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1

Complex Interval-valued Intuitionistic Fuzzy Sets and their Aggregation Operators

Garg Harish, Rani Dimple

Fundamenta Informaticae

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2019

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Vol. 164, nr 1

61--101

EN

The objective of this manuscript is to present the concept of the complex interval-valued intuitionistic fuzzy (CIVIF) set, their algebraic operations and their corresponding aggregation operators, which can better represent the time-periodic problems and two-dimensional information in a single set. The proposed CIVIF set includes the characteristics of both complex intuitionistic fuzzy set, as well as the interval-valued intuitionistic fuzzy sets. Some of the basic operational laws and their properties have been investigated in details. Also, we have developed some new weighted and ordered weighted averaging and geometric aggregation operators with complex interval-valued intuitionistic fuzzy information. The proposed operations are the generalization of the operations of interval-valued intuitionistic fuzzy, complex fuzzy and complex intuitionistic fuzzy theories. Furthermore, a group decision-making method is established based on these operators. Finally, an illustrative example is used to illustrate the applicability and validity of the proposed approach and compare the results with the existing methods to show the effectiveness of it.

2

Interval-valued intuitionistic fuzzy failure modes and effect analysis of the system failure risk estimation

Nguyen H.

Journal of KONES

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2017

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Vol. 24, No. 2

159--166

EN

Among the risk assessment methods, failure modes and effects analysis (FMEA) is a popular, widely used engineering technique in many areas. It can be used to identify and eliminate known or potential failure modes to enhance reliability and safety of complex systems. In practice, risk estimations encounter difficulties connected with shortage of data. In such cases, we have to rely on subjective estimations made by persons with practical knowledge in the field of interest, i.e. experts. However, in some realistic situations, the decision makers might be unable to assign the exact values to the evaluation judgments due to his/her limited knowledge. In other words, there is a certain degree of hesitancy in human cognition and his/her judgment, who may have insufficient knowledge of the problem domain or uncertainty in assigning the evaluation values to the objects considered. In order to deal with ambiguity and uncertainty in the imperfect information, there have been recently proposed many various such theories as fuzzy sets, interval-valued fuzzy sets, type-2 fuzzy sets, hesitant sets, grey sets, rough sets and intuitionistic fuzzy sets. They have drawn more and more attention of scholars and been adopted in many applications This article addresses the Atanassov’s interval-valued intuitionistic fuzzy sets and FMEA methods in the risk estimation of the system failures based on the expert judgments.

3

An Interval-Valued Intuitionistic Fuzzy Rough Set Model

Zhang Z.

Fundamenta Informaticae

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2009

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Vol. 97, nr 4

471-498

EN

Given a widespread interest in rough sets as being applied to various tasks of data analysis it is not surprising at all that we have witnessed a wave of further generalizations and algorithmic enhancements of this original concept. This paper proposes an interval-valued intuitionistic fuzzy rough model by means of integrating the classical Pawlak rough set theory with the interval-valued intuitionistic fuzzy set theory. Firstly, some concepts and properties of interval-valued intuitionistic fuzzy set and interval-valued intuitionistic fuzzy relation are introduced. Secondly, a pair of lower and upper interval-valued intuitionistic fuzzy rough approximation operators induced from an interval-valued intuitionistic fuzzy relation is defined, and some properties of approximation operators are investigated in detail. Furthermore, by introducing cut sets of interval-valued intuitionistic fuzzy sets, classical representations of interval-valued intuitionistic fuzzy rough approximation operators are presented. Finally, the connections between special interval-valued intuitionistic fuzzy relations and interval-valued intuitionistic fuzzy rough approximation operators are constructed, and the relationships of this model and the others rough set models are also examined.