Moreover it is observed that the proposed algorithm finds multiple optimal paths, when they exist, both for the crisp problems and their fuzzy variations.
Consolidated systems are defined as being stable at the original state, but due to fuzzy variations in their inputs or parameters tend to react accordingly in a manner leading to maintaining their consolidity and strength, or vice versa.
This paper develops a grey fuzzy Markov industrial accidents forecast model for small or incomplete accident data availability situations using non-differential function grey interval analysis, fuzzy logic, variation conditioning and a state transition approach which aims to capture unique accident occurrence characteristics.
We start this section by recalling some pertinent concepts and key lemmas from the functions of bounded variation, fuzzy numbers, and fuzzy equivalence classes which we need for the discussion below.
Open image in new window Fig. 11 Diagram of variation Fuzzy-rationing factors and simple rationing factors.
Wang et al. [23] defined the maximal and minimal reference sets and then proposed the ranking method based on deviation degree and relative variation of fuzzy numbers and subsequent Asady in [5] proposed a revised method of ranking LR fuzzy number based on deviation degree with Wangs method.
However, the boundaries between ASD and normal variation are fuzzy.
This was based on the understanding that due to the fuzzy nature of the variation properties, there exists the tendency for escalation and closure-lag properties to overlap and potentially occur within respective open and closing swings.
To test its performance, a systematic comparison of TSIS versus three famous variations of fuzzy c-means (FCM) and two graph partitioning methods is given.
By Lyapunov function approach, under the designed mode-dependent and variation-dependent fuzzy filter which includes the membership functions, a sufficient condition is presented to ensure that the filtering error dynamic system is stochastically stable and has a prescribed H∞ performance index.
