New logarithmic operational laws and their applications to multiattribute decision making for single-valued neutrosophic numbers

Neutrosophic set, initiated by Smarandache, is a novel tool to deal with vagueness considering the truth, indeterminacy and falsity memberships satisfying the condition that their sum is less than 3. This set can be used to characterize the information more accurately than the intuitionistic fuzzy set. Under this set, the objective of this manuscript is to present some new operational laws called as logarithm operational laws with real number base k for the single-valued neutrosophic (SVN) numbers. Various desirable properties of the proposed operational laws are contemplated. Further, based on these laws, different weighted averaging and geometric aggregation operators are developed

Some New Operations of ( alpha, , ) Interval Cut Set of Interval Valued Neutrosophic Sets

In this paper, we define the disjunctive sum, difference and Cartesian product of two interval valued neutrosophic sets and study their basic properties

Derivatives and indefinite integrals of single valued neutrosophic functions

With the continuous development of the fuzzy set theory, neutrosophic set theory can better solve uncertain, incomplete and inconsistent information. As a special subset of the neutrosophic set, the single-valued neutrosophic set has a significant advantage when the value expressing the degree of membership is a set of finite discrete numbers. Therefore, in this paper, we first discuss the change values of single-valued neutrosophic numbers when treating them as variables and classifying these change values with the help of basic operations. Second, the convergence of sequences of single-valued neutrosophic numbers are proposed based on subtraction and division operations. Further, we depict the concept of single-valued neutrosophic functions (SVNF) and study in detail their derivatives and differentials. Finally, we develop the two kinds of indefinite integrals of SVNF and give the relevant examples

Neutrosophic Statistics to Analyze Prevalence of Dental Fluorosis

Fluorine is a mineral that has been worldwide used for treating teeth, as it is effective in preventing dental cavities. That is why fluorine has been incorporated into toothpastes, as well as in some foods. However, excessive consumption of this mineral constitutes a serious oral health problem. This paper analyzes the occurrence of fluorosis, which is the disease caused by excessive consumption of fluorine, in children belonging to El Oro Educational Unit, located in the Central Ecuadorian Sierra. The study was carried out by means of a survey applied to the children’s parents, and the direct study of the infants’ teeth. Data is statistically processed, however, during the analysis of the data some of them had indeterminacies, so we decided that the best tool to use is Neutrosophic Statistics, because this theory studies statistics techniques in situations where there is indeterminacy in the data, in the population size, or in the parameters of the hypothesis tests. Moreover, this study has an important impact on the knowledge about the oral health of the children who attend this educational unit. In addition, it is a precedent for improving oral hygiene habits in infants

Neutrosophic Project Evaluation and Review Techniques

One of the most important and challenging jobs that any manager can take in the management of a large scale project that requires coordinating numerous activities throughout the organization. Initially, the activity times are static within the CPM technique and probabilistic within the PERT technique. Since neutrosophic set is the generalization of fuzzy set and intuitionistic fuzzy set, a new method of project evaluation and review technique for a project network in neutrosophic environment is proposed in this paper. Considering single valued neutrosophic number as the time of each activity in the project network, neutrosophic expected task time, neutrosophic variance, neutrosophic critical path and the neutrosophic total expected time for completing the project network are calculated here. The main concept of Neutrosophic Project Evaluation and Review Technique(NPERT) method is to solve the ambiguities in the activity times of a project network easily than other existing methods like classical PERT, Fuzzy PERT etc.The proposed method is explained by an illustrative example and the results are discussed here

A hybrid neutrosophic-grey analytic hierarchy process method : decision-making modelling in uncertain environments

The analytic hierarchy process (AHP) is recognised as one of the most commonly applied methods in the multiple attribute decision-making (MADM) literature. In the AHP, encompassing uncertainty feature necessitates using suitable uncertainty theories, since dealing efficiently with uncertainty in subjective judgements is of great importance in real-world decision-making problems. The neutrosophic set (NS) theory and grey systems are two reliable uncertainty theories which can bring considerable benefits to uncertain decision-making. The aim of this study is to improve uncertain decision-making by incorporating advantages of the NS and grey systems theories with the AHP in investigating sustainability through agility readiness evaluation in large manufacturing plants. This study pioneers a combined neutrosophic-grey AHP (NG-AHP) method for uncertain decision-making modelling. The applicability of the hybrid NG-AHP method is shown in an illustrative real-case study for agility evaluations in the Iranian steel industry. The computational results indicate the effectiveness of the proposed method in adequately capturing uncertainty in the subjective judgements of decision makers. In addition, the results verify the significance of the research in group decision-making under uncertainty. The practical outcome reveals that, to become a more sustainable agile steel producer in the case country, they should first focus on the “organisation management agility” as the most significant criterion in the assessment followed by “manufacturing process agility,” “product design agility,” “integration of information system,” and “partnership formation capability,” respectively

NIDUS IDEARUM. Scilogs, IV: vinculum vinculorum

Welcome into my scientific lab! My lab[oratory] is a virtual facility with non-controlled conditions in which I mostly perform scientific meditation and chats: a nest of ideas (nidus idearum, in Latin). I called the jottings herein scilogs (truncations of the words scientific, and gr. Λόγος – appealing rather to its original meanings ground , opinion , expectation ), combining the welly of both science and informal (via internet) talks (in English, French, and Romanian). * In this fourth book of scilogs collected from my nest of ideas, one may find new and old questions and solutions, referring mostly to topics on NEUTROSOPHY – email messages to research colleagues, or replies, notes about authors, articles, or books, so on. Feel free to budge in or just use the scilogs as open source for your own ideas

Some New Operations of (α,β,γ) Interval Cut Set of Interval Valued Neutrosophic Sets

In this paper, we define the disjunctive sum, difference and Cartesian product of two interval valued neutrosophic sets and study their basic properties. The notions of the (α,β,γ) interval cut set of interval valued neutrosophic sets and the (α,β,γ) strong interval cut set of interval valued neutrosophic sets are put forward. Some related properties have been established with proof, examples and counter examples

NIDUS IDEARUM. Scilogs, V: joining the dots

My lab[oratory] is a virtual facility with noncontrolled conditions in which I mostly perform scientific meditation and chats: a nest of ideas (nidus idearum, in Latin). I called the jottings herein scilogs (truncations of the words scientific, and gr. Λόγος – appealing rather to its original meanings ground , opinion , expectation ), combining the welly of both science and informal (via internet) talks (in English, French, and Romanian). * In this fifth book of scilogs collected from my nest of ideas, one may find new and old questions and solutions, mostly referring to topics on NEUTROSOPHY – email messages to research colleagues, or replies, notes about authors, articles, or books, so on. Feel free to budge in or just use the scilogs as open source for your own ideas