Fuzzy risk analysis based on interval-valued fuzzy numbers

An interval type-2 fuzzy technique for order preference by similarity to ideal solutions using a likelihood-based comparison approach for multiple criteria decision analysis

“…A number of studies have presented specific linguistic rating systems for converting decision makers' linguistic responses into proper IT2TrF numbers. For example, the IT2TrF data can be conveniently established by employing the following useful linguistic scales, including threepoint linguistic scales (Chen & Lee, 2010a;Han & Mendel, 2012;Zhai & Mendel, 2011), four-point linguistic scales (Chen & Lee, 2010a), five-point linguistic scales (Chen & Lee, 2010a;Ngan, 2013), seven-point linguistic scales (Abdullah & Najib, 2014;Chen & Lee, 2010b;Gilan, Sebt, & Shahhosseini, 2012;Wang, Liu, & Qin, 2012;Zhang & Zhang, 2013), and nine-point linguistic scales (Chen, 2011b(Chen, , 2013a(Chen, , 2013c(Chen, , 2014bChen, Chang, & Lu, 2013;Wang & Chen, 2014;Wei & Chen, 2009). Note that most of the IT2TrF numbers corresponding to linguistic terms are bounded within [0, 1], such as the linguistic rating systems presented by Chen and Chen (2009), Wei and Chen (2009), Chen and Lee (2010b), Wang et al (2012), Chen et al (2013), Chen (2011b), Chen (2013a), Chen (2013c), Chen (2014b), Ngan (2013), Zhang and Zhang (2013), Abdullah and Najib (2014), and Wang and Chen (2014).…”

A weighted aggregation operators multi-attribute group decision-making method based on interval-valued trapezoidal fuzzy numbers

“…2, where 0 6 a L 1 6 a L 2 6 a L 3 6 a L 4 6 1; 0 6 a U 1 6 a U 2 6 a U 3 6 a U (2) The operation of interval-valued trapezoidal fuzzy numbers (Wei & Chen, 2009). Suppose that…”

“…Ashtiani, Haghighirad, Makui and Montazer (2009) proposed the extended TOPSIS group decision-making method based on the interval-valued triangular fuzzy numbers. Wei and Chen (2009) proposed similarity measures between generalized interval-valued trapezoidal fuzzy numbers (GIVTFN) for risk analysis. For the multi-attribute decision making that the weights of attributes and attribute values is general interval-valued trapezoidal fuzzy number, this paper proposed a group decision-making method based on weighted aggregation operator, ordered weighted aggregation operator and hybrid aggregation operator.…”

Analogy-based software effort estimation using Fuzzy numbers

“…In this section, we briefly review some fundamental concepts of generalized Fuzzy numbers Wei & Chen, 2009a, 2009b …”

“…Later we will use   Chen (1985) proposed some arithmetic operations for generalized Fuzzy numbers that have been later subject of debate by Hsieh et al (1999) who emphasized that these arithmetic operations do not change the shape of generalized Fuzzy number after carrying out any arithmetic operation. The Fuzzy arithmetic operations proposed by Chen (1985) where a1, b1, c1, d1, a2, b2, c2 and d2 are any real numbers (2) Generalized Fuzzy numbers subtraction (Ө): (Wei & Chen, 2009a, 2009b …”