New indices for analysing partial ranking diagrams

Interest is growing in decision making strategies and several techniques are now available. The assessment of priorities is a typical premise before final decisions are taken. Total and partial order ranking (POR) strategies, which from a mathematical point of view are based on elementary methods of discrete mathematics, appear as an attractive and simple tool to asses priorities. Despite the well-known total ranking strategies, which are scalar methods combining the different criteria values into a global index which always ranks elements in an ordered sequence, the partial order ranking is a vectorial approach which recognises that not all the elements can be directly compared with all the others. In fact when many criteria are considered, contradictions in the ranking are bound to exist and the higher the number of criteria, the higher the probability that contradictions in the ranking occur. The Hasse diagram technique (HDT) is a very useful tool to perform partial order ranking. The results of the partial order ranking are visualised in a diagram, called Hasse diagram. Incomparable elements are located at the same geometrical height and as high as possible in the diagram, thus incomparable elements are arranged in levels. The quality of a ranking procedure has to be evaluated by a deep analysis and by several indices, i.e. scalar functions that describe features of an ordered set and allow comparison among different rankings. For this purpose, new indices for ranking analysis are proposed here, compared with the ones found in literature and tested on theoretical examples and on real data.     

分子的模糊对称性

将模糊数学方法引入对分子对称点群的研究,建立描述具有不完整分子对称性的模糊点对称群(集合).建立具有模糊对称性分子轨道的模糊表示及其模糊特征标(模糊广义宇称).通过对典型的线状分子、平面分子以及非平面的立体分子等进行分析,展示了一个新的理论化学园地.初步探讨了具有模糊对称性的动态反应体系.从模糊对称性出发,探讨了分子轨道对称守恒原理的半定量特征.     

Correlation coefficient of dual hesitant fuzzy sets and its application to multiple attribute decision making

A dual hesitant fuzzy set (DHFS) consists of two parts, that is, the membership hesitancy function and the nonmembership hesitancy function, supporting a more exemplary and flexible access to assign values for each element in the domain, and can handle two kinds of hesitancy in this situation. It can be considered as a powerful tool to express uncertain information in the process of group decision making. Therefore, we propose a correlation coefficient between DHFSs as a new extension of existing correlation coefficients for hesitant fuzzy sets and intuitionistic fuzzy sets and apply it to multiple attribute decision making under dual hesitant fuzzy environments. Through the weighted correlation coefficient between each alternative and the ideal alternative, the ranking order of all alternatives can be determined and the best alternative can be easily identified as well. Finally, a practical example of investment alternatives is given to demonstrate the practicality and effectiveness of the developed approach.     

Performance investigation of an advanced tracked prime mover on the low bearing soil

This study has presented a performance investigation of an advanced tracked prime mover for the operation of agricultural goods and other operations on peat terrain. The maximum and continuous traction torque of the prime mover has been developed by designing an advanced controller for controlling the intelligent system. The prime mover’s mobility is studied with ultrasonic displacement sensor, torque transducer, National Instrument cRIO-9004 Compact-RIO Real-time Controller Unit (RCU), a National Instrument TPC 2106T Touch Panel Control (TPC), a Trimble AG132 GPS antenna and receiver unit, and a Dlink DIR-655 router. The fuzzy logic controller (FLC) has been equipped with the prime mover hydraulic system to increase the traction torque of the hydraulic motor when the prime mover’s sinkage is more than or equal to 70 mm. The prime mover’s design demonstrates good potential in traversing peat terrain as the measured tractive effort was found to be 48% of the vehicle’s gross weight while the recommended tractive effort is in the range of 30–36% of the vehicle’s gross weight.     

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.     

On the nonlinear stochastic realization problem

In this paper we construct a first solution of the stochastic realization problem in a nonlinear setting. The great bulk of previous work on stochastic realization has been in the linear Gaussian setting. Such Markovian representations are used e.g., to apply certain filtering and stochastic control techniques. Our methods consist of an amalgamation of methods introduced by Nelson with the Lax-Phillips type geometric approach to linear Gaussian stochastic realization which has been developed by Lindquist and Picci and by Ruckebusch. The result of this that we are able to realize any purely nondeterministic process satisfying suitable continuity conditions as an instantaneous function of a Markov process.     

Fuzzy structure-activity relationships

While quantitative structure-activity relationships attempt to predict the numerical value of the activities, it is found that statistically good predictors do not always do a good job of qualitatively determining the activity. This study shows how Fuzzy classifiers can be used to generate Fuzzy structure-activity relationships which can more accurately determine whether or not a compound will be highly inactive, moderately inactive or active, or highly active. Four examples of these classifiers are presented and applied to a well-studied activity dataset.     

Dynamic models of segregation†

Some segregation results from the practices of organizations, some from specialized communication systems, some from correlation with a variable that is non‐random; and some results from the interplay of individual choices. This is an abstract study of the interactive dynamics of discriminatory individual choices. One model is a simulation in which individual members of two recognizable groups distribute themselves in neighborhoods defined by reference to their own locations. A second model is analytic and deals with compartmented space. A final section applies the analytics to ‘neighborhood tipping.’ The systemic effects are found to be overwhelming: there is no simple correspondence of individual incentive to collective results. Exaggerated separation and patterning result from the dynamics of movement. Inferences about individual motives can usually not be drawn from aggregate patterns. Some unexpected phenomena, like density and vacancy, are generated. A general theory of ‘tipping’ begins to emerge.     

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.