7 Arithmetic operations on generalized semielliptic intuitionistic fuzzy numbers and their application in multicriteria decision making

AbstractIn a real world situation, whenever ambiguity exists in the modeling of intuitionistic fuzzy numbers (IFNs), interval valued intuitionistic fuzzy numbers (IVIFNs) are often used in order to represent a range of IFNs unstable from the most pessimistic evaluation to the most optimistic one. IVIFNs are a construction which helps us to avoid such a prohibitive complexity. This paper is focused on two types of arithmetic operations on interval valued intuitionistic fuzzy numbers (IVIFNs) to solve the interval valued intuitionistic fuzzy multi-objective linear programming problem with pentagonal intuitionistic fuzzy numbers (PIFNs) by assuming differentαandβcut values in a comparative manner. The objective functions involved in the problem are ranked by the ratio ranking method and the problem is solved by the preemptive optimization method. An illustrative example with MATLAB outputs is presented in order to clarify the potential approach.

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Generalized Choquet Integral Operator of Triangular Atanassov’s Intuitionistic Fuzzy Numbers and Application to Multi-Attribute Group Decision Making

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488516500306 ◽

2016 ◽

Vol 24 (05) ◽

pp. 647-683 ◽

Cited By ~ 5

Author(s):

Jiu-Ying Dong ◽

Li-Lian Lin ◽

Feng Wang ◽

Shu-Ping Wan

Keyword(s):

Decision Making ◽

Integral Operator ◽

Group Decision Making ◽

Fuzzy Numbers ◽

Group Decision ◽

Weighted Average ◽

Intuitionistic Fuzzy Numbers ◽

Intuitionistic Fuzzy ◽

Goal Programming Model ◽

Ordered Weighted Average

The purpose of this paper is to propose a new approach to interactive multi-attribute group decision making with triangular Atanassov's intuitionistic fuzzy numbers (TAIFNs). The contribution of this study is fivefold: (1) Minkowski distance between TAIFNs is firstly defined; (2) We define the possibility attitudinal expected values of TAIFNs and thereby present a novel risk attitudinal ranking method of TAIFNs which can sufficiently consider the risk attitude of decision maker; (3) The weighted average operator (TAIFWA) and generalized ordered weighted average (TAIFGWA) operator of TAIFNs are defined as well as the hybrid ordered weighted average (TAIFHOWA) operator; (4) To study the interaction between attributes, we further develop the generalized Choquet (TAIF-GC) integral operator and generalized hybrid Choquet (TAIF-GHC) integral operator of TAIFNs. Their desirable properties are also discussed; (5) The individual overall value of alternative is obtained by TAIF-GC operator and the collective one is derived through TAIFWA operator. Fuzzy measures of attribute subsets and expert weights are objectively derived through constructing multi-objective optimization model which is transformed into the goal programming model to solve. The system analyst selection example verifies effectiveness of the proposed approach.

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