Indeterminate Information Research Articles

Expression and Analysis of Joint Roughness Coefficient Using Neutrosophic Number Functions

In nature, the mechanical properties of geological bodies are very complex, and its various mechanical parameters are vague, incomplete, imprecise, and indeterminate. In these cases, we cannot always compute or provide exact/crisp values for the joint roughness coefficient (JRC), which is a quite crucial parameter for determining the shear strength in rock mechanics, but we need to approximate them. Hence, we need to investigate the anisotropy and scale effect of indeterminate JRC values by neutrosophic number (NN) functions, because the NN is composed of its determinate part and the indeterminate part and is very suitable for the expression of JRC data with determinate and/or indeterminate information. In this study, the lower limit of JRC data is chosen as the determinate information, and the difference between the lower and upper limits is chosen as the indeterminate information. In this case, the NN functions of the anisotropic ellipse and logarithmic equation of JRC are developed to reflect the anisotropy and scale effect of JRC values. Additionally, the NN parameter ψ is defined to quantify the anisotropy of JRC values. Then, a two-variable NN function is introduced based on the factors of both the sample size and measurement orientation. Further, the changing rates in various sample sizes and/or measurement orientations are investigated by their derivative and partial derivative NN functions. However, an actual case study shows that the proposed NN functions are effective and reasonable in the expression and analysis of the indeterminate values of JRC. Obviously, NN functions provide a new, effective way for passing from the classical crisp expression and analyses to the neutrosophic ones.

Neutrosophic number linear programming method and its application under neutrosophic number environments

In real world, there exists determinate and/or indeterminate information. Hence, the indeterminate problems are inevitable and have to be taken into account in optimization problems. Then, a neutrosophic number (NN) is very suitable for expressing determinate and/or indeterminate information because a NN (\(z=a + bI\)) consists of its determinate part a and its indeterminate part bI for \(a,b\in R\), where the symbol “I” denotes indeterminacy and R is all real numbers. This paper firstly presents some basic operations of NNs and a neutrosophic function involving NNs, which is simply called a NN function and then develops a NN linear programming (NNLP) method to handle NN optimization problems. Moreover, a numerical example and an application of production planning are provided, respectively, to show the solving method and application of NNLP problems. In general, the NNLP method yields the basic NN solutions. Further, the possible ranges of the optimal solution are discussed when the indeterminacy I is specified as a possible interval ranges corresponding to actual requirements in real applications.

Validation of a Medicare Claims-based Algorithm for Identifying Freestanding Ambulatory Surgery Centers

With visits to ambulatory surgery centers (ASCs) on the rise, accountability in the care provided by these facilities and the surgeons who staff them is required. This requires the ability to measure and monitor ASC-based care over time. For this reason, we developed and validated a claims-based algorithm to identify ASCs. Using a 20% sample of Medicare claims (2002-2008), we developed 3 ASC definitions. Definition 1 identified unique facilities with tax identification numbers and appropriate Place of Service and Type of Service codes. Definition 2 had the same conditions but also required specific Specialty codes. Definition 3 involved a multistep cleansing stage, in which facilities with indeterminate information in the fields of interest were eliminated. We assessed agreement between these definitions and findings from alternative data sources. Placing additional requirements on how a freestanding ASC was defined within Medicare claims helped in the refinement of our algorithm. Agreement on the number of unique ASCs in Florida over the study interval was greatest between Definition 3 and the State Ambulatory Surgery Databases (concordance correlation coefficient=0.984; 95%, confidence interval, 0.967-0.992). With the Provider of Services Extract serving as the reference standard, our algorithm (based on Definition 3) had a positive predictive value of 99.0% (95% confidence interval, 98.6%-99.4%) for determining health care markets that experienced the opening of an ASC. The consequent inference is that our algorithm represents an accurate tool for distinguishing and tracking ASCs in Medicare data.

Study on a New Fault Diagnosis Method Based on Combining Intelligent Technologies

In allusion to more indeterminate information and higher speed request characteristic in fault diagnosis system, according to the intelligence complementary strategy, a new fault diagnosis(SWPSO-BPN) model based on combining improved particle swarm optimization (PSO) algorithm and Back-propagation(BP) neural network is proposed in this paper. In the SWPSO-BPN method, an improved PSO (SWPSO) algorithm is proposed to optimize the parameters of BP neural network in order to overcome the shortcomings of slow learning speed and being easy to fall into local minimum, and obtain the optimal values of parameter combination in the BP neural network(SWPSOBPN) model. Then proposed SWPSO-BPN model is applied to diagnose the fault in order to obtain a new fault diagnosis (SWPSO-BPN-FD) method. Finally, the proposed SWPSO-BPN-FD method is used to test the data from bearing data center of CWRU. The experimental results show that the proposed SWPSO-BPN-FD method can accurately and effectively realize high precision fault diagnosis of rolling bearing. And this method takes on strong robustness and generalization ability.

ON NEUTROSOPHIC REFINED SETS AND THEIR APPLICATIONS IN MEDICAL DIAGNOSIS

In this paper, we present some definitions of neutrosophic re¯ned sets such as; union, intersection, convex and strongly convex in a new way to handle the indeterminate information and inconsistent information. Also we have examined some desired properties of neutrosophic refined sets based on these definitions. Then, we give distance measures of neutrosophic refined sets with properties. Finally, an application of neutrosophic re¯ned set is given in medical diagnosis problem (heart disease diagnosis problem) to illustrate the advantage of the proposed approach.

A Neutrosophic Recommender System for Medical Diagnosis Based on Algebraic Neutrosophic Measures

Neutrosophic set has the ability to handle uncertain, incomplete, inconsistent, indeterminate information in a more accurate way. In this paper, we proposed a neutrosophic recommender system to predict the diseases based on neutrosophic set which includes single-criterion neutrosophic recommender system (SC-NRS) and multi-criterion neutrosophic recommender system (MC-NRS). Further, we investigated some algebraic operations of neutrosophic recommender system such as union, complement, intersection, probabilistic sum, bold sum, bold intersection, bounded difference, symmetric difference, convex linear sum of min and max operators, Cartesian product, associativity, commutativity and distributive. Based on these operations, we studied the algebraic structures such as lattices, Kleen algebra, de Morgan algebra, Brouwerian algebra, BCK algebra, Stone algebra and MV algebra. In addition, we introduced several types of similarity measures based on these algebraic operations and studied some of their theoretic properties. Moreover, we accomplished a prediction formula using the proposed algebraic similarity measure. We also proposed a new algorithm for medical diagnosis based on neutrosophic recommender system. Finally to check the validity of the proposed methodology, we made experiments on the datasets Heart, RHC, Breast cancer, Diabetes and DMD. At the end, we presented the MSE and computational time by comparing the proposed algorithm with the relevant ones such as ICSM, DSM, CARE, CFMD, as well as other variants namely Variant 67, Variant 69, and Varian 71 both in tabular and graphical form to analyze the efficiency and accuracy. Finally we analyzed the strength of all 8 algorithms by ANOVA statistical tool.

Neutrosophic Functions of the Joint Roughness Coefficient and the Shear Strength: A Case Study from the Pyroclastic Rock Mass in Shaoxing City, China

Many studies have been carried out to investigate the scale effect on the shear behavior of rock joints. However, existing methods are difficult to determinate the joint roughness coefficient (JRC) and the shear strength of rock joints with incomplete and indeterminate information; the nature of scale dependency of rock joints is still unknown and remains an ongoing debate. Thus, this paper establishes two neutrosophic functions of the JRC values and the shear strength based on neutrosophic theory to express and handle the incomplete and indeterminate problems in the analyses of the JRC and the shear strength. An example, including four rock joint samples derived from the pyroclastic rock mass in Shaoxing city, China, is provided to show the effectiveness and rationality of the developed method. The experimental results demonstrate that the proposed neutrosophic functions can express and deal with the incomplete and indeterminate problems of the test data caused by geometry complexity of the rock joint surface and sampling bias. They provide a new approach for estimating the JRC values of the different-sized test profiles and the peak shear strength of rock joints.

Cross-entropy measure on interval neutrosophic sets and its applications in multicriteria decision making

The neutrosophic set model is an important tool for dealing with real scientific and engineering applications because it can handle not only incomplete information but also the inconsistent information and indeterminate information which exist commonly in real situations. In this paper, we firstly propose two practical techniques converting an interval neutrosophic set into a fuzzy set and a single-valued neutrosophic set, respectively. Then, we define the interval neutrosophic cross-entropy in two different ways, which are based on extension of fuzzy cross-entropy and single-valued neutrosophic cross-entropy. Additionally, two multicriteria decision-making methods using the interval neutrosophic cross-entropy between an alternative and the ideal alternative are developed in order to determine the order of the alternatives and choose most preferred one(s). Finally, an illustrative example is presented to verify the proposed methods and to demonstrate their effectiveness and practicality.

Cross-entropy measure on interval neutrosophic sets and its applications in Multicriteria decision making

The neutrosophic set model is an important tool for dealing with real scientific and engineering applications because it can handle not only incomplete information but also the inconsistent information and indeterminate information which exist commonly in real situations.

Multiple-Attribute Group Decision-Making Method under a Neutrosophic Number Environment

As a neutrosophic number, which consists of a determinate part and an indeterminate part, can more easily and better express incomplete and indeterminate information that exists commonly in real situations.

Dice Similarity Measure between Single Valued Neutrosophic Multisets and Its Application in Medical Diagnosis

This paper introduces the concept of a single valued neutrosophic multiset (SVNM) as a generalization of an intuitionistic fuzzy multiset (IFM) and some basic operational relations of SVNMs, and then proposes the Dice similarity measure and the weighted Dice similarity measure for SVNMs and investigates their properties. Finally, the Dice similarity measure is applied to a medical diagnosis problem with SVNM information. This diagnosis method can deal with the medical diagnosis problem with indeterminate and inconsistent information which cannot be handled by the diagnosis method based on IFMs.

ON NEUTROSOPHIC REFINED SETS AND THEIR APPLICATIONS IN MEDICAL DIAGNOSIS

− In this paper, we present some definitions of neutrosophic refined sets such as; union,intersection, convex and strongly convex in a new way to handle the indeterminate information andinconsistent information. Also we have examined some desired properties of neutrosophic refinedsets based on these definitions. Then, we give distance measures of neutrosophic refined sets withproperties. Finally, an application of neutrosophic refined set is given in medical diagnosis problem(heart disease diagnosis problem) to illustrate the advantage of the proposed approach

Neutrosophic soft matrices and NSM-decision making

In this paper, we have firstly redefined the notion of neutrosophic soft set and its operations in a new way to handle the indeterminate information and inconsistent information which exists commonly in belief systems. Then, we defined neutrosophic soft matrix and their operators which are more fun ctional to make theoretical studies and application in the neutrosophic soft set theory. The matrix is useful for storing a neutrosophic soft set in computer memory which are very useful and applicable. We finally construct a decision making method, called NSM-decision making, based on the neutrosophic soft sets.

Multiple-Attribute Group Decision-Making Method under a Neutrosophic Number Environment

AbstractAs a neutrosophic number, which consists of a determinate part and an indeterminate part, can more easily and better express incomplete and indeterminate information that exists commonly in real situations, the main purposes of this paper are to provide a neutrosophic number tool for group decision-making problems with indeterminate information under a neutrosophic number environment and to develop a de-neutrosophication method and a possibility degree ranking method for neutrosophic numbers from the probability viewpoint as a methodological support for group decision-making problems. In group decision-making problems with neutrosophic numbers, through the de-neutrosophication and possibility degree ranking order of neutrosophic numbers, the ranking order of alternatives is performed well as the possibility degree ranking method has the intuitive meaning from the probability viewpoint, and then the best one(s) can be determined as well. Finally, two illustrative examples show the applications and effectiveness of the proposed method.

Single Valued Neutrosophic Similarity Measures for Multiple Attribute Decision-Making

Similarity measures play an important role in data mining, pattern recognition, decision making, machine learning, image process etc. Then, single valued neutrosophic sets (SVNSs) can describe and handle the indeterminate and inconsistent information, which fuzzy sets and intuitionistic fuzzy sets cannot describe and deal with. Therefore, the paper proposes new similarity meas-ures between SVNSs based on the minimum and maxi-mum operators. Then a multiple attribute decision-making method based on the weighted similarity measure of SVNSs is established in which attribute values for al- ternatives are represented by the form of single valued neutrosophic values (SVNVs) and the attribute weights and the weights of the three independent elements (i.e., truth- membership degree, indeterminacy-membership degree, and falsity-membership degree) in a SVNV are considered in the decision-making method. In the decision making, we utilize the single-valued neutrosophic weighted similarity measure between the ideal alternative and an alternative to rank the alternatives corresponding to the measure values and to select the most desirable one(s). Finally, two practical examples are provided to demonstrate the applications and effectiveness of the single valued neutrosophic multiple attribute decision-making method.

Single valued neutrosophic trapezoid linguistic aggregation operators based multi-attribute decision making

Multi-attribute decision making (MADM). Play an important role in many applications, due to the efficiency to handle indeterminate and inconsistent information, single valued neutrosophic sets is widely used to model indeterminate information. In this paper, a new MADM method based on neutrosophic trapezoid linguistic weighted arithmetic averaging aggregation SVNTrLWAA operator and neutrosophic trapezoid linguistic weighted geometric aggregation SVNTrLWGA operator is presented. A numerical example is presented to demonstrate the application and efficiency of the proposed method.

Single valued neutrosophic cross-entropy for multicriteria decision making problems

A single valued neutrosophic set (SVNS) is an instance of a neutrosophic set, which give us an additional possibility to represent uncertainty, imprecise, incomplete, and inconsistent information which exist in real world. It would be more suitable to apply indeterminate information and inconsistent information measures. In this paper, the cross entropy of SVNSs, called single valued neutrosophic cross entropy, is proposed as an extension of the cross entropy of fuzzy sets. Then, a multicriteria decision-making method based on the proposed single valued neutrosophic cross entropy is established in which criteria values for alternatives are SVNSs. In decision making process, we utilize the single-valued neutrosophic weighted cross entropy between the ideal alternative and an alternative to rank the alternatives corresponding to the cross entropy values and to select the most desirable one(s). Finally, a practical example of the choosing problem of suppliers is provided to illustrate the application of the developed approach.

Risk-Constrained Unit Commitment of Power System Incorporating PV and Wind Farms

Wind and solar (photovoltaic) power generations have rapidly evolved over the recent decades. Efficient and reliable planning of power system with significant penetration of these resources brings challenges due to their fluctuating and uncertain characteristics. In this paper, incorporation of both PV and wind units in the unit commitment of power system is investigated and a risk-constrained solution to this problem is presented. Considering the contribution of PV and wind units, the aim is to determine the start-up/shut-down status as well as the amount of generating power for all thermal units at minimum operating cost during the scheduling horizon, subject to the system and unit operational constraints. Using the probabilistic method of confidence interval, the uncertainties associated with wind and PV generation are modeled by analyzing the error in the forecasted wind speed and solar irradiation data. Differential evolution algorithm is proposed to solve the two-stage mixed-integer nonlinear optimization problem. Numerical results indicate that with indeterminate information about the wind and PV generation, a reliable day-ahead scheduling of other units is achieved by considering the estimated dependable generation of PV and wind units.

P2-13-07: Prevalence of Germline BRCA1 and BRCA2 Deleterious Mutations in Brazilian Patients with High-Risk of Breast and Ovarian Cancer.

Abstract Background: Germline mutations in the BRCA1/2 genes account for the majority of hereditary breast ovarian cancer (HBOC). Distribution and prevalence of clinically relevant mutations in BRCA1/2 differ among different populations. All of the Brazilian studies published to date have not performed complete sequencing of both genes, restricting their analyses to selected exons. In addition, a highly heterogeneous mutation spectrum was observed. The lack of data concerning the prevalence and profile of BRCA1/2 deleterious mutation and the appropriated screening criteria for DNA sequencing in the Brazilian population complicates the design of screening strategies. Objective: To accurately determine the contribution of BRCA1/2 germline mutations in a well characterized sample of Brazilian breast and ovarian high-risk pts. Methodology: A total of 73 unrelated pts attending a Brazilian public hospital from September 2005 to July 2006, with HBOC risk ≥10% according to Frank, Evans or BRCAPRO algorithms, underwent complete sequencing and MLPA analysis of BRCA1/2 genes. Demographic data and tumor pathological features were extracted from prospectively registered medical records. Results: Mean age, median of cancer cases in families and median score by Frank, Evans and BRCAPRO algorithms were respectively 48y (24-78), 4 (0-13), 11.2 (0-56,3), 13.4 (0,1-100) and 16 (2-75). A total of 79 unknown clinical significance mutations were identified: 44 in BRCA1 and 35 in BRCA2. Known deleterious mutations were identified in 8 pts. Four in BRCA1: R71G at exon 5, 5382insC at exon 20 (2 patients) and R1751X at exon 20; and four in BRCA2: R2318X at exon 13, R3128X at exon 25, 5844del5 and 6633del5 at exon 11. Several polymorphisms were found in all pts. No mutation was detected by MLPA technique. One novel frameshift deleterious mutation in BRCA2: 6610insTT at exon 11 which results in a stop codon was detected in a breast cancer patient and in four of her relatives from a family with high-risk of HBOC. Taking into account the novel mutation, the prevalence of BRCA1/2 mutation in high-risk pts in our cohort is 12,3%. Pts characteristics presented in [table 1]. Conclusion: To the best of our knowledge, the study represents the first report of the complete sequencing and MLPA analysis of BRCA1/2 genes in large Brazilian series of HBOC high-risk pts. The prevalence of germline mutations found in the present study was similar to the reported by other studies examining high-risk populations. B1=BRCA1; B2=BRCA2; BC=breast cancer; IDC=invasive ductal carcinoma; MC=medullary carcinoma; ILC=invasive lobular carcinoma; HR=hormone receptor; (b)=bilateral, N/A=not available; N/C=never had cancer; pos=positive; neg=negative, ind=indeterminate Citation Information: Cancer Res 2011;71(24 Suppl):Abstract nr P2-13-07.

A Stochastic Model for the Optimal Operation of a Wind-Thermal Power System

This paper presents a stochastic cost model and a solution technique for optimal scheduling of the generators in a wind integrated power system considering the demand and wind generation uncertainties. The proposed robust unit commitment solution methodology will help the power system operators in optimal day-ahead planning even with indeterminate information about the wind generation. A particle swarm optimization based scenario generation and reduction algorithm is used for modeling the uncertainties. The stochastic unit commitment problem is solved using a new parameter free self adaptive particle swarm optimization algorithm. The numerical results indicate the low risk involved in day-ahead power system planning when the stochastic model is used instead of the deterministic model.