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Interval Cut-Set of Generalized Interval-Valued Intuitionistic Fuzzy Sets

Amal Kumar Adak (Vidyasagar University, India), Monoranjan Bhowmik (Vidyasagar Teacher’s Training College, India) and Madhumangal Pal (Vidyasagar University, India)

Source Title: International Journal of Fuzzy System Applications (IJFSA) 2(3)

DOI: 10.4018/ijfsa.2012070103

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Abstract

In this paper, some different types of interval cut-set of genaralized interval-valued intuitionistic fuzzy sets (GIVIFSs), complement of these cut-sets are introduced. Some properties of those cut-set of GIVIFSs are investigated. Also three decomposition theorems of GIVIFSs are obtained based on the different cut-set of GIVIFSs. These works can also be used in setting up the basic theory of GIVIFSs.

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Preliminaries

In this section, the concept of interval arithmetics are recalled. Let be the set of all closed subintervals of the interval . An interval on , say , is a closed subinterval of i.e., where and are lower and upper limits of respectively and satisfy the condition . For any two interval and where and then (i) , , (ii) , and (iii) , and .