In 2011 Alkhazaleh and Salleh defined the concept of soft expert sets where the user can know the opinion of all the experts in one model and give an application of this concept in decision-making problems. Also, they introduced the concept of the fuzzy soft expert set as a combination between the soft expert set and the fuzzy set. In 2010 Majumdar and Samanta presented the concept of a generalized fuzzy soft sets. The purpose of this paper is to combine the work of Alkhazaleh and Salleh (2011) and Majumdar and Samanta (2010), from which we can obtain a new concept: generalized fuzzy soft expert sets (GFSESs). We also introduce its operations, namely, complement, union intersection, “AND” and “OR”, and study their properties. The generalized fuzzy soft expert sets are used to analyze a decision-making problem. Also in our model the user can know the opinion of all experts in one model. In this work we also introduce the concept of a generalized fuzzy soft expert sets with multiopinions (four opinions), which will be more effective and useful. Finally, we give an application of this concept in decision-making problem.

Background:Within a setting without organised breast cancer screening, the characteristics and survival of very early breast cancer were determined.Methods:All 4930 women diagnosed with breast cancer in University Malaya Medical Center, Malaysia from 1993 to 2011 were included. Factors associated with very early presentation (stage I) at diagnosis were identified. Tumour characteristics, management patterns, and survival of very early breast cancer were described, and where appropriate, compared with other settings.Results:Proportion of women presenting with stage I breast cancer significantly increased from 15.2% to 25.2% over two decades. Factors associated with very early presentation were Chinese ethnicity, positive family history of breast cancer, and recent period of diagnosis. Within stage I breast cancers, median tumour size at presentation was 1.5 cm. A majority of stage I breast cancer patients received mastectomy, which was associated with older age, Chinese ethnicity, postmenopausal status, and larger tumours. Chemotherapy was administered in 36% of patients. Five-year age-adjusted relative survival for women with stage I breast cancer was 99.1% (95% CI: 97.6–99.6%).Conclusions:The proportion of women presenting with very early breast cancer in this setting without organised screening is increasing. These women seem to survive just as well as their counterparts from affluent settings.

Abstract. The population of many countries might undergo dramatic changes in the coming decades due to continuous increases in life expectancy. The sustained reduction in mortality rates and its systematic underestimation has been attracting the significant interest of researchers in recent years because of its potential impact on population size and structure, social security systems, and (from an actuarial perspective) the life insurance and pensions industry worldwide. Among all projection methods, the Lee-Carter method has been widely accepted by the actuarial community. This paper explores the use of the Lee-Carter method to forecast the mortality rates for Malaysian population. The index of the level of mortality for each gender, and the shape and sensitivity coefficients for 18 age groups were obtained through the LeeCarter method. The Singular Values Decomposition (SVD) is used to forecast the general index for the time period that goes from 2011 to 2030. Since the model involves nonlinear equations that are explicitly difficult to solve, the Matrix Laboratory Version 7.0 (MATLAB 7.0) software will be used in the study. The empirical data sets of Malaysia population for the period of 1981-2010 and for both genders will be considered.

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