The neutrosophic set consists of three fuzzy sets called true membership function, false membership function and indeterminate membership function. MBJ-neutrosophic structure is a structure constructed using interval-valued fuzzy set instead of indeterminate membership function in the neutrosophic set. In general, the indeterminate part appears in a wide range. So instead of treating the indeterminate part as a single value, it is treated as an interval value, allowing a much more comprehensive processing. In an attempt to apply the MBJ-neutrosophic structure to ordered BCI-algebras, the notion of MBJ-neutrosophic (ordered) subalgebras is introduced and their properties are studied. The relationship between MBJ-neutrosophic subalgebra and MBJ-neutrosophic ordered subalgebra is established, and MBJ-neutrosophic ordered subalgebra is formed using (intuitionistic) fuzzy ordered subalgebra.

<p>The development of smart cities has been gaining attention not only in India but across borders. The development of these cities is supposed to bring India as a smart India in the global market. With all odds in favor; these projects are not gaining their expected on-time results. This has motivated us to think that there are loopholes that are putting hindrance to smart cities development. The aim of this study is to identify and prioritize mathematically the key barriers using the neutrosophic PESTEL analysis technique. An extensive literature survey of the problem provides a lot of factors which are categorized in six main factors such as social, political, legal, ethical and technological factors. Present work using neutrosophic PESTEL analysis finds that social and political factors with 93% and 83% are the key barriers to the development of smart cities in India. Other factors such as Technological and economic factors come at second position securing percentage 75% and 60% respectively. Environmental and legal factors come at last securing 49% and 43% respectively. The research’s main focus is to identify and prioritize quantitatively the most important barriers which come into smart cities development in India. This research in many ways would aid the Government agencies and policymakers to prioritize the key barriers at an early stage so that the development may take place as expected and get completed within the stipulated time frame.</p>

This research is an extension of classical statistics distribution theory as the theory did not deal with the problems having ambiguity, impreciseness, or indeterminacy. An important life-time distribution called Beta distribution from classical statistics is proposed by considering the indeterminate environment and named the new proposed distribution as neutrosophic beta distribution. Various distributional properties like mean, variance, moment generating function, r-th moment order statistics that includes smallest order statistics, largest order statistics, joint order statistics, and median order statistics are derived. The parameters of the proposed distribution are estimated via maximum likelihood method. Proposed distribution is applied on two real data sets and goodness of fit is assessed through AIC and BIC criteria’s. The estimates of the proposed distribution suggested a better fit than the classical form of Beta distribution and recommended to use when the data in the interval form follows a Beta distribution and have some sort of indeterminacy.

<p>Abstract. For software development companies, deciding which development methodology to use when starting a project is in many cases an important task to perform. The selection of development methodology can be modeled as a decision-making problem. Neutrosophy is a philosophical current that starts from Paradoxism. In this article, we describe a methodology selection proposal using neutrosophic numbers, from which the development methodology proposal is decided. The method allows taking into account the indeterminacy in decision-making, in addition to the use of linguistic terms that are more appropriate than numerical ones. The applicability of the proposal is confirmed through a demonstrative example. The paper ends with the conclusions and recommendations for future work.</p>

<p><strong>Abstract: </strong>Care during pregnancy is a task of high importance for the health system. In Ecuador, special importance has been given to pregnant teenagers. However, there are various factors that influence pregnancy and in many cases it is not possible to prioritize their care. This research aims to develop a model to prioritize the factors that influence teenage pregnancy. The model operates using the neutrosophic DEMATEL method for the study of cause and effect in complex situations. The method implements as a principle the modeling of neutrality using neutrosophic numbers and allows evaluation through the use of linguistic terms, which is a natural form of evaluation for humans.</p>

The purpose of this paper is to introduce new types of neutrosophic crisp sets with three types 1, 2, 3. After given the fundamental definitions and operations, we obtain several properties, and discussed the relation- ship between neutrosophic crisp sets and others. Also, we introduce and study the neutrosophic crisp point and neu- trosophic crisp relations. Possible applications to data- base are touched upon.

Social media is a new observable fact in computer-based technology and neutrosophic theory.Researchers are now thinking of the power of social media in banks as it is the fastest expandingonline noticeable fact and banks with poor presence in social media are facing identity crisis underuncertainty fields. Through social media we can share ideas and information through establishingvirtual networks. Initially it was evident that people used it for personal interaction with friends andrelatives but with changing time it is established that business houses and financial institutionsincluding Banks are using this popular technology to reach out to the prospective customers.Especially in the banking industry digital communication is becoming most popular and powerfulas here consumers' interface is obligatory. Online communication has become a powerful mediumbetween banks and consumers. The power of social media is to connect and share information withpeople across globe. Social Media in Indian Bank is not only a medium of advertising but it alsohelps the Banks to be a part of their customers’ life as this relation involves conversation beyondbusiness under neutrosophic environment. The aim of this study is to find out the best social mediaas per users’ preference and explore its impact on Banks’ business in pentagonal neutrosophic(PNN) arena by increasing customer satisfaction and augment customer relationship managementin banking industry.

The scientific research proposal is part of the task to be carried out in academic and research institutions around the world. This is a complex decision-making problem, because decision-makers must determine the projects that are appropriate to the subjects addressed by the institution, those projects must be achievable within a reasonable deadline, they must have the financial means and the budget necessary to be carried out, the staff must be sufficiently qualified and an optimum number ofpersonnel must be available tosucceed the tasks and not interfere with other research projects. This is a predictive problem, thus, the proposed model is based on Delphi method for evaluating research projects and is supported by neutrosophy. Delphi method is widely applied in the prediction of future events, in this model we introduce the uncertainty and indeterminacy modeled with neutrosophy. As the best of our knowledge, this model is the first one, which applies a neutrosophic Delphi method in the evaluation of scientific research proposals. Finally, a hypothetical case study illustrates the applicability of the method.

Stress is an inevitable way of adapting each individual to the challenges of the surrounding environment. When the adaptation is done in a negative way and produces physiological or psychological imbalances in the person, then stress is called distress. However, stress is not always harmful to the person, there is stress in situations of joy or happiness, which is known by eustress. In the work environment, distress can cause physical and mental health problems for workers and therefore damage to the dynamics of the job. This paper aims to propose an index of occupational stress measurement based on the Integrative Model Focused on Personality and the Neutrosophical Psychology Theory. The Integrative Model Focused on Personality considers personality as the result of a combination of dynamically interacting elements, while Neutrosophical Psychology understands personality traits as a triad (<A>, <neutA>, <antiA>), where A is a personality trait, antiA is its opposite, and the trait manifests itself in each person in an intermediate way between <A> and <antiA>, where <neutA> is an intermediate state of indeterminacy, where it is neither A nor antiA. Particularly, we explicitly consider the case in which the individual is identified in an intermediate state of stress and therefore has a risk to be conducted towards either the distress or the eustress