A Study of Normal Fuzzy Subgroups and Characteristic Fuzzy Subgroups of a Fuzzy GroupAjmal, Naseem; Jahan, Iffat
2012 Fuzzy Information and Engineering
doi: 10.1007/s12543-012-0106-0
AbstractIn this paper, we investigate the properties of normal fuzzy subgroups of a fuzzy group. We also introduce the notion of a characteristic fuzzy subgroup of a fuzzy group, of which we provide level subset and strong level subset characterizations. Then we prove that a characteristic fuzzy subgroup of a fuzzy group is a normal fuzzy subgroup. Besides we prove that the commutator subgroup generated by the commutator of two normal fuzzy subgroups of a fuzzy group is contained in their intersection. Finally, we construct many new lattices and sublattices of fuzzy subgroups and normal fuzzy subgroups of a given fuzzy group. We also construct lattices of characteristic fuzzy subgroups possessing sup-property.
Priority Based Fuzzy Goal Programming Technique to Fractional Fuzzy Goals Using Dynamic ProgrammingBiswas, Animesh; Dewan, Shyamali
2012 Fuzzy Information and Engineering
doi: 10.1007/s12543-012-0109-x
AbstractThis paper describes the use of preemptive priority based fuzzy goal programming method to fuzzy multiobjective fractional decision making problems under the framework of multistage dynamic programming. In the proposed approach, the membership functions for the defined objective goals with fuzzy aspiration levels are determined first without linearizing the fractional objectives which may have linear or nonlinear forms. Then the problem is solved recursively for achievement of the highest membership value (unity) by using priority based goal programming methodology at each decision stages and thereby identifying the optimal decision in the present decision making arena. A numerical example is solved to represent potentiality of the proposed approach.
Mutually Dependent Multi-criteria Decision MakingDalalah, Doraid; Al-Tahat, Mohammad; Bataineh, Khaled
2012 Fuzzy Information and Engineering
doi: 10.1007/s12543-012-0111-3
AbstractIn this paper, a model to estimate the weights of mutually dependent criteria, based on cause-effect assessments of a group of professionals, is developed for problem of multiple criteria decision making (MCDM). Here, both DEMATEL (Decision Making Trial and Evaluation Laboratory) and TOPSIS (Technique for Order Performance by Similarity to Ideal Solution) models are combined and extended to handle fuzzy evaluations where the first is used to set the weights of the interdependent criteria and the second for drawing a decision from a group of professionals who use linguistic ratings in their evaluation.The presented model is characterized by the capability to estimate the criteria weights when the criteria are interrelated. The strict determination of the criteria weights prior to the assessment process is eliminated as they are computed by the DEMATEL part. A classical case-study of optimal sore throat treatment in primary care unit is used to demonstrate the efficiency of the proposed model.
Application Research on FSDM-based GA in Optimizing Curriculum Schedule Model in UniversitiesDuan, Yuan; Zhong, Yu-bin; Li, Yan-qiang
2012 Fuzzy Information and Engineering
doi: 10.1007/s12543-012-0112-2
AbstractIn this paper, we first analyze the relationship between curricula, teachers, classes, time slices and classrooms in a graph. Then on the basis of constraint conditions in curriculum schedule practically in universities, we presents its optimization model, in which the fuzzy synthetic decision-making (FSDM) is used to optimize genetic algorithm (GA), and a new GA encoding scheme is employed to design fitness and punishment functions for the curriculum schedule problem. This model effectively improved a running performance, which provides a better implementation approach to improvements of the existing curriculum schedule systems. The experimental results show that fitness values of the FSDM-based GA are of obvious evolutional tendency, the chromosome encoding scheme and the fitness function can meet its requirements preferably, and the more adequate computation resources, the greater possibilities of no restoration for the obtained optimal individual.