Supplier Evaluation Model Based on Fuzzy Measures and Choquet Integral

To identify interactions among evaluation criteria and describe their importance,a new identification method making use of a fuzzy measure is presented.The relative weight and interaction degree of every evaluation criteria pair are obtained by using the diamond pairwise comparison method.Based on comparison results,the maximum eigenvector method of analytic hierarchy process （AHP）,the hierarchical clustering method,and the phi（s） transformation are utilized to generate values of the fuzzy measure for each subset of the evaluation criterion set.Overall evaluation on each supplier is aggregated by Choquet integral with respect to the fuzzy measure.Finally,an illustrative example demonstrates the practical feasibility and validity of the proposed method.

Hidden Markov Models Incorporating Fuzzy Measures and Integrals for Protein Sequence Identification and Alignment

Profile hidden Markov models （HMMs） based on classical HMMs have been widely applied for protein sequence identification. The formulation of the forward and backward variables in profile HMMs is made under statistical independence assumption of the probability theory. We propose a fuzzy profile HMM to overcome the limitations of that assumption and to achieve an improved alignment for protein sequences belonging to a given family. The proposed model fuzzifies the forward and backward variables by incorporating Sugeno fuzzy measures and Choquet integrals, thus further extends the generalized HMM. Based on the fuzzified forward and backward variables, we propose a fuzzy Baum-Welch parameter estimation algorithm for profiles. The strong correlations and the sequence preference involved in the protein structures make this fuzzy architecture based model as a suitable candidate for building profiles of a given family, since the fuzzy set can handle uncertainties better than classical methods.

Decompositions of Revised Monotone Signed Fuzzy Measures

The concept of fuzzy measure was introduced by Sugeno in 1974. A notion of signed fuzzy measure is introduced in this paper, and its elementary properties are briefly discussed. An analogue of Hahn decomposition theorem is established under the null-null-additive condition. A version of the Jordan decomposition theorem is proved under the null-additive condition.

New Class of Doubt Bipolar Fuzzy Sub Measure Algebra

The ideas of ambiguous bipolar skepticism under algebra and closed skepticism ambiguous bipolar ideals and related features have been developed.The fuzzy measure ideal is described in terms of bipolar ambiguous measure algebra and bipolar skepticism,and the linkages between bipolar fuzzy measure algebra are determined.A bipolar misty ideal’s skepticism is examined.InBCW andBCL-measure algebra,homogeneous ideas and dubious pictures of fuzzy bipolar measure ideas are examined.Also,we gave the relationship between these concepts.Finally,it is given the perfect terms for an occult bipolar doubt to be a measure of ideal fuzzy bipolar closed doubt.

Extension of TOPSIS for fuzzy multi-attribute decision making problem based on experimental analysis

This paper is concerned with a technique for order performance by similarity to ideal solution（TOPSIS） method for fuzzy multi-attribute decision making,in which the information about attribute weights is partly known and the attribute values take form of triangular fuzzy numbers.Considering the fact that the triangular fuzzy TOPSIS results yielded by different distance measures are different from others,a comparative analysis of triangular fuzzy TOPSIS ranking from each distance measure is illustrated with discussion on standard deviation.By applying the most reasonable distance,the deviation degrees between attribute values are measured.A linear programming model based on the maximal deviation of weighted attribute values is established to obtain the attribute weights.Therefore,alternatives are ranked by using TOPSIS method.Finally,a numerical example is given to show the feasibility and effectiveness of the method.

Variations and Absolute Continuity of Set Functions on T_∞-tribe

some properties of the inclusion variation and the disjoint variation of set functions on T∞-tribe are studied in detail.The absolute continuity and singularity of set functions on T∞-tribe are discussed.The triangular norms T∞ and S∞ are considered as the operators of intersection and union between the fuzzy sets.As a result,some important conclusions about the variations and absolute continuity of set functions on T∞-tribe are obtained such as the superadditivity of inclusion variation,the relation between the variations and the equivalence proposition of absolute continuity of set functions on T∞-tribe.In addition,two small mistakes about T∞-measure are pointed out by the counterexamples and are revised.

Towards Improving Predictive Statistical Learning Model Accuracy by Enhancing Learning Technique

The accuracy of the statistical learning model depends on the learning technique used which in turn depends on the dataset’s values.In most research studies,the existence of missing values(MVs)is a vital problem.In addition,any dataset with MVs cannot be used for further analysis or with any data driven tool especially when the percentage of MVs are high.In this paper,the authors propose a novel algorithm for dealing with MVs depending on the feature selec-tion(FS)of similarity classifier with fuzzy entropy measure.The proposed algo-rithm imputes MVs in cumulative order.The candidate feature to be manipulated is selected using similarity classifier with Parkash’s fuzzy entropy measure.The predictive model to predict MVs within the candidate feature is the Bayesian Ridge Regression(BRR)technique.Furthermore,any imputed features will be incorporated within the BRR equation to impute the MVs in the next chosen incomplete feature.The proposed algorithm was compared against some practical state-of-the-art imputation methods by conducting an experiment on four medical datasets which were gathered from several databases repository with MVs gener-ated from the three missingness mechanisms.The evaluation metrics of mean abso-lute error(MAE),root mean square error(RMSE)and coefficient of determination(R2 score)were used to measure the performance.The results exhibited that perfor-mance vary depending on the size of the dataset,amount of MVs and the missing-ness mechanism type.Moreover,compared to other methods,the results showed that the proposed method gives better accuracy and less error in most cases.

Border effect-based precise measurement of any frequency signal

Limited detection resolution leads to fuzzy areas during the measurement, and the discrimination of the border of a fuzzy area helps to use the resolution stability. In this way, measurement precision is greatly improved, hence this phenomenon is named the border effect. The resolution fuzzy area and its application should be studied to realize highresolution measurement. During the measurement of any frequency signal, the fuzzy areas of phase-coincidence detection are always discrete and irregular. In this paper the difficulty in capturing the border information of discrete fuzzy areas is overcome and extra-high resolution measurement is implemented. Measurement precision of any frequency-signal can easily reach better than 1 × 10^-11/s in a wide range of frequencies, showing the great importance of the border effect. An in-depth study of this issue has great significance for frequency standard comparison, signal processing, telecommunication,and fundamental subjects.

Some General Inequalities for Choquet Integral

With the development of fuzzy measure theory, the integral inequalities based on Sugeno integral are extensively investigated. We concern on the inequalities of Choquuet integral. The main purpose of this paper is to prove the H?lder inequality for any arbitrary fuzzy measure-based Choquet integral whenever any two of these integrated functions f, g and h are comonotone, and there are three weights. Then we prove Minkowski inequality and Lyapunov inequality for Choquet integral. Moreover, when any two of these integrated functions f1, f2, …, fn are comonotone, we also obtain the Hölder inequality, Minkowski inequality and Lyapunov inequality hold for Choquet integral.

Software Defect Prediction Using Fuzzy Integral Fusion Based on GA-FM

The fuzzy measure and fuzzy integral are applied to the classification of software defects in this paper. The fuzzy measure of software attributes and attributes＇ sets are treated by genetic algorithm, and then software attributes are fused by the Choquet fuzzy integral algorithm. Finally, the class labels of soft- ware modules can be output. Experimental results have shown that there are interactions between characteristic attributes of software modules, and also proved that the fuzzy integral fusing method using Fuzzy Measure based on Genetic Algorithm （GA-FM） can significantly improve the accuracy for software defect prediction.

Fuzzy Set Operation Based on Measure Theory

Differrent kinds of operations have been proposed in fuzzy set theory although Zadeh's operation is the most popoular. We discuss a new kind of fuzzy set operations which is based on measurement. In the measure based operation, there are only two basic operators: operator for intersection and operator for union. These two operators are interrelated with each other, and conditional fuzzy measures(or conditional membership functions) are also included in these operators. Moreover, the operator for complement is not independently defined, and it is derived from the above two basic operators. The measure based operation brings to light some relations between Zadeh's operation and probabilistic operation. We show that both Zadeh's operation and probabilistic operation are special cases of measure based operators.We also discuss the problem of the law of excluded middle and the law of contradiction. It is shown that these laws still hold in fuzzy sets and this conclusion causes no difficulty in explaining the nature of fuzziness.

Identification of Critical Components of Complex Product Based on Hybrid Intuitionistic Fuzzy Set and Improved Mahalanobis-Taguchi System

To avoid the decrease of system reliability due to insufficient component maintenance and the resource waste caused by excessive component maintenance,identifying the critical components of complex products is an effective way to improve the efficiency of maintenance activities.Existing studies on identifying critical components of complex products are mainly from two aspects i.e.,topological properties and functional properties,respectively.In this paper,we combine these two aspects to establish a hybrid intuitionistic fuzzy set to incorporate the different types of attribute values.Considering the mutual correlation between attributes,a combination of AHP(Analytic Hierarchy Process)and Improved Mahalanobis-Taguchi System(MTS)is used to determine the λ-Shapley fuzzy measures for attributes.Then,the λ-Shapley Choquet integral intuitionistic fuzzy TOPSIS(Technique for Order Preference by Similarity to an Ideal Solution)method is proposed for calculating the closeness degrees of components to generate their ranking order.Finally,a case study which is about the right gear of airbus 320 is taken as an example to verify the feasibility and effectiveness of this method.This novel methodology can effectively solve the critical components identification problem with different types of evaluation information and completely unknown weight information of attributes,which provides the implementation of protection measures for the system reliability of complex products.

GENERALIZED INTUITIONISTIC FUZZY HYBRID CHOQUET AVERAGING OPERATORS

In this study a new hybrid aggregation operator named as the generalized intuitionistic fuzzy hybrid Choquet averaging（GIFHCA） operator is defined.Meantime,some desirable properties are studied, and several important cases are examined.Furthermore,we define the generalized Shapley GIFHCA （GS-GIFHCA） operator,which does not only overall consider the importance of elements and their ordered positions,but also globally reflect the correlations among them and their ordered positions.In order to simplify the complexity of solving a fuzzy measure,we further define the generalizedλ-Shapley GIFHCA（GλS-GIFHCA） operator.

Properties of Measure-based Fuzzy Logic

Measure based fuzzy logic, which is constructed on the basis of eight axioms, is a seemingly powerful fuzzy logic. It possesses several remarkable properties. (1) It is an extended Boolean logic, satisfying all the properties of Boolean algebra, including the law of excluded middle and the law of contradiction. (2) It is conditional. Conditional membership functions play an important role in this logic. (3) The negation operator is not independently defined with the conjunction and disjunction operators, but on the contrary, it is derived from them. (4) Zadehs fuzzy logic is included in it as a particular case. (5) It gives more hints to the relationship between fuzzy logic and probability logic.

Nonadditive Set Functions Defined by Aumann Fuzzy Integrals

A novel concept, called nonadditive set-valued measure, is first defined as a monotone and continuous set function. Then the interconnections between nonadditive set-valued measure and the additive set-valued measure as well as the fuzzy measure are discussed. Finally, an approach to construct a nonadditive compact set-valued measure is presented via Aumann fuzzy integral.

Trapezoidal Intuitionistic Fuzzy Aggregation Operator Based on Choquet Integral and Its Application to Multi-Criteria Decision-Making Problems

The Choquet integral can serve as a useful tool to aggregate interacting criteria in an uncertain environment. In this paper, a trapezoidal intuitionistic fuzzy aggregation operator based on the Choquet integral is proposed for multi-criteria decision-making problems. The decision information takes the form of trapezoidal intuitionistic fuzzy numbers and both the importance and the interaction information among decision-making criteria are considered. On the basis of the introduction of trapezoidal intuitionistic fuzzy numbers, its operational laws and expected value are defined. A trapezoidal intuitionistic fuzzy aggregation operator based on the Choquet integral is then defined and some of its properties are investigated. A new multi-criteria decision-making method based on a trapezoidal intuitionistic fuzzy Choquet integral operator is proposed. Finally, an illustrative example is used to show the feasibility and availability of the proposed method.