Iranian journal of fuzzy systems
Volume:3 Issue: 1, 2006

Fuzzy Linear Programming models and methods has been one of the most and well studied topics inside the broad area of Soft Computing. Its applications as well as practical realizations can be found in all the real world areas. In this paper a basic introduction to the main models and methods in fuzzy mathematical programming, with special emphasis on those developed by the authors, is presented. As a whole, Linear Programming problems with fuzzy costs, fuzzy constraints and fuzzy coefficients in the technological matrix are analyzed. Finally, future research and development lines are also pointed out by focusing on fuzzy sets based heuristic algorithms.

In this paper, we introduce intuitionistic fuzzy contraction mapping and prove a fixed point theorem in intuitionistic fuzzy metric spaces.

This paper addresses the design of control charts for both variable (x chart) and attribute (u and c charts) quality characteristics, when there is uncertainty about the process parameters or samples data. Derived control charts are more flexible than the strict crisp case, due to the ability of encompassing the effects of vagueness in form of the degree of expert’s presumption. We extend the use of proposed fuzzy control charts in case of linguistic data using a developed defuzzifier index, which is based on the metric distance between fuzzy sets.

We introduce the concepts of intuitionistic fuzzy group congruences, intuitionistic fuzzy semilattice congruences and intuitionistic fuzzy normal congruences. And we obtain some results.

Polygroups are multi-valued systems that satisfy group like axioms. Using the notion of “belongingness ()” and “quasi-coincidence ()” of fuzzy points with fuzzy sets, the concept of ()-fuzzy subpolygroup is introduced. The study of ()-fuzzy normal subpolygroups of a polygroup are dealt with. Characterization and some of the fundamental properties of such fuzzy subpolygroups are obtained. ()-fuzzy cosets determined by ()-fuzzy subpolygroups are discussed. Finally, we give the defi-nition of a fuzzy subpolygroup with thresholds which is a generalization of an ordinary fuzzy subpolygroup and an ()-fuzzy subpolygroup and discus relations between two fuzzy subpolygroups.

Designing an effective criterion for selecting the best rule is a major problem in the process of implementing Fuzzy Learning Classifier (FLC) systems. Conventionally confidence and support or combined measures of these are used as criteria for fuzzy rule evaluation. In this paper new entities namely precision and recall from the field of Information Retrieval (IR) systems is adapted as alternative criteria for fuzzy rule evaluation. Several different combinations of precision and recall are redesigned to produce a metric measure. These newly introduced criteria are utilized as a rule selection mechanism in the method of Iterative Rule Learning (IRL) of FLC. In several experiments, three standard datasets are used to compare and contrast the novel IR based criteria with other previously developed measures. Experimental results illustrate the effectiveness of the proposed techniques in terms of classification performance and computational efficiency.