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In this paper, we introduce the complex fuzzy ordered weighted distance (CFOWD) measure. It is a new measure that uses the main characteristics of the the ordered weighted averaging (OWA) operator and uncertain information represented as complex fuzzy values. This measure includes a wide range of distance measures such as the complex fuzzy maximum distance, the complex fuzzy minimum distance, the normalized complex fuzzy distance (NCFD), the complex fuzzy ordered weighted Hamming distance (CFOWHD), complex fuzzy ordered weighted Euclidean distance (CFOWED), complex fuzzy ordered weighted geometric distance (CFOWGD), the normalized complex fuzzy Ham- ming distance (NCFHD) and the normalized complex fuzzy Euclidean distance (NCFED). We study some of its main properties. Finally, based on CFOWD measures, we give an illustrative example regarding the selected problem. [ABSTRACT FROM AUTHOR]

It is doubtless that intuitionistic fuzzy set (IFS) theory plays an increasingly important role in solving the problems under uncertain situation. As one of the most critical members in the theory, distance measure is widely used in many aspects. Nevertheless, it is a pity that part of the existing distance measures has some drawbacks in practical significance and accuracy. To make up for their drawbacks and pursue more accuracy and effectiveness, in this paper, we propose a new inclusion relation of IFSs and a new definition called strict distance measure. Based on this new relation, an analysis is given to point out that the common shortcoming of Hamming distance measure and Euclidean distance measure is the mishandling of hesitancy degree. Therefore, the role of hesitancy degree in distance measure is studied deeply and then three strict distance measures are put forward to overcome the above shortcoming. In addition, a novel definition called the characteristic function of distance measure is defined to describe the character of strict distance measure. On this basis, a theorem is presented to illustrate the inevitability of the occurrence of unrecognized result in pattern recognition problems in some special cases. This theorem also shows that the problem cannot be entirely attributed to distance measures. In view of this condition, we provide an appropriate solution. Compared with other existing distance measures in some examples, the superiorities of our improved distance measures are demonstrated to be more effective and more significant. [ABSTRACT FROM AUTHOR]