multi-Q-FSS, which includes a Q-fuzzy soft aggregation operator that allows constructing more efficient decision-making methods. Broumi [39] presented the notion of the Q-intuitionistic fuzzy soft set (Q-IFSS), and defined some basic properties and basic operations. Actually, these notions cannot handle indeterminate data that appear in two universal sets. Inspired by this, Abu Qamar and Hassan [40] initiated the concept of the Q-neutrosophic soft set (Q-NSS) by upgrading the membership functions of the NSS to a two-dimensional entity. As a result, Q-NSS is premium to these models with three two-dimensional independent membership functions. Hence, this concept serves indeterminacy and two-dimensionality at the same time. Moreover, the Q-neutrosophic set (Q-NS) is basically an NS defined over a two-dimensional set. Thus, it has added advantages to NS by treating a two-dimensional universal set, which makes it mor...

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“…Sahin and Küçük [18] constructed generalised neutrosophic soft sets. Deli and Broumi [19] refined the concept and operations of Maji's neutrosophic soft sets. In addition, they also studied the neutrosophic soft matrix and their operators.…”

Section: Introductionmentioning

confidence: 99%

Algorithm for Neutrosophic Soft Sets in Stochastic Multi-Criteria Group Decision Making Based on Prospect Theory

2019

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To address issues involving inconsistencies, this paper proposes a stochastic multi-criteria group decision making algorithm based on neutrosophic soft sets, which includes a pair of asymmetric functions: Truth-membership and false-membership, and an indeterminacy-membership function. For integrating an inherent stochastic, the algorithm expresses the weights of decision makers and parameter subjective weights by neutrosophic numbers instead of determinate values. Additionally, the algorithm is guided by the prospect theory, which incorporates psychological expectations of decision makers into decision making. To construct the prospect decision matrix, this research establishes a conflict degree measure of neutrosophic numbers and improves it to accommodate the stochastic multi-criteria group decision making. Moreover, we introduce the weighted average aggregation rule and weighted geometric aggregation rule of neutrosophic soft sets. Later, this study presents an algorithm for neutrosophic soft sets in the stochastic multi-criteria group decision making based on the prospect theory. Finally, we perform an illustrative example and a comparative analysis to prove the effectiveness and feasibility of the proposed algorithm.

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Neutrosophic soft matrices and NSM-decision making

Cited by 119 publications

References 30 publications

2-Dimension Uncertain Linguistic Generalized Normalized Weighted Geometric Bonferroni Mean and Its Application in Multiple Attribute Decision Making

2-Dimension Uncertain Linguistic Generalized Normalized Weighted Geometric Bonferroni Mean and Its Application in Multiple Attribute Decision Making

An Approach toward a Q-Neutrosophic Soft Set and Its Application in Decision Making

Algorithm for Neutrosophic Soft Sets in Stochastic Multi-Criteria Group Decision Making Based on Prospect Theory

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