Mathematics

Research

14 pages, 275 KiB

Open AccessArticle

Single-Valued Neutrosophic Linguistic Logarithmic Weighted Distance Measures and Their Application to Supplier Selection of Fresh Aquatic Products

by Jiefeng Wang, Shouzhen Zeng and Chonghui Zhang

Mathematics 2020, 8(3), 439; https://doi.org/10.3390/math8030439 - 17 Mar 2020

Cited by 30 | Viewed by 4430

Abstract

A single-valued neutrosophic linguistic set (SVNLS) is a popular fuzzy tool for describing deviation information in uncertain complex situations. The aim of this paper is to study some logarithmic distance measures and study their usefulness in multiple attribute group decision making (MAGDM) problems [...] Read more.

A single-valued neutrosophic linguistic set (SVNLS) is a popular fuzzy tool for describing deviation information in uncertain complex situations. The aim of this paper is to study some logarithmic distance measures and study their usefulness in multiple attribute group decision making (MAGDM) problems within single-valued neutrosophic linguistic (SVNL) environments. For achieving the purpose, SVNL weighted logarithmic averaging distance (SVNLWLAD) and SVNL ordered weighted logarithmic averaging distance (SVNLOWLAD) measures are firstly developed based on the logarithmic aggregation method. Then, the SVNL combined weighted logarithmic averaging distance (SVNLCWLAD) measure is presented by unifying the advantages of the previous SVNLWLAD and SVNLOWLAD measures. Moreover, a new MAGDM model by utilizing the SVNLCWLAD measure is presented under SVNL environments. Finally, a supplier selection for fresh aquatic products is taken as a case to illustrate the performance of the proposed framework. Full article

(This article belongs to the Special Issue New Challenges in Neutrosophic Theory and Applications)

15 pages, 1255 KiB

Open AccessArticle

An Extended TOPSIS Method with Unknown Weight Information in Dynamic Neutrosophic Environment

by Nguyen Tho Thong, Luong Thi Hong Lan, Shuo-Yan Chou, Le Hoang Son, Do Duc Dong and Tran Thi Ngan

Mathematics 2020, 8(3), 401; https://doi.org/10.3390/math8030401 - 11 Mar 2020

Cited by 17 | Viewed by 2794

Abstract

Decision-making activities are prevalent in human life. Many methods have been developed to address real-world decision problems. In some practical situations, decision-makers prefer to provide their evaluations over a set of criteria and weights. However, in many real-world situations, problems include a lack [...] Read more.

Decision-making activities are prevalent in human life. Many methods have been developed to address real-world decision problems. In some practical situations, decision-makers prefer to provide their evaluations over a set of criteria and weights. However, in many real-world situations, problems include a lack of weight information for the times, criteria, and decision-makers (DMs). To remedy such discrepancies, an optimization model has been proposed to determine the weights of attributes, times, and DMs. A new concept related to the correlation measure and some distance measures for the dynamic interval-valued neutrosophic set (DIVNS) are defined in this paper. An extend Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method in the interval-valued neutrosophic set with unknown weight information in dynamic neutrosophic environments is developed. Finally, a practical example is discussed to illustrate the feasibility and effectiveness of the proposed method. Full article

(This article belongs to the Special Issue New Challenges in Neutrosophic Theory and Applications)

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21 pages, 342 KiB

Open AccessArticle

Multi-Attribute Group Decision Making Based on Multigranulation Probabilistic Models with Interval-Valued Neutrosophic Information

by Chao Zhang, Deyu Li, Xiangping Kang, Yudong Liang, Said Broumi and Arun Kumar Sangaiah

Mathematics 2020, 8(2), 223; https://doi.org/10.3390/math8020223 - 9 Feb 2020

Cited by 14 | Viewed by 2279

Abstract

In plenty of realistic situations, multi-attribute group decision-making (MAGDM) is ubiquitous and significant in daily activities of individuals and organizations. Among diverse tools for coping with MAGDM, granular computing-based approaches constitute a series of viable and efficient theories by means of multi-view problem [...] Read more.

In plenty of realistic situations, multi-attribute group decision-making (MAGDM) is ubiquitous and significant in daily activities of individuals and organizations. Among diverse tools for coping with MAGDM, granular computing-based approaches constitute a series of viable and efficient theories by means of multi-view problem solving strategies. In this paper, in order to handle MAGDM issues with interval-valued neutrosophic (IN) information, we adopt one of the granular computing (GrC)-based approaches, known as multigranulation probabilistic models, to address IN MAGDM problems. More specifically, after revisiting the related fundamental knowledge, three types of IN multigranulation probabilistic models are designed at first. Then, some key properties of the developed theoretical models are explored. Afterwards, a MAGDM algorithm for merger and acquisition target selections (M&A TSs) with IN information is summed up. Finally, a real-life case study together with several detailed discussions is investigated to present the validity of the developed models. Full article

(This article belongs to the Special Issue New Challenges in Neutrosophic Theory and Applications)

21 pages, 454 KiB

Open AccessArticle

Regular CA-Groupoids and Cyclic Associative Neutrosophic Extended Triplet Groupoids (CA-NET-Groupoids) with Green Relations

by Wangtao Yuan and Xiaohong Zhang

Mathematics 2020, 8(2), 204; https://doi.org/10.3390/math8020204 - 6 Feb 2020

Cited by 6 | Viewed by 1958

Abstract

Based on the theories of AG-groupoid, neutrosophic extended triplet (NET) and semigroup, the characteristics of regular cyclic associative groupoids (CA-groupoids) and cyclic associative neutrosophic extended triplet groupoids (CA-NET-groupoids) are further studied, and some important results are obtained. In particular, the following conclusions are [...] Read more.

Based on the theories of AG-groupoid, neutrosophic extended triplet (NET) and semigroup, the characteristics of regular cyclic associative groupoids (CA-groupoids) and cyclic associative neutrosophic extended triplet groupoids (CA-NET-groupoids) are further studied, and some important results are obtained. In particular, the following conclusions are strictly proved: (1) an algebraic system is a regular CA-groupoid if and only if it is a CA-NET-groupoid; (2) if (S, *) is a regular CA-groupoid, then every element of S lies in a subgroup of S, and every

ℋ

-class in S is a group; and (3) an algebraic system is an inverse CA-groupoid if and only if it is a regular CA-groupoid and its idempotent elements are commutative. Moreover, the Green relations of CA-groupoids are investigated, and some examples are presented for studying the structure of regular CA-groupoids. Full article

(This article belongs to the Special Issue New Challenges in Neutrosophic Theory and Applications)

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20 pages, 286 KiB

Open AccessArticle

Generalized Abel-Grassmann’s Neutrosophic Extended Triplet Loop

by Xiaogang An, Xiaohong Zhang and Yingcang Ma

Mathematics 2019, 7(12), 1206; https://doi.org/10.3390/math7121206 - 9 Dec 2019

Cited by 5 | Viewed by 1751

Abstract

A group is an algebraic system that characterizes symmetry. As a generalization of the concept of a group, semigroups and various non-associative groupoids can be considered as algebraic abstractions of generalized symmetry. In this paper, the notion of generalized Abel-Grassmann’s neutrosophic extended triplet [...] Read more.

A group is an algebraic system that characterizes symmetry. As a generalization of the concept of a group, semigroups and various non-associative groupoids can be considered as algebraic abstractions of generalized symmetry. In this paper, the notion of generalized Abel-Grassmann’s neutrosophic extended triplet loop (GAG-NET-Loop) is proposed and some properties are discussed. In particular, the following conclusions are strictly proved: (1) an algebraic system is an AG-NET-Loop if and only if it is a strong inverse AG-groupoid; (2) an algebraic system is a GAG-NET-Loop if and only if it is a quasi strong inverse AG-groupoid; (3) an algebraic system is a weak commutative GAG-NET-Loop if and only if it is a quasi Clifford AG-groupoid; and (4) a finite interlaced AG-(l,l)-Loop is a strong AG-(l,l)-Loop. Full article

(This article belongs to the Special Issue New Challenges in Neutrosophic Theory and Applications)

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27 pages, 335 KiB

Open AccessArticle

Neutrosophic Portfolios of Financial Assets. Minimizing the Risk of Neutrosophic Portfolios

by Marcel-Ioan Boloș, Ioana-Alexandra Bradea and Camelia Delcea

Mathematics 2019, 7(11), 1046; https://doi.org/10.3390/math7111046 - 3 Nov 2019

Cited by 7 | Viewed by 2227

Abstract

This paper studies the problem of neutrosophic portfolios of financial assets as part of the modern portfolio theory. Neutrosophic portfolios comprise those categories of portfolios made up of financial assets for which the neutrosophic return, risk and covariance can be determined and which [...] Read more.

This paper studies the problem of neutrosophic portfolios of financial assets as part of the modern portfolio theory. Neutrosophic portfolios comprise those categories of portfolios made up of financial assets for which the neutrosophic return, risk and covariance can be determined and which provide concomitant information regarding the probability of achieving the neutrosophic return, both at each financial asset and portfolio level and also information on the probability of manifestation of the neutrosophic risk. Neutrosophic portfolios are characterized by two fundamental performance indicators, namely: the neutrosophic portfolio return and the neutrosophic portfolio risk. Neutrosophic portfolio return is dependent on the weight of the financial assets in the total value of the portfolio but also on the specific neutrosophic return of each financial asset category that enters into the portfolio structure. The neutrosophic portfolio risk is dependent on the weight of the financial assets that enter the portfolio structure but also on the individual risk of each financial asset. Within this scientific paper was studied the minimum neutrosophic risk at the portfolio level, respectively, to establish what should be the weight that the financial assets must hold in the total value of the portfolio so that the risk is minimum. These financial assets weights, after calculations, were found to be dependent on the individual risk of each financial asset but also on the covariance between two financial assets that enter into the portfolio structure. The problem of the minimum risk that characterizes the neutrosophic portfolios is of interest for the financial market investors. Thus, the neutrosophic portfolios provide complete information about the probabilities of achieving the neutrosophic portfolio return but also of risk manifestation probability. In this context, the innovative character of the paper is determined by the use of the neutrosophic triangular fuzzy numbers and by the specific concepts of financial assets, in order to substantiating the decisions on the financial markets. Full article

(This article belongs to the Special Issue New Challenges in Neutrosophic Theory and Applications)

13 pages, 1170 KiB

Open AccessArticle

A New X-Bar Control Chart for Using Neutrosophic Exponentially Weighted Moving Average

by Muhammad Aslam, Ali Hussein AL-Marshadi and Nasrullah Khan

Mathematics 2019, 7(10), 957; https://doi.org/10.3390/math7100957 - 12 Oct 2019

Cited by 14 | Viewed by 3347

Abstract

The existing Shewhart X-bar control charts using the exponentially weighted moving average statistic are designed under the assumption that all observations are precise, determined, and known. In practice, it may be possible that the sample or the population observations are imprecise or fuzzy. [...] Read more.

The existing Shewhart X-bar control charts using the exponentially weighted moving average statistic are designed under the assumption that all observations are precise, determined, and known. In practice, it may be possible that the sample or the population observations are imprecise or fuzzy. In this paper, we present the designing of the X-bar control chart under the symmetry property of normal distribution using the neutrosophic exponentially weighted moving average statistics. We will first introduce the neutrosophic exponentially weighted moving average statistic, and then use it to design the X-bar control chart for monitoring the data under an uncertainty environment. We will determine the neutrosophic average run length using the neutrosophic Monte Carlo simulation. The efficiency of the proposed plan will be compared with existing control charts. Full article

(This article belongs to the Special Issue New Challenges in Neutrosophic Theory and Applications)

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11 pages, 509 KiB

Open AccessArticle

Time-Truncated Group Plan under a Weibull Distribution based on Neutrosophic Statistics

by Muhammad Aslam, P. Jeyadurga, Saminathan Balamurali and Ali Hussein AL-Marshadi

Mathematics 2019, 7(10), 905; https://doi.org/10.3390/math7100905 - 27 Sep 2019

Cited by 14 | Viewed by 2152

Abstract

The aim of reducing the inspection cost and time using acceptance sampling can be achieved by utilizing the features of allocating more than one sample item to a single tester. Therefore, group acceptance sampling plans are occupying an important place in the literature [...] Read more.

The aim of reducing the inspection cost and time using acceptance sampling can be achieved by utilizing the features of allocating more than one sample item to a single tester. Therefore, group acceptance sampling plans are occupying an important place in the literature because they have the above-mentioned facility. In this paper, the designing of a group acceptance sampling plan is considered to provide assurance on the product’s mean life. We design the proposed plan based on neutrosophic statistics under the assumption that the product’s lifetime follows a Weibull distribution. We determine the optimal parameters using two specified points on the operating characteristic curve. The discussion on how to implement the proposed plan is provided by an illustrative example. Full article

(This article belongs to the Special Issue New Challenges in Neutrosophic Theory and Applications)

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8 pages, 432 KiB

Open AccessArticle

Classification of the State of Manufacturing Process under Indeterminacy

by Muhammad Aslam and Osama Hasan Arif

Mathematics 2019, 7(9), 870; https://doi.org/10.3390/math7090870 - 19 Sep 2019

Cited by 2 | Viewed by 2299

Abstract

In this paper, the diagnosis of the manufacturing process under the indeterminate environment is presented. The similarity measure index was used to find the probability of the in-control and the out-of-control of the process. The average run length (ARL) was also computed for [...] Read more.

In this paper, the diagnosis of the manufacturing process under the indeterminate environment is presented. The similarity measure index was used to find the probability of the in-control and the out-of-control of the process. The average run length (ARL) was also computed for various values of specified parameters. An example from the Juice Company is considered under the indeterminate environment. From this study, it is concluded that the proposed diagnosis scheme under the neutrosophic statistics is quite simple and effective for the current state of the manufacturing process under uncertainty. The use of the proposed method under the uncertainty environment in the Juice Company may eliminate the non-conforming items and alternatively increase the profit of the company. Full article

(This article belongs to the Special Issue New Challenges in Neutrosophic Theory and Applications)

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8 pages, 738 KiB

Open AccessArticle

Neutrosophic Quadruple Vector Spaces and Their Properties

by Vasantha Kandasamy W.B., Ilanthenral Kandasamy and Florentin Smarandache

Mathematics 2019, 7(8), 758; https://doi.org/10.3390/math7080758 - 19 Aug 2019

Cited by 16 | Viewed by 3125

Abstract

In this paper authors for the first time introduce the concept of Neutrosophic Quadruple (NQ) vector spaces and Neutrosophic Quadruple linear algebras and study their properties. Most of the properties of vector spaces are true in case of Neutrosophic Quadruple vector spaces. Two [...] Read more.

In this paper authors for the first time introduce the concept of Neutrosophic Quadruple (NQ) vector spaces and Neutrosophic Quadruple linear algebras and study their properties. Most of the properties of vector spaces are true in case of Neutrosophic Quadruple vector spaces. Two vital observations are, all quadruple vector spaces are of dimension four, be it defined over the field of reals R or the field of complex numbers C or the finite field of characteristic p,

Z_{p}

; p a prime. Secondly all of them are distinct and none of them satisfy the classical property of finite dimensional vector spaces. So this problem is proposed as a conjecture in the final section. Full article

(This article belongs to the Special Issue New Challenges in Neutrosophic Theory and Applications)

23 pages, 859 KiB

Open AccessArticle

Measures of Probabilistic Neutrosophic Hesitant Fuzzy Sets and the Application in Reducing Unnecessary Evaluation Processes

by Songtao Shao and Xiaohong Zhang

Mathematics 2019, 7(7), 649; https://doi.org/10.3390/math7070649 - 19 Jul 2019

Cited by 9 | Viewed by 2908

Abstract

Distance measure and similarity measure have been applied to various multi-criteria decision-making environments, like talent selections, fault diagnoses and so on. Some improved distance and similarity measures have been proposed by some researchers. However, hesitancy is reflected in all aspects of life, thus [...] Read more.

Distance measure and similarity measure have been applied to various multi-criteria decision-making environments, like talent selections, fault diagnoses and so on. Some improved distance and similarity measures have been proposed by some researchers. However, hesitancy is reflected in all aspects of life, thus the hesitant information needs to be considered in measures. Then, it can effectively avoid the loss of fuzzy information. However, regarding fuzzy information, it only reflects the subjective factor. Obviously, this is a shortcoming that will result in an inaccurate decision conclusion. Thus, based on the definition of a probabilistic neutrosophic hesitant fuzzy set (PNHFS), as an extended theory of fuzzy set, the basic definition of distance, similarity and entropy measures of PNHFS are established. Next, the interconnection among the distance, similarity and entropy measures are studied. Simultaneously, a novel measure model is established based on the PNHFSs. In addition, the new measure model is compared by some existed measures. Finally, we display their applicability concerning the investment problems, which can be utilized to avoid redundant evaluation processes. Full article

(This article belongs to the Special Issue New Challenges in Neutrosophic Theory and Applications)

10 pages, 246 KiB

Open AccessArticle

Inspection Plan Based on the Process Capability Index Using the Neutrosophic Statistical Method

by Muhammad Aslam and Mohammed Albassam

Mathematics 2019, 7(7), 631; https://doi.org/10.3390/math7070631 - 16 Jul 2019

Cited by 22 | Viewed by 3328

Abstract

The Process Capability Index (PCI) has been widely used in industry to advance the quality of a product. Neutrosophic statistics is the more generalized form of classical statistics and is applied when the data from the production process or a product lot is [...] Read more.

The Process Capability Index (PCI) has been widely used in industry to advance the quality of a product. Neutrosophic statistics is the more generalized form of classical statistics and is applied when the data from the production process or a product lot is incomplete, incredible, and indeterminate. In this paper, we will originally propose a variable sampling plan for the PCI using neutrosophic statistics. The neutrosophic operating function will be given. The neutrosophic plan parameters will be determined using the neutrosophic optimization solution. A comparison between plans based on neutrosophic statistics and classical statistics is given. The application of the proposed neutrosophic sampling plan will be given using company data. Full article

(This article belongs to the Special Issue New Challenges in Neutrosophic Theory and Applications)

9 pages, 731 KiB

Open AccessArticle

Neutrosophic Triplets in Neutrosophic Rings

by Vasantha Kandasamy W. B., Ilanthenral Kandasamy and Florentin Smarandache

Mathematics 2019, 7(6), 563; https://doi.org/10.3390/math7060563 - 20 Jun 2019

Cited by 14 | Viewed by 2694

Abstract

The neutrosophic triplets in neutrosophic rings

⟨ Q \cup I ⟩

and

⟨ R \cup I ⟩

are investigated in this paper. However, non-trivial neutrosophic triplets are not found in

⟨ Z \cup I ⟩

. In the neutrosophic ring of integers [...] Read more.

The neutrosophic triplets in neutrosophic rings

⟨ Q \cup I ⟩

and

⟨ R \cup I ⟩

are investigated in this paper. However, non-trivial neutrosophic triplets are not found in

⟨ Z \cup I ⟩

. In the neutrosophic ring of integers

Z \ {0, 1}

, no element has inverse in Z. It is proved that these rings can contain only three types of neutrosophic triplets, these collections are distinct, and these collections form a torsion free abelian group as triplets under component wise product. However, these collections are not even closed under component wise addition. Full article

(This article belongs to the Special Issue New Challenges in Neutrosophic Theory and Applications)

7 pages, 238 KiB

Open AccessArticle

Semi-Idempotents in Neutrosophic Rings

by Vasantha Kandasamy W.B., Ilanthenral Kandasamy and Florentin Smarandache

Mathematics 2019, 7(6), 507; https://doi.org/10.3390/math7060507 - 3 Jun 2019

Cited by 16 | Viewed by 2228

Abstract

In complex rings or complex fields, the notion of imaginary element i with

i^{2} = - 1

or the complex number i is included, while, in the neutrosophic rings, the indeterminate element I where

I^{2} = I

is included. The neutrosophic [...] Read more.

In complex rings or complex fields, the notion of imaginary element i with

i^{2} = - 1

or the complex number i is included, while, in the neutrosophic rings, the indeterminate element I where

I^{2} = I

is included. The neutrosophic ring

⟨ R \cup I ⟩

is also a ring generated by R and I under the operations of R. In this paper we obtain a characterization theorem for a semi-idempotent to be in

⟨ Z_{p} \cup I ⟩

, the neutrosophic ring of modulo integers, where p a prime. Here, we discuss only about neutrosophic semi-idempotents in these neutrosophic rings. Several interesting properties about them are also derived and some open problems are suggested. Full article

(This article belongs to the Special Issue New Challenges in Neutrosophic Theory and Applications)

12 pages, 291 KiB

Open AccessArticle

Linguistic Neutrosophic Numbers Einstein Operator and Its Application in Decision Making

by Changxing Fan, Sheng Feng and Keli Hu

Mathematics 2019, 7(5), 389; https://doi.org/10.3390/math7050389 - 28 Apr 2019

Cited by 15 | Viewed by 2267

Abstract

Linguistic neutrosophic numbers (LNNs) include single-value neutrosophic numbers and linguistic variable numbers, which have been proposed by Fang and Ye. In this paper, we define the linguistic neutrosophic number Einstein sum, linguistic neutrosophic number Einstein product, and linguistic neutrosophic number Einstein exponentiation operations [...] Read more.

Linguistic neutrosophic numbers (LNNs) include single-value neutrosophic numbers and linguistic variable numbers, which have been proposed by Fang and Ye. In this paper, we define the linguistic neutrosophic number Einstein sum, linguistic neutrosophic number Einstein product, and linguistic neutrosophic number Einstein exponentiation operations based on the Einstein operation. Then, we analyze some of the relationships between these operations. For LNN aggregation problems, we put forward two kinds of LNN aggregation operators, one is the LNN Einstein weighted average operator and the other is the LNN Einstein geometry (LNNEWG) operator. Then we present a method for solving decision-making problems based on LNNEWA and LNNEWG operators in the linguistic neutrosophic environment. Finally, we apply an example to verify the feasibility of these two methods. Full article

(This article belongs to the Special Issue New Challenges in Neutrosophic Theory and Applications)

16 pages, 592 KiB

Open AccessArticle

Refined Neutrosophy and Lattices vs. Pair Structures and YinYang Bipolar Fuzzy Set

by Florentin Smarandache

Mathematics 2019, 7(4), 353; https://doi.org/10.3390/math7040353 - 16 Apr 2019

Cited by 7 | Viewed by 2715

Abstract

In this paper, we present the lattice structures of neutrosophic theories. We prove that Zhang-Zhang’s YinYang bipolar fuzzy set is a subclass of the Single-Valued bipolar neutrosophic set. Then we show that the pair structure is a particular case of refined neutrosophy, and [...] Read more.

In this paper, we present the lattice structures of neutrosophic theories. We prove that Zhang-Zhang’s YinYang bipolar fuzzy set is a subclass of the Single-Valued bipolar neutrosophic set. Then we show that the pair structure is a particular case of refined neutrosophy, and the number of types of neutralities (sub-indeterminacies) may be any finite or infinite number. Full article

(This article belongs to the Special Issue New Challenges in Neutrosophic Theory and Applications)

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16 pages, 433 KiB

Open AccessArticle

Neutrosophic Cubic Einstein Hybrid Geometric Aggregation Operators with Application in Prioritization Using Multiple Attribute Decision-Making Method

by Khaleed Alhazaymeh, Muhammad Gulistan, Majid Khan and Seifedine Kadry

Mathematics 2019, 7(4), 346; https://doi.org/10.3390/math7040346 - 10 Apr 2019

Cited by 19 | Viewed by 2635

Abstract

Viable collection is one of the imperative instruments of decision-making hypothesis. Collection operators are not simply the operators that normalize the value; they represent progressively broad values that can underline the entire information. Geometric weighted operators weight the values only, and the ordered [...] Read more.

Viable collection is one of the imperative instruments of decision-making hypothesis. Collection operators are not simply the operators that normalize the value; they represent progressively broad values that can underline the entire information. Geometric weighted operators weight the values only, and the ordered weighted geometric operators weight the ordering position only. Both of these operators tend to the value that relates to the biggest weight segment. Hybrid collection operators beat these impediments of weighted total and request total operators. Hybrid collection operators weight the incentive as well as the requesting position. Neutrosophic cubic sets (NCs) are a classification of interim neutrosophic set and neutrosophic set. This distinguishing of neutrosophic cubic set empowers the decision-maker to manage ambiguous and conflicting data even more productively. In this paper, we characterized neutrosophic cubic hybrid geometric accumulation operator (NCHG) and neutrosophic cubic Einstein hybrid geometric collection operator (NCEHG). At that point, we outfitted these operators upon an everyday life issue which empoweredus to organize the key objective to develop the industry. Full article

(This article belongs to the Special Issue New Challenges in Neutrosophic Theory and Applications)

16 pages, 582 KiB

Open AccessArticle

Multi-Criteria Decision-Making Method Using Heronian Mean Operators under a Bipolar Neutrosophic Environment

by Changxing Fan, Jun Ye, Sheng Feng, En Fan and Keli Hu

Mathematics 2019, 7(1), 97; https://doi.org/10.3390/math7010097 - 17 Jan 2019

Cited by 19 | Viewed by 3471

Abstract

In real applications, most decisions are fuzzy decisions, and the decision results mainly depend on the choice of aggregation operators. In order to aggregate information more scientifically and reasonably, the Heronian mean operator was studied in this paper. Considering the advantages and limitations [...] Read more.

In real applications, most decisions are fuzzy decisions, and the decision results mainly depend on the choice of aggregation operators. In order to aggregate information more scientifically and reasonably, the Heronian mean operator was studied in this paper. Considering the advantages and limitations of the Heronian mean (HM) operator, four Heronian mean operators for bipolar neutrosophic number (BNN) are proposed: the BNN generalized weighted HM (BNNGWHM) operator, the BNN improved generalized weighted HM (BNNIGWHM) operator, the BNN generalized weighted geometry HM (BNNGWGHM) operator, and the BNN improved generalized weighted geometry HM (BNNIGWGHM) operator. Then, their propositions were examined. Furthermore, two multi-criteria decision methods based on the proposed BNNIGWHM and BNNIGWGHM operator are introduced under a BNN environment. Lastly, the effectiveness of the new methods was verified with an example. Full article

(This article belongs to the Special Issue New Challenges in Neutrosophic Theory and Applications)

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17 pages, 280 KiB

Open AccessArticle

Neutrosophic Multigroups and Applications

by Vakkas Uluçay and Memet Şahin

Mathematics 2019, 7(1), 95; https://doi.org/10.3390/math7010095 - 17 Jan 2019

Cited by 19 | Viewed by 3315

Abstract

In recent years, fuzzy multisets and neutrosophic sets have become a subject of great interest for researchers and have been widely applied to algebraic structures include groups, rings, fields and lattices. Neutrosophic multiset is a generalization of multisets and neutrosophic sets. In this [...] Read more.

In recent years, fuzzy multisets and neutrosophic sets have become a subject of great interest for researchers and have been widely applied to algebraic structures include groups, rings, fields and lattices. Neutrosophic multiset is a generalization of multisets and neutrosophic sets. In this paper, we proposed a algebraic structure on neutrosophic multisets is called neutrosophic multigroups which allow the truth-membership, indeterminacy-membership and falsity-membership sequence have a set of real values between zero and one. This new notation of group as a bridge among neutrosophic multiset theory, set theory and group theory and also shows the effect of neutrosophic multisets on a group structure. We finally derive the basic properties of neutrosophic multigroups and give its applications to group theory. Full article

(This article belongs to the Special Issue New Challenges in Neutrosophic Theory and Applications)

17 pages, 334 KiB

Open AccessArticle

Neutrosophic Soft Expert Multiset and Their Application to Multiple Criteria Decision Making

by Derya Bakbak, Vakkas Uluçay and Memet Şahin

Mathematics 2019, 7(1), 50; https://doi.org/10.3390/math7010050 - 6 Jan 2019

Cited by 21 | Viewed by 3135

Abstract

In this paper, we have investigated neutrosophic soft expert multisets (NSEMs) in detail. The concept of NSEMs is introduced. Several operations have been defined for them and their important algebraic properties are studied. Finally, we define a NSEMs aggregation operator to construct an [...] Read more.

In this paper, we have investigated neutrosophic soft expert multisets (NSEMs) in detail. The concept of NSEMs is introduced. Several operations have been defined for them and their important algebraic properties are studied. Finally, we define a NSEMs aggregation operator to construct an algorithm for a NSEM decision-making method that allows for a more efficient decision-making process. Full article

(This article belongs to the Special Issue New Challenges in Neutrosophic Theory and Applications)

9 pages, 909 KiB

Open AccessArticle

Design of Fuzzy Sampling Plan Using the Birnbaum-Saunders Distribution

by Muhammad Zahir Khan, Muhammad Farid Khan, Muhammad Aslam and Abdur Razzaque Mughal

Mathematics 2019, 7(1), 9; https://doi.org/10.3390/math7010009 - 21 Dec 2018

Cited by 9 | Viewed by 3605

Abstract

Acceptance sampling is one of the essential areas of quality control. In a conventional environment, probability theory is used to study acceptance sampling plans. In some situations, it is not possible to apply conventional techniques due to vagueness in the values emerging from [...] Read more.

Acceptance sampling is one of the essential areas of quality control. In a conventional environment, probability theory is used to study acceptance sampling plans. In some situations, it is not possible to apply conventional techniques due to vagueness in the values emerging from the complexities of processor measurement methods. There are two types of acceptance sampling plans: attribute and variable. One of the important elements in attribute acceptance sampling is the proportion of defective items. In some situations, this proportion is not a precise value, but vague. In this case, it is suitable to apply flexible techniques to study the fuzzy proportion. Fuzzy set theory is used to investigate such concepts. It is observed there is no research available to apply Birnbaum-Saunders distribution in fuzzy acceptance sampling. In this article, it is assumed that the proportion of defective items is fuzzy and follows the Birnbaum-Saunders distribution. A single acceptance sampling plan, based on binomial distribution, is used to design the fuzzy operating characteristic (FOC) curve. Results are illustrated with examples. One real-life example is also presented in the article. The results show the behavior of curves with different combinations of parameters of Birnbaum-Saunders distribution. The novelty of this study is to use the probability distribution function of Birnbaum-Saunders distribution as a proportion of defective items and find the acceptance probability in a fuzzy environment. This is an application of Birnbaum-Saunders distribution in fuzzy acceptance sampling. Full article

(This article belongs to the Special Issue New Challenges in Neutrosophic Theory and Applications)

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12 pages, 300 KiB

Open AccessArticle

On Generalized Closed Sets and Generalized Pre-Closed Sets in Neutrosophic Topological Spaces

by Wadei Al-Omeri and Saeid Jafari

Mathematics 2019, 7(1), 1; https://doi.org/10.3390/math7010001 - 20 Dec 2018

Cited by 26 | Viewed by 4132

Abstract

In this paper, the concept of generalized neutrosophic pre-closed sets and generalized neutrosophic pre-open sets are introduced. We also study relations and various properties between the other existing neutrosophic open and closed sets. In addition, we discuss some applications of generalized neutrosophic pre-closed [...] Read more.

In this paper, the concept of generalized neutrosophic pre-closed sets and generalized neutrosophic pre-open sets are introduced. We also study relations and various properties between the other existing neutrosophic open and closed sets. In addition, we discuss some applications of generalized neutrosophic pre-closed sets, namely neutrosophic

p T_{\frac{1}{2}}

space and neutrosophic

g p T_{\frac{1}{2}}

space. The concepts of generalized neutrosophic connected spaces, generalized neutrosophic compact spaces and generalized neutrosophic extremally disconnected spaces are established. Some interesting properties are investigated in addition to giving some examples. Full article

(This article belongs to the Special Issue New Challenges in Neutrosophic Theory and Applications)

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