Several new results based on the study of distance measures of intuitionistic fuzzy sets

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CHEN C.; DENG X.

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Journal: Iranian Journal of Fuzzy Systems Year:2020 | Volume:17 | Issue:2 Page(s): 147-163

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Title

Several new results based on the study of distance measures of intuitionistic fuzzy sets

Author(s)

CHEN C. | DENG X. | Issue Writer Certificate

Keywords

Intuitionistic fuzzy setQ2

distance measureQ2

inclusion relationQ2

hesitancy degreeQ2

characteristic functionQ2

Abstract

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.

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APA: Copy

CHEN, C., & DENG, X.. (2020). Several new results based on the study of distance measures of intuitionistic fuzzy sets. IRANIAN JOURNAL OF FUZZY SYSTEMS, 17(2 ), 147-163. SID. https://sid.ir/paper/375740/en

Vancouver: Copy

CHEN C., DENG X.. Several new results based on the study of distance measures of intuitionistic fuzzy sets. IRANIAN JOURNAL OF FUZZY SYSTEMS[Internet]. 2020;17(2 ):147-163. Available from: https://sid.ir/paper/375740/en

IEEE: Copy

C. CHEN, and X. DENG, “Several new results based on the study of distance measures of intuitionistic fuzzy sets,” IRANIAN JOURNAL OF FUZZY SYSTEMS, vol. 17, no. 2 , pp. 147–163, 2020, [Online]. Available: https://sid.ir/paper/375740/en

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