Entropy, Measures of Distance and Similarity of Q-Neutrosophic Soft Sets and Some Applications

Qamar, Majdoleen Abu; Hassan, Nasruddin

doi:10.3390/e20090672

Cited by 24 publications

(11 citation statements)

References 39 publications

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“…Thirdly, the research successfully combines the prospect theory with neutrosophic softs sets to construct the stochastic multi-criteria group decision making algorithm. Compared with the existing literatures based on the expected utility theory [16,17,25,26] (pp. 1-2), this research considers the influence of psychological expectations on decision results.…”

Section: Discussionmentioning

confidence: 99%

“…This paper employs the Hamming distance of information theory, which is a well-known measure designed to provide insights into the similarity of information [33,34] and has been widely employed in distance measures [26,35], to measure the determinacy degree and conflict degree. Before this, we present the concept of a minimum conflict neutrosophic number and maximum conflict neutrosophic number.…”

Section: The Measures Of Determinacy Degree and Conflict Degreementioning

confidence: 99%

“…Peng and Liu [25] constructed three decision making algorithms of neutrosophic soft sets by evaluation based on the distance from average solution (EDAS), similarity measure, and level soft sets, respectively. Abu Qamar and Hassan [26] presented the similarity, distance, and fuzzy degree measures of Q-neutrosophic soft sets, and put forward the corresponding decision rule. Karaaslan [21] constructed a decision making method for the possibility of neutrosophic soft sets based on the and-product.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Discussionmentioning

confidence: 99%

Section: The Measures Of Determinacy Degree and Conflict Degreementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

2019

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“…Therefore, it incorporates the benefits of these models. Abu Qamar and Hassan studied different aspects of Q-NSS, such as their relations [40], measures of Q-NSS information [41], generalized Q-neutrosophic soft expert set [42], and different decision problems of these concepts.Motivated by these studies, in this study we discuss the different operations and properties of Q-NSS. To facilitate the discussion, we arranged this article as follows.…”

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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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“…Finally, an algorithm on generalized Q-neutrosophic soft expert set is proposed and applied to a real-life example to show the efficiency of this notion in handling such problems.2 of 16 memberships are independent. Relations between Q-NSSs were studied in [13] while their measures of distance, similarity and entropy were discussed in [14].Decision-making is an exploration point of research especially in uncertain environments. Recently, many researchers applied neutrosophic sets to real-life decision making problems containing uncertain, indeterminate and incompatible information [15][16][17][18][19][20][21][22][23][24][25].Recently, the need for models incorporating opinions of experts and validating information supplied by observers has been recognized.…”

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confidence: 99%

Generalized Q-Neutrosophic Soft Expert Set for Decision under Uncertainty

Qamar

Hassan

2018

Symmetry

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Neutrosophic triplet structure yields a symmetric property of truth membership on the left, indeterminacy membership in the centre and false membership on the right, as do points of object, centre and image of reflection. As an extension of a neutrosophic set, the Q-neutrosophic set was introduced to handle two-dimensional uncertain and inconsistent situations. We extend the soft expert set to generalized Q-neutrosophic soft expert set by incorporating the idea of soft expert set to the concept of Q-neutrosophic set and attaching the parameter of fuzzy set while defining a Q-neutrosophic soft expert set. This pattern carries the benefits of Q-neutrosophic sets and soft sets, enabling decision makers to recognize the views of specialists with no requirement for extra lumbering tasks, thus making it exceedingly reasonable for use in decision-making issues that include imprecise, indeterminate and inconsistent two-dimensional data. Some essential operations namely subset, equal, complement, union, intersection, AND and OR operations and additionally several properties relating to the notion of generalized Q-neutrosophic soft expert set are characterized. Finally, an algorithm on generalized Q-neutrosophic soft expert set is proposed and applied to a real-life example to show the efficiency of this notion in handling such problems.

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Entropy, Measures of Distance and Similarity of Q-Neutrosophic Soft Sets and Some Applications

Cited by 24 publications

References 39 publications

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

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

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

Generalized Q-Neutrosophic Soft Expert Set for Decision under Uncertainty

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