A new dempster-shafer theory-based method with fuzzy targets for fuzzy sets ranking

In this paper, a new Fuzzy Set (FS) ranking method (for type-1 and interval type-2 FSs), which is based on the Dempster-Shafer Theory (DST) of evidence with fuzzy targets, is investigated. Fuzzy targets are adopted to reflect human viewpoints on fuzzy ranking. Two important measures in DST, i.e., the belief and plausibility measures, are used to rank FSs. The proposed approach is evaluated with several benchmark examples. The use of the belief and plausibility measures in fuzzy ranking are discussed and compared. We further analyze the capability of the proposed approach in fulfilling six reasonable fuzzy ordering properties as discussed in [9]-[11].

Linguistic computational model based on 2-tuples and intervals

Herrera and Mart́inez initiated a 2-tuple fuzzy linguistic representation model for computing with words.Moreover, Wang and Hao further developed a new 2-tuple fuzzy linguistic representation model to deal with the linguistic term sets that are not uniformly and symmetrically distributed. This study proposes another linguistic computational model based on 2-tuples and intervals, which we call an interval version of the 2-tuple fuzzy linguistic representation model. The proposed model possesses three steps: 1) interval numerical scale; 2) computation based on interval numbers; and 3) a generalized inverse operation of the interval numerical scale. The first step transforms linguistic terms into interval numbers, based on which the second step is executed with output as an interval number. Finally, this number is then mapped into the interval of the linguistic 2-tuples by the generalized inverse operation. This study also generalizes the numerical scale approach, presented in the Wang and Hao model, to set the interval numerical scale, by considering the context where semantics of linguistic terms are defined by interval type-2 fuzzy sets (IT2 FSs). In order to compare the proposed model with the existing linguistic computational model based on IT2 FSs, we have conducted extensive simulations. The simulations demonstrate that the results obtained by our proposal are consistent with the results of the linguistic computational model based on IT2 FSs (in some sense) in a vast majority of cases.

A new fuzzy ranking method using fuzzy preference relations

In this paper, a new fuzzy ranking method for both type-1 and interval type-2 fuzzy sets (FSs) using fuzzy preference relations is proposed. The use of fuzzy preference relations to rank FSs with vertices has been introduced, and successfully implemented to undertake fuzzy multiple criteria hierarchical group decision-making problems. The proposed fuzzy ranking method is an extension of the results published in [1], and it is able to rank FSs with and without vertices. Besides that, it is important for a fuzzy ranking method to satisfy six reasonable fuzzy ordering properties as discussed in [6]-[8]. As a result, the capability of the proposed fuzzy ranking method in fulfilling these properties is analyzed and discussed. Issues related to time complexity of the proposed method are also examined.

Weak monotonicity of Lehmer and Gini means

We analyze directional monotonicity of several mixture functions in the direction (1,1...,1), called weak monotonicity. Our particular focus is on power weighting functions and the special cases of Lehmer and Gini means. We establish limits on the number of arguments of these means for which they are weakly monotone. These bounds significantly improve the earlier results and hence increase the range of applicability of Gini and Lehmer means. We also discuss the case of affine weighting functions and find the smallest constant which ensures weak monotonicity of such mixture functions.

Anxiety, depression and fatigue at 5-year review following CNS demyelination

BACKGROUND: Anxiety and depression are common in multiple sclerosis (MS). We evaluated the prevalence and factors associated with anxiety, depression and fatigue at the 5-year review of a longitudinal cohort study following a first clinical diagnosis of CNS demyelination (FCD).

METHODS: Cases with a FCD were recruited soon after diagnosis and followed annually thereafter. A variety of environmental, behavioural and clinical covariates were measured at five-year review. Anxiety and depression were measured using the Hospital Anxiety & Depression Scale (HADS), and fatigue by the Fatigue Severity Scale (FSS).

RESULTS: Of the 236 cases, 40.2% had clinical anxiety (median HADS-A: 6.0), 16.0% had clinical depression (median HADS-D: 3.0), and 41.3% had clinical fatigue (median FSS: 4.56). The co-occurrence of all three symptoms was 3.76 times greater than expectation. Younger age, higher disability, concussion or other disease diagnosis were independently associated with a higher anxiety score; male sex, higher disability, being unemployed, less physical activity, and antidepressant and/or anxiolytic-sedative medication use were independently associated with a higher depression score. Higher disability, immunomodulatory medication use, other disease diagnosis and anxiolytic-sedative medication use were independently associated with having fatigue, while female sex, higher BMI, having had a concussion, being unemployed and higher disability were associated with a higher fatigue score.

CONCLUSION: These results support previous findings of the commonality of anxiety, depression and fatigue in established MS and extend this to post-FCD and early MS cases. The clustering of the three symptoms indicates that they may share common antecedents.