Degree Of Indeterminacy Research Articles

An application of neutrosophic logic in the confirmatory data analysis of the satisfaction with life scale

The main concept of neutrosophy is that any idea has not only a certain degree of truth but also a degree of falsity and indeterminacy in its own right. Although there are many applications of neutrosophy in different disciplines, the incorporation of its logic in education and psychology is rather scarce compared to other fields. In this study, the Satisfaction with Life Scale was converted into the neutrosophic form and the results were compared in terms of confirmatory analysis by convolutional neural networks. To sum up, two different formulas are proposed at the end of the study to determine the validity of any scale in terms of neutrosophy. While the Lawshe methodology concentrates on the dominating opinions of experts limited by a one-dimensional data space analysis, it should be advocated that the options can be placed in three-dimensional data space in the neutrosophic analysis . The effect may be negligible for a small number of items and participants, but it may create enormous changes for a large number of items and participants. Secondly, the degree of freedom of Lawshe technique is only 1 in 3D space, whereas the degree of freedom of neutrosophical scale is 3, so researchers have to employ three separate parameters of 3D space in neutrosophical scale while a resarcher is restricted in a 1D space in Lawshe technique in 3D space. The third distinction relates to the analysis of statistics. The Lawhe technical approach focuses on the experts' ratio of choices, whereas the importance and correlation level of each item for the analysis in neutrosophical logic are analysed. The fourth relates to the opinion of experts. The Lawshe technique is focused on expert opinions, yet in many ways the word expert is not defined. In a neutrosophical scale, however, researchers primarily address actual participants in order to understand whether the item is comprehended or opposed to or is imprecise. In this research, an alternative technique is presented to construct a valid scale in which the scale first is transformed into a neutrosophical one before being compared using neural networks. It may be concluded that each measuring scale is used for the desired aim to evaluate how suitable and representative the measurements obtained are so that its content validity can be evaluated.

STRESS STATE OF COMPRESSED REINFORCED CONCRETE ELEMENTS CONSIDERING CREEP AND INFLUENCE OF AN AGGRESSIVE ENVIRONMENT

Problems associated with the joint long-term action of load and aggressive environment, both in limiting and over-limiting states, are studied bad. Such a combination leads to degradation of materials and changes in the stress-strain state of reinforced concrete structures over time. In case of joint action, they can have mutually increasing damaging effect. Among the many environmental influences encountered, the most aggressive in relation to concrete on cement binder is the impact of sulfates, and in relation to steel reinforcement – the impact of chlorides. It is shown that the stress-strain state of reinforced concrete compressed elements with regard to creep and influence of aggressive environment is formed in time. The deformation in concrete and reinforced concrete compressed elements depends on the stress level. If the stresses are less than the long-term strength, the deformations in time are attenuated, when the stresses in concrete are greater than the long-term strength, the deformations increase. Reinforcement restrains deformations in concrete, while corrosive medium increases creep deformations. When solving these problems we encounter internally statically indeterminate systems. The degree of static indeterminacy is greater than in the case of calculation of reinforced concrete structures without taking into account the influence of the external environment. When the process of soaking is considered, it is possible to consider the influence of the external environment as not aggressive. A solution to the problem using the theory of elastic heredity has been obtained, but it can be shown that a solution using other theories - the theory of aging or the hereditary theory of aging - is also possible. The above solution is true for reinforced concrete elements exposed to external influences at a sufficiently mature age, which can be considered one year or more from the date of manufacture of the structure.

Initial abundance and stochasticity influence competitive outcome in communities.

Predicting competitive outcomes in communities frequently involves inferences based on deterministic population models since these provide clear criteria for exclusion (e.g. R* rule) or long-term coexistence (e.g. mutual invasibility). However, incorporating stochasticity into population- or community-level processes into models is necessary if the goal is to explain variation in natural systems, which are inherently stochastic. Similarly, in systems with demographic or environmental stochasticity, weaker competitors have the potential to exclude superior competitors, contributing to what is known as 'competitive indeterminacy'. The importance of such effects for natural communities is unknown, in part because it is difficult to demonstrate that multiple forms of stochasticity are present in these communities. Moreover, the effects of multiple forms of stochasticity on competitive outcomes are largely untested, even in theory. Here, we address these issues by examining the role of stochasticity in replicated communities of flour beetles (Tribolium sp.). To do so, we developed a set of two-species stochastic Ricker models incorporating four distinct forms of stochasticity: environmental stochasticity, demographic stochasticity, demographic heterogeneity and stochastic sex determination. By fitting models to experimental data, and simulating fit models to examine long- term behaviour, we found that both the duration of transient coexistence and the degree of competitive indeterminacy were sensitive to the forms of stochasticity included in our models. These findings suggest the current estimates of extinction risk, coexistence and time until competitive exclusion in communities may not be accurate when based on models that exclude relevant forms of stochasticity.

On the Forms and Thorns of Linguistic Indeterminacy in Chinese Law

Abstract This study addresses the different types and implications of linguistic indeterminacy in Chinese law. It firstly draws on the studies of scholars of different disciplines, such as linguistics and philosophy of language, to provide a taxonomy of indeterminacy in language. It then provides examples of each type, highlighting the implications in law and legal interpretation. It uses linguistic data from various texts, such as statutory laws and judgements, and analyses them with various methods, including discourse analysis and corpus linguistics. This study argues that when the language of the law is indeterminate, the legal outcomes may be particularly uncertain. It suggests that although it is difficult to ascertain whether the degree of indeterminacy is higher in some languages more than in others, some linguistic mechanisms at the word-formation level in Chinese, such as portmanteaus and the modifier-modified structure, are remarkably ambiguous. When uncertain terms are in key parts of the law, the consequences may be more serious. The study of linguistic indeterminacy in Chinese has implications for the study of forensic linguistics, and Chinese studies in general.

Triangular Neutrosophic Cognitive Map for Multistage Sequential Decision-Making Problems

Nowadays, fuzzy cognitive maps (FCMs) are one of the most efficient artificial intelligence techniques for modeling large and complex systems. However, traditional FCMs have the limitation of not representing the indeterminacy situations presented in many decision-making problems. To overcome this limitation, neutrosophic cognitive maps (NCMs) were proposed as a new extension of traditional FCMs. Nevertheless, the way that NCMs reported in the bibliography handle the indeterminacy is still insufficient since they cannot quantify the degree of indeterminacy. Moreover, there are decision-making problems in which decisions should be considered as a sequence of decisions hardly interconnected in sequential order. This situation is presented in scenarios such as projects evaluation characterized by the existence of multiple interconnected processes (diagnosis, decision, and prediction). The lack of a suitable FCMs topology for modeling this kind of decision-making problems constitutes another challenging issue of FCMs. This paper presents a new neutrosophic cognitive map based on triangular neutrosophic numbers for multistage sequential decision-making problems (MS-TrNCM). In the proposed model, all the map’s connections are represented by triangular neutrosophic numbers, making it possible for decision makers to express their preferences considering the truth, indeterminacy, and falsity degrees. Furthermore, a new topology for representing multistage sequential processes is introduced. The suggested MS-TrNCM is applied to make diagnoses, decisions, and predictions during the evaluation of 1011 projects records from project evaluation database ”uci-gp-eval-201903051137” provided by the University of Informatics Sciences. In validation process, the superiority of the proposed MS-TrNCM over the NCMs and traditional FCMs has been demonstrated.

Characterization of a new rice OsMADS1 null mutant generated by homologous recombination-mediated gene targeting.

A new, stable, null mutant of OsMADS1 generated by homologous recombination-based gene targeting in an indica rice confirms its regulatory role for floral meristem identity, its determinate development and floral organ differentiation. OsMADS1, an E-class MADS-box gene, is an important regulator of rice flower development. Studies of several partial loss-of-function and knockdown mutants show varied floret organ defects and degrees of meristem indeterminacy. The developmental consequences of a true null mutant on floret meristem identity, its determinate development and differentiation of grass-specific organs such as the lemma and palea remain unclear. In this study, we generated an OsMADS1 null mutant by homologous recombination-mediated gene targeting by inserting a selectable marker gene (hpt) in OsMADS1 and replacing parts of its cis-regulatory and coding sequences. A binary vector was constructed with diphtheria toxin A chain gene (DT-A) as a negative marker to eliminate random integrations and the hpt marker for positive selection of homologous recombination. Precise disruption of the endogenous OsMADS1 locus in the rice genome was confirmed by Southern hybridization. The homozygous osmads1ko null mutant displayed severe defects in all floral organs including the lemma and palea. We also noticed striking instances of floral reversion to inflorescence and vegetative states which has not been reported for other mutant alleles of OsMADS1 and further reinforces the role of OsMADS1 in controlling floral meristem determinacy. Our data suggest, OsMADS1 commits and maintains determinate floret development by regulating floral meristem termination, carpel and ovule differentiation genes (OsMADS58, OsMADS13) while its modulation of genes such as OsMADS15, OsIG1 and OsMADS32 could be relevant in the differentiation and development of palea. Further, our study provides an important perspective on developmental stage-dependent modulation of some OsMADS1 target genes.

Supplier Selection Problem with Type-2 Fuzzy Parameters: A Neutrosophic Optimization Approach

This paper investigates the multiobjective supplier selection problem (SSP) with type-2 fuzzy parameters. All the involved parameters such as aggregate demand, budget allocation, quota flexibility, rating values, are depicted as type-2 triangular fuzzy (T-2TF) parameters. To tackle the T-2TF, first, critical values (CV)-based reduction method is introduced, and then chance-constrained programming is modeled to obtain the crisp version of the multiobjective SSP. Secondly, an interval-based approximation method is also developed for defuzzifying the T-2TF parameters. Further, a novel interactive neutrosophic programming approach is also suggested to solve the deterministic multiobjective SSP, which allows the decision-makers to incorporate the neutral thoughts or indeterminacy degrees efficiently. The computational study is presented to verify and validate the defuzzfied techniques and the proposed solution approach. An ample opportunity to select the most desired compromise solution with maximum overall satisfaction level is also addressed. Finally, the conclusions and future research direction are revealed based on the discussed work.

A generalized approach to indeterminacy in linear rational expectations models

We propose a novel approach to deal with the problem of indeterminacy in linear rational expectations models. The method consists of augmenting the original state space with a set of auxiliary exogenous equations to provide the adequate number of explosive roots in presence of indeterminacy. The solution in this expanded state space, if it exists, is always determinate, and is identical to the indeterminate solution of the original model. The proposed approach accommodates determinacy and any degree of indeterminacy, and it can be implemented even when the boundaries of the determinacy region are unknown. Thus, the researcher can estimate the model using standard software packages without restricting the estimates to the determinacy region. We combine our solution method with a novel hybrid Metropolis–Hastings algorithm to estimate the New–Keynesian model with rational bubbles by Galí (2021) over the period 1982:Q4–2007:Q3. We find that the data support the presence of two degrees of indeterminacy, implying that the central bank was not reacting strongly enough to the bubble component.

Analytical model for the basement wall horizontally supported by flexible floor diaphragms

Subterranean floors are treated as the rigid lateral support in the current practice for the basement wall design. The structural performance of the basement wall will be influenced by the floor openings, which are inevitable to satisfy building functional requirements. An analytical model for the basement wall being presented is able to analyze the effect of such opening quantitatively. The magnitude of the horizontal support stiffness is determined based on deformation analysis of the diaphragm opening area. Idealized models of the basement wall are continuous beams with various degrees of indeterminacy. The force method is used to deduce the functions for internal forces acting towards the basement wall. The proposed analytical model is verified with results derived by finite element analyses through consideration of various factors, including various numbers of stories, combinations of beam-slab sections, and percentages of floor opening dimensions. The maximum deviations on critical design sections for all prototype basement structures are less than 15.99%. Comparisons with conventional rigid support models are also performed, providing an estimation of the effect of the opening on the mechanical behavior of the basement wall.

Introduction to Neutrosophic Genetics

Neutrosophic Genetics is the study of genetics using neutrosophic logic, set, probability, statistics, measurement, and other neutrosophic tools and procedures. In this paper, based on the Neutrosophic Theory of Evolution (that includes degrees of Evolution, Neutrality (or Indeterminacy), and Involution) – as an extension of Darwin’s Theory of Evolution, we show the applicability of neutrosophy in genetics, and we present within the frame of neutrosophic genetics the following concepts: neutrosophic mutation, neutrosophic speciation, and neutrosophic coevolution

Nonlinear analysis of constructions from different materials based on unified plastic constitutive relations

In the paper the plastic constitutive relations based on the hypotheses of the plastic flow theory, unified for different materials, such as soil ground, concrete, metal etc. are proposed. These plastic constitutive relations are based on the hypotheses of the Mises-Schleicher-Botkin theory of failure. The strength characteristics of materials, determined by standard methods, are redefined for octahedral sites, they are invariants for. The problem is solved by the finite element method (FEM). The calculation model MFOE made up of singular finite elements (tetrahedral, triangular plates, rods). This fact increases the accuracy of the description of loading paths in finite elements and ensures a unique correspondence of the constitutive equations to elementary volumes of the construction. The use of singular finite elements is associated with a large amount of access memory for storing the stiffness matrix of the system. So, the range of practically solvable problems limits significantly. To eliminate this contradiction, the Newton’s iteration method – SOR method is developed for equilibrium equations solving in the design of finite elements structures. An iterative algorithm is obtained. It does not require assembly of the system stiffness matrix for its implementation. The volume of operational information is proportional to the number of finite elements in the system. Due to the traditional approach, which requires the assembly of the system stiffness matrix, the amount of operational information is proportional to the square of the degree of kinematic indeterminacy of the system. While using the iterative algorithm, the size of the stiffness matrix and the time of solving are reduced. The results of a nonlinear analysis of soil massifs and concrete structures are represented.

Solving intuitionistic fuzzy multiobjective linear programming problem under neutrosophic environment

The existence of neutral /indeterminacy degrees reflects the more practical aspects of decision-making scenarios. Thus, this paper has studied the intuitionistic fuzzy multiobjective linear programming problems (IFMOLPPs) under neutrosophic uncertainty. To highlight the degrees of neutrality in IFMOLPPs, we have investigated the neutrosophic optimization techniques with intuitionistic fuzzy parameters. The marginal evaluation of each objective is determined by three different membership functions, such as truth, indeterminacy, and falsity membership degrees under the neutrosophic environment. The marginal evaluation of each objective function is elicited by various sorts of membership functions such as linear, exponential, and hyperbolic types of membership functions, which signifies an opportunity for decision-makers to select the desired membership functions. The developed neutrosophic optimization technique is implemented on existing numerical problems that reveal the validity and applicability of the proposed methods. A comparative study is also presented with other approaches. At last, conclusions and future research directions are addressed based on the proposed work.

Quantification of the redundancy distribution in truss and beam structures

The degree of statical indeterminacy as a fundamental property in structural mechanics is today mainly known as a property of a complete system without any information about its spatial distribution. The redundancy matrix provides information about the distribution of statical indeterminacy in the system and by this gives an additional valuable insight into the load-bearing behaviour. The derivation and definition of the redundancy matrix are presented based on truss systems and its mathematical properties and their mechanical interpretations are provided. The definition of the redundancy matrix is extended to other discrete systems like beam structures and a definition of the redundancy density is given for the continuous 1D case. Potential applications of the concept include robust design of structures, quantification of imperfection sensitivity as well as assessment of optimal actuator placement in adaptive structures.

Modelling imperfections in unreinforced masonry structures: Discrete element simulations and scale model experiments of a pavilion vault

The structural assessment of doubly-curved vaulted masonry structures, such as pavilion vaults, poses challenges specific to their high degree of indeterminacy. Two-dimensional equilibrium analysis methods may provide a lower bound of load or displacement capacity, but they do not accurately describe the three-dimensional (3D) behaviour of these structures, particularly when shear deformation (e.g. sliding) is important. Therefore, discrete element modelling (DEM) methods, which can effectively simulate 3D load re-distribution, have been used to investigate support displacement capacity and corresponding 3D collapse mechanisms. DEM analyses are usually conducted on perfect digital geometries. Meanwhile, both real structures and small-scale physical models have implicit assembly and fabrication imperfections, which may significantly alter their response. The present paper aims to investigate the influence of geometrical and mechanical imperfections by comparing DEM analyses with the results obtained from tests on a scale model. In particular, a new method to simulate imperfections within the DEM framework is proposed, and a DEM parametric analysis is compared to the measured behaviour of a 3D-printed scale model of a pavilion (or cloister) vault on spreading supports. The influence of both mechanical imperfections andgeometrical imperfections, due to element geometry deviations or imprecision of the assembly process, have been investigated. Based on these analyses, the three-dimensional behaviour of a pavilion vault subjected to horizontal displacement of the supports is described, and the variability of results due to imperfections is demonstrated. A good agreement between DEM analyses and 3D-printed scale model tests is achieved, in terms of crack patterns and mechanisms. Geometrical imperfections did change the load paths within the vault, as expected, and also influenced the displacement capacity.

Some aggregation operators of neutrosophic Z-numbers and their multicriteria decision making method

As the generalization of the classical fuzzy number, the concept of Z-number introduced by Zadeh indicates more ability to depict the human knowledge and judgments of both restraint and reliability as an order pair of fuzzy numbers. In indeterminacy and inconsistent environment, a neutrosophic set is described by the truth, falsity, and indeterminacy degrees, but they lack measures related to reliability. To describe the hybrid information of combining the truth, falsity and indeterminacy degrees with their corresponding reliability degrees, this paper first proposes the concept of a neutrosophic Z-number (NZN) set, which is a new framework of neutrosophic values combined with the neutrosophic measures of reliability, as the generalization of the Z-number and the neutrosophic set. Then, we define the operations of neutrosophic Z-numbers (NZNs) and a score function for ranking NZNs. Next, we present NZN weighted arithmetic averaging (NZNWAA) and NZN weighted geometric averaging (NZNWGA) operators to aggregate NZN information and investigate their properties. Regarding the NZNWAA and NZNWGA operators and the score function, a multicriteria decision making (MDM) approach is developed in the NZN environment. Finally, an illustrative example about the selection problem of business partners is given to demonstrate the applicability and effectiveness of the developed MDM approach in NZN setting.

An Ultrasound Image Enhancement Method Using Neutrosophic Similarity Score.

Ultrasound images, having low contrast and noise, adversely impact in the detection of abnormalities. In view of this, an enhancement method is proposed in this work to reduce noise and improve contrast of ultrasound images. The proposed method is based on scaling with neutrosophic similarity score (NSS), where an image is represented in the neutrosophic domain through three membership subsets T, I, and F denoting the degree of truth, indeterminacy, and falseness, respectively. The NSS measures the belonging degree of pixel to the texture using multi-criteria that is based on intensity, local mean intensity and edge detection. Then, NSS is utilized to extract the enhanced coefficient and this enhanced coefficient is applied to scale the input image. This scaling reflects contrast improvement and denoising effect on ultrasound images. The performance of proposed enhancement method is evaluated on clinical ultrasound images, using both subjective and objective image quality measures. In subjective evaluation, with proposed method, overall best score of 4.3 was obtained and that was 44% higher than the score of original images. These results were also supported by objective measures. The results demonstrated that the proposed method outperformed the other methods in terms of mean brightness preservation, edge preservation, structural similarity, and human perception-based image quality assessment. Thus, the proposed method can be used in computer-aided diagnosis systems and to visually assist radiologists in their interactive-decision-making task.

Multi-objective linguistic-neutrosophic matrix game and its applications to tourism management

Game theory plays an important role in numerous decision-oriented real-life problems. Nowadays, many such problems are basically characterized by various uncertainties. Uncertainties come to happen due to decision makers' collection of data, intuition, assumption, judgement, behaviour, evaluation and lastly, due to the problem itself. Fuzzy concept with membership degree made an initialization towards the treatment of uncertainty, but it was not enough. Intuitionistic fuzzy concept was evolved concerning with both membership and non-membership degrees but failed to express reality more accurately. Then, neutrosophy logic was developed with a new degree in uncertainty, say, indeterminacy degree besides membership and non-membership degrees. Multi-objective optimization is an area of multiple-criteria decision making related with mathematical optimization problems involving more than one objective function to be optimized at the same time. Game theory (matrix game) problems with imprecise, vague information, like neutrosophic, can be formed with multiple objective functions. We develop and analyse a matrix game with multiple objectives, and solve the problem under a single-valued neutrosophic environment in linguistic approach. The main achievement of our study is that we here introduce a problem-oriented example to justify our designed methodologies with a successful real-life implications using linguistic neutrosophic data rather than crisp data as used in previous researches.

The current state of development of the no significant harm principle: How far have we come?

The duty to prevent significant transboundary harm remains a cornerstone principle of international law, and especially of international environmental and water resources law. However, this rule focuses on the conduct of a State where harm originates, rather than on the fact that harm has resulted from such conduct, and thus requires that States exercise due diligence in anticipating and in preventing or mitigating such harm. At a practical level, the due diligence standard of conduct expected of States can be uncertain and difficult to determine, as it must be deduced from the applicable primary rules of international environmental or water resources law, which have traditionally been elaborated in rather vague terms. In addition, the standard of due diligence required under the no-harm rule may be influenced by a range of variable and context-specific factors which might prove relevant in the particular circumstances of any dispute. Such uncertainty is further compounded in the field of international water law by the complex interrelationship between the no-harm rule and the other key norms of international water law, particularly the cardinal principle of equitable and reasonable utilization, which embodies a high degree of flexibility and adaptability and suffers from a corresponding degree of normative indeterminacy. Thankfully, recent developments in international water law and related practice regarding the requirement to protect riverine ecosystems and maintain related ecosystem services lend a welcome measure of clarity as regards the preventive measures expected of watercourse States under international law. Judicial recognition of obligations to maintain minimum environmental flows and to preserve or restore riverine ecosystem services, based on the proliferation of such values in treaty and declarative practice, along with the continuing development of sophisticated technical methodologies for ecosystems assessment and evaluation, do much to inform the due diligence conduct required of States. Such advances can only enhance the practical utility of the no-harm rule, and thus of the entire corpus of international water law, in addressing the challenges emerging globally for water resources management in the twenty-first century.

Dimensionality Reduction Technique in Decision Making Using Pythagorean Fuzzy Soft Matrices

Background:Dimensionality reduction plays an effective role in downsizing the data having irregular factors and acquires an arrangement of important factors in the information. Sometimes, most of the attributes in the information are found to be correlated and hence redundant. The process of dimensionality reduction has a wider applicability in dealing with the decision making problems where a large number of factors are involved.Objective:To take care of the impreciseness in the decision making factors in terms of the Pythagorean fuzzy information which is in the form of soft matrix. The perception of the information has the parameters - degree of membership, degree of indeterminacy (neutral) and degree of nonmembership, for a broader coverage of the information.Methods:We first provided a technique for finding a threshold element and value for the information provided in the form of Pythagorean fuzzy soft matrix. Further, the proposed definitions of the object-oriented Pythagorean fuzzy soft matrix and the parameter-oriented Pythagorean fuzzy soft matrix have been utilized to outline an algorithm for the dimensionality reduction in the process of decision making.Results:The proposed algorithm has been applied in a decision making problem with the help of a numerical example. A comparative analysis in contrast with the existing methodologies has also been presented with comparative remarks and additional advantages.Conclusion:The example clearly validates the contribution and demonstrates that the proposed algorithm efficiently encounters the dimension reduction. The proposed dimensionality reduction technique may further be applied in enhancing the performance of large scale image retrieval.

Pythagorean fuzzy MULTIMOORA method based on distance measure and score function: its application in multicriteria decision making process

The MULTIMOORA method is better than some of the existing decision making methods. However, it has not been improved to process Pythagorean fuzzy sets (PFSs). The decision results of the MULTIMOORA method greatly depend on the distance measure and score function. Although there are many studies focusing on proposing distance measures and score functions for PFSs, they still show some defects. In this paper, we propose two novel distance measures and a novel score function for PFSs for proposing a novel Pythagorean fuzzy MULTIMOORA method. To this end, two distance measures, Dice distance and Jaccard distance, are proposed for computing the deviation degree between two PFSs, and their general forms are also discussed. Afterward, a novel score function based on determinacy degree and indeterminacy degree is put forward for approximately representing PFSs. Then, the original MULTIMOORA method is extended by using the Dice distance and score function and it is used to solve the multicriteria decision making problems under the PFS information context. Finally, a real case for evaluating solid-state disk productions is handled using the proposed Pythagorean fuzzy MULTIMOORA method and another case for evaluating energy projects is given to verify the advantages of our studies by comparing them with the existing Pythagorean fuzzy distance measures, score functions, and decision making methods.