On the law S ( S ( x , y ), T ( x , y )) = S ( x , y ) of fuzzy logic

Motivated by some functional models arising in fuzzy logic, when classical boolean relations between sets are generalized, we study the functional equation S(S(x, y), T(x, y)) = S(x, y), where S is a continuous t-conorm and T is a continuous t-norm. Some interesting methods for solving this type of equations are introduced.     

Neuro-fuzzy approach to processing inputs with missing values in pattern recognition problems

An approach to dealing with missing data, both during the design and normal operation of a neuro-fuzzy classifier is presented in this paper. Missing values are processed within a general fuzzy min–max neural network architecture utilising hyperbox fuzzy sets as input data cluster prototypes. An emphasis is put on ways of quantifying the uncertainty which missing data might have caused. This takes a form of classification procedure whose primary objective is the reduction of a number of viable alternatives rather than attempting to produce one winning class without supporting evidence. If required, the ways of selecting the most probable class among the viable alternatives found during the primary classification step, which are based on utilising the data frequency information, are also proposed. The reliability of the classification and the completeness of information is communicated by producing upper and lower classification membership values similar in essence to plausibility and belief measures to be found in the theory of evidence or possibility and necessity values to be found in the fuzzy sets theory. Similarities and differences between the proposed method and various fuzzy, neuro-fuzzy and probabilistic algorithms are also discussed. A number of simulation results for well-known data sets are provided in order to illustrate the properties and performance of the proposed approach.     

A parametric representation of linguistic hedges in Zadeh’s fuzzy logic

This paper proposes a model for the parametric representation of linguistic hedges in Zadeh’s fuzzy logic. In this model each linguistic truth-value, which is generated from a primary term of the linguistic truth variable, is identified by a real number r depending on the primary term. It is shown that the model yields a method of efficiently computing linguistic truth expressions accompanied with a rich algebraic structure of the linguistic truth domain, namely De Morgan algebra. Also, a fuzzy logic based on the parametric representation of linguistic truth-values is introduced.     

基于SPA的双枝模糊决策分析

将集对理论(SPA)与双枝模糊决策理论相结合,用集对分析的方法研究进行双枝模糊决策的方法,分别对双枝模糊决策因素域和双枝模糊决策的上枝、下枝和双枝进行了集对分析,给出了用SPA进行双枝模糊决策的性质,同时讨论了双枝模糊决策的动态分析方法,以及双枝模糊决策度强弱态势预测的方法,从而为双枝模糊决策理论的研究提供了新的视角和方法,为双枝模糊决策的应用提供了更方便的工具和更强的理论支持。     

关于K-拟可加模糊积分的几点注记

在K-拟可加模糊积分定义及积分转换定理的基础上，证明这种模糊积分恰好构成K-拟可加模糊测度，并依据积分转换定理讨论这种K-拟可加模糊积分的一些补充性质。     

Pre—Separation Axioms in Fuzzifying Topology

1　 IntroductionYing[5,6 ] introduced and elementally developed so called fuzzifying topology with the semanticmethod of continuous valued L ogic.Shen[7] introduced and studied T0 -,T1-,T2 (Hausdorff) -,T3(regularity) -,T4 (normality) -separation axioms in fuzzifying topology.In [3 ]the concepts of thefamily of fuzzifying pre-open sets,fuzzifying pre-neighbourhood structure of a point and fuzzifyingpre-closure are introduced and studied.It is worth to mention that pre-separation axioms are …     

Bilevel programming approach applied to the flow shop scheduling problem under fuzziness

This paper presents a fuzzy bilevel programming approach to solve the flow shop scheduling problem. The problem considered here differs from the standard form in that operators are assigned to the machines and imposing a hierarchy of two decision makers with fuzzy processing times. The shop owner considered higher level and assigns the jobs to the machines in order to minimize the flow time while the customer is the lower level and decides on a job schedule in order to minimize the makespan. In this paper, we use the concepts of tolerance membership function at each level to define a fuzzy decision model for generating optimal (satisfactory) solution for bilevel flow shop scheduling problem. A solution algorithm for solving this problem is given. Mathematics Subject Classification: 90C70, 90B36, 90C99     

A note on inverses in arithmetic with fuzzy numbers

Algorithms for systematical search of inverse in arithmetic operations with fuzzy numbers are discussed. The fuzzy number derived is considered either in a discrete representation of its support or described by the parameters of the corresponding membership function formula. Both algorithms are easy to be programmed for desk calculators.     

Optimisation of fault-tolerant fabric-cutting schedules using genetic algorithms and fuzzy set theory

In apparel industry, manufacturers developed standard allowed minutes (SAMs) databases on various manufacturing operations in order to facilitate better scheduling, while effective production schedules ensure smoothness of downstream operations. As apparel manufacturing environment is fuzzy and dynamic, rigid production schedules based on SAMs become futile in the presence of any uncertainty. In this paper, a fuzzification scheme is proposed to fuzzify the static standard time so as to incorporate some uncertainties, in terms of both job-specific and human related factors, into the fabric-cutting scheduling problem. A genetic optimisation procedure is also proposed to search for fault-tolerant schedules using genetic algorithms, such that makespan and scheduling uncertainties are minimised. Two sets of real production data were collected to validate the proposed method. Experimental results indicate that the genetically optimised fault-tolerant schedules not only improve the operation performance but also minimise the scheduling risks.     

Fuzzy Model of Regional Economic Competitiveness in GIS Spatial Analysis: Case Study of Gansu, Western China

After more than 20 years of impressive development since the economic reforms in 1978, today western China is facing an increasing development gap between its regions, particularly between urban and rural areas. Using the fuzzy comprehensive evaluation model, this paper aims to demonstrate the evolution of the economic competitiveness levels base on two categories of geographical unity in the province of Gansu located in Northwest China between 2000 and 2004. The results of fuzzy modeling are integrated into GIS spatiotemporal analyses in order to identify the spatial variation of each significant change in terms of the regional economic development. Our research effectively illustrates that there is a particular spatial dynamic of the economic development from region to region. Although the cities have improved very well in their economic competitiveness, the rural areas and minority regions still have a lot of progress to be achieved.