A comparison of three approaches for estimating (synthesizing) an interval type-2 fuzzy set model of a linguistic term for computing with words

Abstract

This article compares three methods [Interval Approach (IA), Enhanced Interval Approach (EIA) and Hao-Mendel Approach (HMA)] for estimating (synthesizing) an interval type-2 fuzzy set (IT2 FS) model for a word, beginning with data that are collected from a group of subjects, or from a single subject. It summarizes the stages for each of the methods in tables so it is possible to compare the steps of each stage side-by-side. It also demonstrates, by means of an example of three words, that using more information contained in the collected data intervals is equivalent to reducing the uncertainty in the IT2 FS model. It recommends the HMA because it uses more information contained in the collected data intervals than does the IA or the EIA, and because it is the only method to-date that leads to normal IT2 FSs. Such fuzzy sets are easier to compute with than are non-normal IT2 FSs.

Type-2 fuzzy linear systems

“…With successful applications in medicine (John and Innocent 2005;Garibaldi et al 2012;Mazandarani and Kamyad 2011;Najariyan et al 2011), control theory (Najariyan and Farahi 2015), food science (Zolfaghari et al 2014), mathematics (Najariyan and Mazandarani 2015), computing with words (Mendel 2016), decision making (Wang et al 2016;Das et al 2016), fuzzy logic is well known as an effective tool for dealing with uncertainty in modeling processes. Generalization of concepts and achievements already obtained in the field of mathematics using fuzzy logic have recently captured much attention.…”

Interval type-2 fuzzy Hamy mean operators and their application in multiple criteria decision making

“…Definition 1 (Mendel et al 2016) Let X be the universe of discourse. Then, a type-2 fuzzy set A can be represented by type-2 membership function A (x, u) as follows:…”

“…Definition 2 (Mendel et al 2016) Let à be a type-2 fuzzy set (T2FS) in the universe of discourse X represented by a type-2 membership function A (x, u). If all A (x, u) = 1, then à is called an interval type-2 fuzzy set (IT2FS).…”

“…In the last decade, the T2FS theory has been one of the most popular artificial intelligence research topics that attracted the attention of many researchers. A large number of studies have been published (Karnik and Mendel 2001a, b;Mendel and John 2002;Mendel et al 2006;Mendel 2007;Wu and Mendel 2009;Liu et al 2012a;Zhai and Mendel 2012;Greenfield and Chiclana 2013a, b;Chiclana and Zhou 2013), mainly in interval type-2 MCDM field (Wu and Mendel 2010;Chen and Lee 2010a, b, c, d;Chen and Wang 2013;Chen et al 2012;Chen 2013a, b, c;Qin and Liu 2015a, b;Qin et al 2015Qin et al , 2016Mendel 2016). For example, Wu and Mendel (2010) developed a computing with word-based method for interval type-2 fuzzy hierarchical MCDM method, and then applied to evaluating a weapon system.…”

Granular computing: from granularity optimization to multi-granularity joint problem solving

“…The principal types of granules include possibilistic, veristic and probabilistic (Pawlak 1992). The principal modes of generalization in fuzzy information granulation theory can be mainly generalized to fuzzification; granulation and fuzzy granulation (Zadeh 1997;Mendel 2016). 2.…”