Mathematical Foundation of Basic Algorithms of Fuzzy Reasoning

Algorithm of fuzzy reasoning has been successful applied in fuzzy control,but its theoretical foundation of algorithms has not been thoroughly investigated. In this paper,structure of basic algorithms of fuzzy reasoning was studied, its rationality was discussed from the viewpoint of logic and mathematics, and three theorems were proved. These theorems shows that there always exists a mathe-~matical relation (that is, a bounded real function) between the premises and the conclusion for fuzzy reasoning, and in fact various algorithms of fuzzy reasoning are specific forms of this function. Thus these results show that algorithms of fuzzy reasoning are theoretically reliable.

New reasoning algorithm based on EFALC

The current extended fuzzy description logics lack reasoning algorithms with TBoxes. The problem of the satisfiability of the extended fuzzy description logic EFALC cut concepts w. r. t. TBoxes is proposed, and a reasoning algorithm is given. This algorithm is designed in the style of tableau algorithms, which is usually used in classical description logics. The transformation rules and the process of this algorithm is described and optimized with three main techniques： recursive procedure call, branch cutting and introducing sets of mesne results. The optimized algorithm is proved sound, complete and with an EXPTime complexity, and the satisfiability problem is EXPTime-complete.

Risk assessment of water security in Haihe River Basin during drought periods based on D-S evidence theory

The weights of the drought risk index （DRI）, which linearly combines the reliability, resiliency, and vulnerability, are difficult to obtain due to complexities in water security during drought periods. Therefore, drought entropy was used to determine the weights of the three critical indices. Conventional simulation results regarding the risk load of water security during drought periods were often regarded as precise. However, neither the simulation process nor the DRI gives any consideration to uncertainties in drought events. Therefore, the Dempster-Shafer （D-S） evidence theory and the evidential reasoning algorithm were introduced, and the DRI values were calculated with consideration of uncertainties of the three indices. The drought entropy and evidential reasoning algorithm were used in a case study of the Haihe River Basin to assess water security risks during drought periods. The results of the new DRI values in two scenarios were compared and analyzed. It is shown that the values of the DRI in the D-S evidence algorithm increase slightly from the original results of Zhang et al. （2005）, and the results of risk assessment of water security during drought periods are reasonable according to the situation in the study area. This study can serve as a reference for further practical application and planning in the Haihe River Basin, and other relevant or similar studies.

A STUDY OF FUZZY LOGICAL PETRI NETS AND ITS APPLICATION

In this paper, a fuzzy Petri net approach to modelling fuzzy rule-based reasoning is proposed. Logical Petri net (LPN) and fuzzy logical Petri net (FLPN) are defined. The backward reasoning algorithm based on sub-fuzzy logical Petri net is given. It is simpler than the conventional algorithm of forward reasoning from initial propositions. An application to the partial fault model of a car engine in paper Portinale's(1993) is used as an illustrative example of FLPN.

A hierarchical analytical model for performance management of integrated logistics

In this paper,a holistic hierarchical analytical model is proposed to assess the performance of enablers in an integrated logistics system.Due to the ambiguous and complex environment,various refinements are needed to assess enablers and prioritize for the criteria such as economic,operational,and environment.The proposed hierarchical model is developed by a systematic approach that includes fuzzy analytical hierarchy process(FAHP),triangular fuzzy numbers(TFN),an evidential reasoning algorithm(ERA),and expected utility theory(EUT).The FAHP is used to analyze and obtain the weights of the criteria by considering the expert’s opinions.ERA is used to synthesize the enablers based on the selected criteria.These enablers are represented using subjective assessment along with a set of evaluation grades for a qualitative attribute.EUT helps in obtaining crisp values of enablers for their performance estimation.With these set of methodologies,a hierarchical model is proposed that prevent low flexibility and inadequate appropriateness of the proposed model.Further,the model helps in scenario generation for the logistics professionals who are facing various problems in integrating logistics and incorporating sustainability due to lack of appropriate methodologies and evaluation techniques.Finally,sensitivity analysis is used for overall model validation.