A note on "A novel approach to multi attribute group decision making based on trapezoidal interval type-2 fuzzy soft sets"

Ahmed Mostafa Khalil, Nasruddin Hassan

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

Zhang and Zhang (2013) proposed an extended soft set model called trapezoidal interval type-2 fuzzy soft sets by combining trapezoidal interval type-2 fuzzy sets and soft sets and showed some examples of its operations, along with an application in decision making. However, we found that some results are incorrect. Thus, the purpose of this note is to point out that assertions (3) and (4) of Theorem 3.2 in Zhang and Zhang (2013) are not true, as well, assertion (3) of Theorem 3.5 is generally not true, while assertions (4)-(6) of Theorem 3.5 can be similarly proven to be incorrect. We also introduce the notion of a generalized trapezoidal interval type-2 fuzzy soft subset and fuzzy soft equal, and use these notions to correct the flaw in assertions (3) and (4) of Theorem 3.2 of Zhang and Zhang (2013). Finally we introduce two new definitions and a theorem to improve the work of Zhang and Zhang (2013), along with two examples.

Original languageEnglish
JournalApplied Mathematical Modelling
DOIs
Publication statusAccepted/In press - 8 May 2015

Fingerprint

Soft Set
Group Decision Making
Fuzzy sets
Fuzzy Sets
Assertion
Decision making
Attribute
Defects
Interval
Theorem
Interval type-2 Fuzzy Sets
Decision Making
Subset

Keywords

  • Counterexamples
  • Interval type-2 fuzzy sets
  • Main results
  • Trapezoidal interval type-2 fuzzy soft sets

ASJC Scopus subject areas

  • Applied Mathematics
  • Modelling and Simulation

Cite this

A note on "A novel approach to multi attribute group decision making based on trapezoidal interval type-2 fuzzy soft sets". / Khalil, Ahmed Mostafa; Hassan, Nasruddin.

In: Applied Mathematical Modelling, 08.05.2015.

Research output: Contribution to journalArticle

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