Determination Of Loss Function Research Articles

Hybrid Method Analysis of Variance (ANOVA) and Loss Function to Analyzed Optimizing Composition of Fiber Baggase and Fly Ash

Research on the utilization of baggase fiber as a composite material has been done, but still has shortcomings in the composite material brilliance. Therefore, the use of baggase fiber combined with coal ash can be an alternative to make a composite material. The purpose of this research is to know the effect of baggase fiber composition and fly ash composition to tensile stress and bending stress. This paper discusses the application of Analysis of Variance (ANOVA) on composite material data. There are two variables measured are variable of tensile stress and variable of bending stress. The result obtained that there is influence composition of baggase fiber and composition of fly ash at tensile stress and bending stress. Furthermore, further tests using Tukey method showed that the different composition pairs significantly were 10% -30%, 10% -40% and 20% -40% in both compositions of the two variables studied. In the determination of loss function with Signal-to-Noise (SN) Ratio with larger-is-the-better criteria, the composition of 40% baggase fiber, 10% fly ash composition and 50% matrix can produce optimal tensile and bending strength.

Determining Three-Way Decisions With Decision-Theoretic Rough Sets Using a Relative Value Approach

Three-way decisions play an important role in rough sets and decision theory. As a representative model, decision-theoretic rough sets (DTRSs) provide a sound interpretation of thresholds used in three-way decisions. This problem is associated with the determination of the loss function of DTRSs. In this paper, we investigate a novel way of determining the loss functions of DTRSs with relative values. More specifically, with the aid of analytic hierarchy process (AHP) method, the determination of loss functions is realized in the context of DTRSs. First, a hierarchical structure of DTRSs is constructed. Second, along the hierarchical structure, pairwise comparison matrices are analyzed in a top-down fashion. In light of the generic condition imposed on the loss functions of DTRSs, some constraints on relative values between loss functions are introduced. The relative ratios at each level are computed. Considering the consistency ratio (CR) of the reciprocal matrices, two mathematical programming approaches are developed by exploiting the flexibility of information granularity. Then, we design a decision procedure for the determination of loss functions and deduce three-way decisions. The loss functions are calculated by aggregating the relative ratios being available at each level. With regard to the loss functions, we finally compare the existing studies with the AHP method. We demonstrate that the relative value with AHP improves the restriction of the existing studies and exhibits a certain level of tolerance to inconsistency.

Three-way decisions with intuitionistic fuzzy decision-theoretic rough sets based on point operators

Three-way decisions with decision-theoretic rough sets (DTRSs) as a typical risk decision method, are generated by Bayesian decision theory and have three kinds of decision strategies, i.e., the acceptance decision, the deferment (non-commitment) decision and the rejection decision. The construction of three-way decisions under the complex decision-making context creates enormous challenges. The determination of loss function is one of key steps. In this paper, we discuss the decision principles of three-way decision rules based on the variation of loss functions with intuitionistic fuzzy sets (IFSs). More specifically, we introduce the intuitionistic fuzzy point operator (IFPO) into DTRSs and explore three-way decisions. Firstly, we construct a loss function matrix with the point operator and analyze its corresponding properties. IFPO implies one type of variation modes for the loss functions of three-way decisions. With respect to the point operator, we show that the prerequisites among loss functions still hold in each stage. Secondly, given the loss functions, we construct the corresponding three-way decision model and deduce three-way decisions. Finally, with the aid of information entropy theory, we further investigate which stage may be most suitable to make the decision. This study extends the range of applications of three-way decisions to the new intuitionistic fuzzy environment.