A new design of the elimination and choice translating reality method for multi-criteria group decision-making in an intuitionistic fuzzy environment

The purpose of this paper is to design a new extension of the ELECTRE, known as the elimination and choice translating reality method, for multi-criteria group decision-making problems based on intuitionistic fuzzy sets. This method is widely utilized when a set of alternatives should be identified and evaluated with respect to a set of conflicting criteria by reflecting decision makers’ (DMs’) preferences. However, handling the exact data and numerical measure is difficult to be precisely focused because the DMs’ judgments are often vague in real-life decision problems and applications. A more realistic and practical approach can be to use linguistic variables expressed in intuitionistic fuzzy numbers instead of numerical data to model DMs’ judgments and to describe the inputs in the ELECTRE method. The proposed intuitionsitic fuzzy ELECTRE utilizes the truth-membership function and non-truth-membership function to indicate the degrees of satisfiability and non-satisfiability of each alternative with respect to each criterion and the relative importance of each criterion, respectively. Then, a new discordance intuitionistic index is introduced, which is extended from the concept of the fuzzy distance measure. Outranking relations are defined by pairwise comparisons and a decision graph is depicted to determine which alternative is preferable, incomparable or indifferent in the intuitionistic fuzzy environment. Finally, a comprehensive sensitivity analysis is employed to further study regarding the impact of threshold values on the final evaluation, and a comparative analysis is demonstrated with an application example in flexible manufacturing systems between the proposed ELECTRE method and the existing intuitionistic fuzzy technique for order preference by similarity to ideal solution (IF-TOPSIS) method.     

Cyclohexanones--Source for Selena/Thiadiazoles and Diazaphospholes

Some new heterocyclic compounds containing selenadiazole, thiadiazole and diazaphosphole fused to cyclohexanones have been prepared and characterized by spectral data.     

Propagation of a pre-existing turbulent fluid fracture

The propagation of rough and smooth wall pre-existing turbulent fluid fractures is investigated. The laminar fluid fracture is included as a special case for comparison. Lubrication theory is assumed to apply in the fracture and turbulence is introduced through the wall shear stress. The Perkins–Kern–Nordgren approximation is made in which the fluid pressure is proportional to the half-width of the fracture. The fracture half-width satisfies a non-linear diffusion equation. By using a linear combination of the Lie point symmetries of the non-linear diffusion equation a group invariant solution for the fracture length, volume and half-width is derived. The evolution of the length, half-width and mean flow velocity is analysed for a range of working conditions at the fracture entry. It is found that the mean flow velocity increases approximately linearly along the fracture.     

END GROUP TRANSFORMATION OF POLYMERS PREPARED BY ATRP,SUBSTITUTION TO AZIDES

Polystyrenes, polyacrylates and poly(methyl methacrylate) prepared by atom transfer radical polymerization (ATRP) have predictable molecular weights, low polydispersities and well-defined halogen end groups. The halogen end groups have been substituted by other functionalities such as azides and amines. In order to predict the feasibility and selectivity of nucleophilic substitution reactions, the reactivities of the end groups of the different polymers were studied. First, model studies with benzyl halide (BzX), 1-phenylethyl halide (1-PEX), methyl 2-halopropionate (MXP), ethyl 2-bromoisobutyrate (EBiB) and 2-halopropionitrile (2-XPN) were performed. The models compounds were dissolved in DMF and after adding sodium azide (1.1 eq.), the reaction mixtures were stirred at 25°C. The relative magnitude of the rate constants for the reactions with the chlorinated substrates were found to be BzCl > MClP > 1-PECl ≈ 2-ClPN:22 > 6 > 1. Increased substitution at the carbon center decreased the rate of reaction, benzyl chloride reacted 22 times faster than 1-phenylethyl chloride. The brominated substrates reacted very fast. The rate constant of 1-PEBr, determined by competition experiments, was 4.5 times higher than the rate constant of benzyl chloride. Based on these results, the bromine end groups of different polymers were substituted under reaction conditions simular to those used for the model reactions. The end-functionalized polymers were characterized by ¹H-NMR, IR and MALDI-TOFMS.     

A central limit theorem in nonlinear filtering

It is shown that the probability law of a diffusion process conditioned on weakly corrupted observations is asymptotically Gaussian when properly scaled. The method of proof involves Fisher information matrices and a Cramér-Rao inequality.     

Recent topics of the metallacycles composed of the heavier group 14 elements

This Letter reviews recent advance of metallacycles with chelating Si-, Ge-, and Sn-ligands. Dehydrogenative bond-forming reactions of organosilanes, -germanes, and -stannanes promoted by Pd and Pt complexes afford four- and five-membered metallacycles composed of heavier group 14 elements. It has a couple of advantages such as easier preparation of the starting compounds and reaction procedure than the common metathesis reactions of dianions with transition metal dihalide complexes. These metallacycles are regarded as possible intermediates in catalytic dehydrocoupling polymerizations or as convenient precursors to form discrete oligomers.     

Random frog: An efficient reversible jump Markov Chain Monte Carlo-like approach for variable selection with applications to gene selection and disease classification

The identification of disease-relevant genes represents a challenge in microarray-based disease diagnosis where the sample size is often limited. Among established methods, reversible jump Markov Chain Monte Carlo (RJMCMC) methods have proven to be quite promising for variable selection. However, the design and application of an RJMCMC algorithm requires, for example, special criteria for prior distributions. Also, the simulation from joint posterior distributions of models is computationally extensive, and may even be mathematically intractable. These disadvantages may limit the applications of RJMCMC algorithms. Therefore, the development of algorithms that possess the advantages of RJMCMC methods and are also efficient and easy to follow for selecting disease-associated genes is required. Here we report a RJMCMC-like method, called random frog that possesses the advantages of RJMCMC methods and is much easier to implement. Using the colon and the estrogen gene expression datasets, we show that random frog is effective in identifying discriminating genes. The top 2 ranked genes for colon and estrogen are Z50753, U00968, and Y10871_at, Z22536_at, respectively. (The source codes with GNU General Public License Version 2.0 are freely available to non-commercial users at: http://code.google.com/p/randomfrog/.)     

Arbitration procedures with multiple arbitrators

We consider two final-offer arbitration procedures in the case where there is more than one arbitrator. Two players, labeled 1 and 2 and interpreted here as Labor and Management, respectively, are in dispute about an increase in the wage rate. They submit final offers to a Referee. There are N arbitrators. Each of the arbitrators has her own assessment and selects the offer which is closest to her assessment. After that each arbitrator informs the Referee about her decision. The Referee counts the votes and declares the player obtaining the most votes to be the winner. Under the second arbitration scheme, the Referee takes into account only the assessments which lie between the players’ offers. The game is modeled as a zero-sum game. The Nash equilibrium in this arbitration game is derived.     

Automatic hierarchy classification in venation networks using directional morphological filtering for hierarchical structure traits extraction

The extraction of vein traits from venation networks is of great significance to the development of a variety of research fields, such as evolutionary biology. However, traditional studies normally target to the extraction of reticulate structure traits (ReSTs), which is not sufficient enough to distinguish the difference between vein orders. For hierarchical structure traits (HiSTs), only a few tools have made attempts with human assistance, and obviously are not practical for large-scale traits extraction. Thus, there is a necessity to develop the method of automated vein hierarchy classification, raising a new challenge yet to be addressed. We propose a novel vein hierarchy classification method based on directional morphological filtering to automatically classify vein orders. Different from traditional methods, our method classify vein orders from highly dense venation networks for the extraction of traits with ecological significance. To the best of our knowledge, this is the first attempt to automatically classify vein hierarchy. To evaluate the performance of our method, we prepare a soybean transmission image dataset (STID) composed of 1200 soybean leaf images and the vein orders of these leaves are manually coarsely annotated by experts as ground truth. We apply our method to classify vein orders of each leaf in the dataset. Compared with ground truth, the proposed method achieves great performance, while the average deviation on major vein is less than 5 pixels and the average completeness on second-order veins reaches 54.28%.