∈,∈∨q -fuzzy subgroup

Fuzzy subrings and ideals redefined

A genera1 development of the theory of fuzzy sublattices is provided in the paper. Several characterizations of a fuzzy sublattice, fuzzy idea1 (dual ideal), and fuzzy prime idea1 (dual ideal) are obtained. Structural theorems for fuzzy sublattices, fuzzy ideals (dual ideals) generated by a fuzzy set are proved. Moreover, the notion of fuzzy convex sublattice is introduced and discussed. Various fuzzy analogs of the results of classical lattice theory are established.

Fuzzy lattices

(e, e V q )-fuzzy normal, quasinormal and maximal subgroups

Water quality management policies, which are proposed to prevent, control, or treat environmental problems related to quality of water, are broad and complex issues. We have various types of water resources, different water uses, and a lot of decision parameters with several levels of decision makers involved. Moreover, there are a lot of strategies and technologies available to be applied for water quality management and so environmental decision makers are required to evaluate and prioritize them in order to choose the best possible plan for each particular problem. To provide a comprehensive but easy to use tool in the assessment and evaluation of water quality policies, the concept of water quality index (WQI) has been developed. Due to the abovementioned complexities, to get this index, there is a need for a methodology to not only structure and identify information relevant to the problem but also to help users reach a decision. Designing a multiple-attribute decision support expert system, which makes expert knowledge available to nonexpert users, can do this. In doing so, we may encounter qualitative or linguistic assessments in the index making process. Thus, fuzzy set theory can be applied to recognize this inherent fuzziness of such a process. Briefly, in this study we propose a fuzzy multiple-attribute decision support expert system to compute the water quality index and to provide an outline for the prioritization of alternative plans based on the amount of improvements in WQI. At the end, applicability and usefulness of the proposed methodology is revealed by a case study.

Naseem Ajmal

Papers

Level subgroups and union of fuzzy subgroups

On fuzzy rings

Fuzzy ideals and fuzzy prime ideals of a ring

The lattices of fuzzy subgroups and fuzzy normal subgroups

Homomorphism of fuzzy groups, correspondence theorem and fuzzy quotient groups