A new fuzzy clustering algorithm based on multi-objective mathematical programming

This paper presents a new fuzzy clustering approach based on an efficient fuzzy distance measurement and multi-objective mathematical programming. As the human intuitions implies, it is not rational to measure the distance between two fuzzy clusters by a crisp measurement. Unfortunately, most of the existing fuzzy clustering approaches, consider the distance between two fuzzy clusters as a crisp value. This will yield a rounding error and is assumed a pitfall. In this paper, an efficient fuzzy distance measurement is developed in order to measure distance between multi-dimensional fuzzy clusters as a fuzzy measure. The triangle fuzzy numbers (TFNs) are used to develop the applicable fuzzy clustering approach. Then, multi-objective mathematical programming is utilized to optimize the center, and left and right spreads of fuzzy clusters which are calculated as TFNs. More formally, the advantages of proposed fuzzy clustering in comparison with existing procedure is (a) developing an efficient fuzzy distance measurement, and (b) optimizing the center and spread of the fuzzy clusters using multi-objective mathematical programming. An illustrative random simulated instance is supplied in order to present the mechanism and calculations of the proposed fuzzy clustering approach. The performance of proposed fuzzy clustering approach is compared with an existing Fuzzy C-means approach in the literature on several benchmark instances. Then, the Error Ratio is defined to compare the performance of both methods and comprehensive statistical analysis and hypothesis test are accomplished to test the performance of both methods. Finally, a real case study, called group decision making multi-possibility multi-choice investment partitioning problem, is discussed in order to illustrate the efficacy and applicability of the proposed approach in real world problems. The proposed approach is straightforward, its quality is as well as existing approach in the literature and its results are promising.