Intersection and union of type-n fuzzy sets

Aisbett, Janet; Rickard, John T.; Morgenthaler, David G.

doi:10.1109/fuzzy.2010.5584174

Cited by 5 publications

(3 citation statements)

References 12 publications

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“…In [56], [57], and [58] the authors proposed to handle higher levels of uncertainty using IT3 FLS. Nowadays, several researchers have developed its mathematical foundations and applied it to modeling, predicting, and controlling realworld situations.…”

Section: Introductionmentioning

confidence: 99%

“…The analysis of the state-of-the-art literature shows that IT3 models use singleton inputs [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [33], [34], [35], [36], [37], [38], [39], [40], [41], [42] and type-1, non-singleton inputs [32]. The applications of the IT3 FLS systems mainly covers the areas of: Mathematical theory [1], [2], [3], [4], [6], [11], [19], [24], [56], [57],…”

Section: Introductionmentioning

confidence: 99%

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A New Method for the Design of Interval Type-3 Fuzzy Logic Systems With Uncertain Type-2 Non-Singleton Inputs (IT3 NSFLS-2): A Case Study in a Hot Strip Mill

Mendez¹,

López-Juárez

Dorantes³

et al. 2023

IEEE Access

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This paper presents a new method for the construction and training of interval type-3 fuzzy logic systems whose inputs are uncertain type-2 non-singleton numbers (IT3 NSFLS-2). The proposed methodology is divided in two processes: 1) The novel construction of the structure of the IT3 NSFLS-2 systems based on: a) The level-alpha-0 of the interval type-2 fuzzy logic system (IT2-alpha-0 FLS), and on b) The secondary membership function using Gaussian modeling to construct each rule of the alpha-k fuzzy rule base (FRB), the firing intervals of the antecedent and the centroids of the consequent, and 2) The training methodology based on gradient descent algorithm to train the antecedent and consequent parameters of the alpha-0 FRB. The primary membership functions (MF) of the antecedents of the IT3 NSFLS-2 system are modeled as Gaussians with uncertain means and with common standard deviation. The proposal was applied and tested with the prediction of a transfer bar's surface temperature in an industrial hot strip mill facility located in Monterrey México. The modeling results show that the proposal supports the stability required by this critical process and shows the best performance when compared with similar methods.INDEX TERMS General type-2 fuzzy systems, gradient descent algorithm, hot strip mill, interval type-2 fuzzy systems, interval type-3 fuzzy systems, temperature prediction, type-2 non-singleton inputs.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A New Method for the Design of Interval Type-3 Fuzzy Logic Systems With Uncertain Type-2 Non-Singleton Inputs (IT3 NSFLS-2): A Case Study in a Hot Strip Mill

Mendez¹,

López-Juárez

Dorantes³

et al. 2023

IEEE Access

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“…They showed how to compute subsethood for general Type-2 and interval Type-3 fuzzy sets. Aisbett [91] recursively extended the fundamental set theory operations of intersection and union to Type-3 and higher level fuzzy sets. They assumed a generalized form of convexity and normality.…”

Section: Type-n Fuzzy Setsmentioning

confidence: 99%

A Comprehensive Literature Review of 50 Years of Fuzzy Set Theory

Kahraman¹,

Öztayşi²,

Onar³

2016

IJCIS

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Fuzzy sets have a great progress in every scientific research area. It found many application areas in both theoretical and practical studies from engineering area to arts and humanities, from computer science to health sciences, and from life sciences to physical sciences. In this paper, a comprehensive literature review on the fuzzy set theory is realized. In the recent years, ordinary fuzzy sets have been extended to new types and these extensions have been used in many areas such as energy, medicine, material, economics and pharmacology sciences. This literature review also analyzes the chronological development of these extensions. In the last section of the paper, we present our interpretations on the future of fuzzy sets.

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On the geometry of join and meet calculations for general type-2 fuzzy sets

Mendel

2011

2011 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2011)

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Intersection and union of type-n fuzzy sets

Abstract: This paper recursively extends the fundamental set theory operations of intersection and union to Type-3 and higher level fuzzy sets. A generalized form of convexity and normality is assumed.

Cited by 5 publications

References 12 publications

A New Method for the Design of Interval Type-3 Fuzzy Logic Systems With Uncertain Type-2 Non-Singleton Inputs (IT3 NSFLS-2): A Case Study in a Hot Strip Mill

A New Method for the Design of Interval Type-3 Fuzzy Logic Systems With Uncertain Type-2 Non-Singleton Inputs (IT3 NSFLS-2): A Case Study in a Hot Strip Mill

A Comprehensive Literature Review of 50 Years of Fuzzy Set Theory

On the geometry of join and meet calculations for general type-2 fuzzy sets

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