Measuring Similarity and Ordering Based on Interval Type-2 Fuzzy Numbers

Hesamian, Gholamreza

doi:10.1109/tfuzz.2016.2578342

Cited by 18 publications

(13 citation statements)

References 53 publications

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“…Moreover, as has already been pointed out, the preorder in [19] does not extend the order of R; meanwhile, it can be proven that the preorder in [22] does extend it. Example 3 shows the ranking of two T2GFNs that are not IT2FNs.…”

Section: Propositionmentioning

confidence: 95%

“…Note that the methods provided in [19,22] for ranking IT2FNs are total preorders; however, to the best of our knowledge, there is no previous work where a partial order is established extending the order of the real numbers to T2FNs and not just to IT2FNs or IT2GFNs. Moreover, as has already been pointed out, the preorder in [19] does not extend the order of R; meanwhile, it can be proven that the preorder in [22] does extend it.…”

Section: Propositionmentioning

confidence: 99%

“…For example, intuitionist fuzzy numbers (IFNs) and generalized intuitionist fuzzy numbers (GIFNs), which are intuitionistic sets on the real line satisfying certain conditions, were defined and studied in [16][17][18]. Recently, interval type 2 fuzzy numbers (IT2FNs) have been defined in [19][20][21][22], as interval type 2 fuzzy sets (IT2FSs) on the real line fulfilling some properties. Besides, in [19,22], total preorders were given to ranking IT2FNs, but such preorders do not hold the property of antisymmetry, which is a theoretical and practical weakness.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, interval type 2 fuzzy numbers (IT2FNs) have been defined in [19][20][21][22], as interval type 2 fuzzy sets (IT2FSs) on the real line fulfilling some properties. Besides, in [19,22], total preorders were given to ranking IT2FNs, but such preorders do not hold the property of antisymmetry, which is a theoretical and practical weakness. Moreover, the total preorder given in [19] does not effectively extend the order of real numbers (see Example 2).…”

Section: Introductionmentioning

confidence: 99%

“…These sets are more general than the ones considered in [19,20,22], so that in each application, the expert can choose the linguistic labels that best fit the specifications of the problem. We obtain a partial order in T2GFNs and in T2FNs, extending the order of real numbers, as a first step to obtain in future investigations a total order (or a preorder).…”

Section: Introductionmentioning

confidence: 99%

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Since Lotfi A. Zadeh introduced the concept of fuzzy sets in 1965, many authors have devoted their efforts to the study of these new sets, both from a theoretical and applied point of view. Fuzzy sets were later extended in order to get more adequate and flexible models of inference processes, where uncertainty, imprecision or vagueness is present. Type 2 fuzzy sets comprise one of such extensions. In this paper, we introduce and study an extension of the fuzzy numbers (type 1), the type 2 generalized fuzzy numbers and type 2 fuzzy numbers. Moreover, we also define a partial order on these sets, which extends into these sets the usual order on real numbers, which undoubtedly becomes a new option to be taken into account in the existing total preorders for ranking interval type 2 fuzzy numbers, which are a subset of type 2 generalized fuzzy numbers.

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Section: Propositionmentioning

confidence: 95%

Section: Propositionmentioning

confidence: 99%