Generalized intuitionistic fuzzy geometric aggregation operator and its application to multi-criteria group decision making

Abstract

In general, for multi-criteria group decision making problem, there exist inter-dependent or interactive phenomena among criteria or preference of experts, so that it is not suitable for us to aggregate them by conventional aggregation operators based on additive measures. In this paper, based on fuzzy measures a generalized intuitionistic fuzzy geometric aggregation operator is investigated for multiple criteria group decision making. First, some operational laws on intuitionistic fuzzy values are introduced. Then, a generalized intuitionistic fuzzy ordered geometric averaging (GIFOGA) operator is proposed. Moreover, some of its properties are given in detail. It is shown that GIF-OGA operator can be represented by special t-norms and tconorms and is a generalization of intuitionistic fuzzy ordered weighted geometric averaging operator. Further, an approach to multiple criteria group decision making with intuitionistic fuzzy information is developed where what criteria and preference of experts often have inter-dependent or interactive phenomena among criteria or preference of experts is taken into account. Finally, a practical example is provided to illustrate the developed approaches.

A Method for Multi-Attribute Group Decision Making Based on Generalized Interval-Valued Intuitionistic Fuzzy Choquet Integral Operators

“…Tremendous efforts have been spent, and significant advances have been made in the development of the intuitionistic fuzzy set theory and its applications for solving various decision making problems. [3][4][5][6][7][8][9][10][11][12][13][14] The popularity of the intuitionistic fuzzy sets for solving a variety of decision making problems is due to its capacity for adequately modeling the subjective and imprecise assessment of the decision makers. Later, Atanassov and Gargov 15 further introduced the interval-valued intuitionistic fuzzy sets (IVIFSs), a generalization of IFSs that provides the membership function and nonmembership function with intervals in [0,1] rather than real numbers.…”

A Generalized Triangular Intuitionistic Fuzzy Geometric Averaging Operator for Decision-Making in Engineering and Management

“…In this section, motivated by existing achievements [32,36,37], we develop some triangular intuitionistic fuzzy geometric averaging operators and discuss some of their useful properties and then introduce new generalized geometric operators for TIFNs.…”

Some geometric aggregation operators based on log-normally distributed random variables

“…Xu et al [3][4][5] extended these two operators to accommodate the situations where the input arguments are fuzzy numbers, for example, Xu 3 proposed the fuzzy ordered weighted geometric (FOWG) operator, Xu and Da 4 proposed the uncertain ordered weighted geometric (UOWG) operator, Wang and Yang 5 proposed the trapezoidal fuzzy ordered weighted geometric (TFOWG) operator; Xu et al [6][7][8][9][10][11] extended these two operators to accommodate the situations where the input arguments are intuitionistic fuzzy numbers or extended intuitionistic fuzzy numbers, for instance, Xu and Yager 6 proposed the intuitionistic fuzzy weighted geometric (IFWG) operator, intuitionistic fuzzy ordered weighted geometric (IFOWG) operator and intuitionistic fuzzy hybrid geometric (IFHG) operator, Wei 7 proposed the dynamic intuitionistic fuzzy weighted geometric (DIFWG) operator and uncertain dynamic intuitionistic fuzzy weighted geometric (UDIFWG) operator, Tan 8 proposed the generalized intuitionistic fuzzy ordered geometric averaging (GIFOGA) operator, Xu 9 and Xu and Chen 10 developed the interval-valued intuitionistic fuzzy weighted geometric (IIFWG) operator, intervalvalued intuitionistic fuzzy ordered weighted geometric (IIFOWG) operator and interval-valued intuitionistic fuzzy hybrid geometric (IIFHG) operator, Wang 11 proposed the fuzzy number intuitionistic fuzzy weighted geometric (FIFWG) operator, fuzzy number intuitionistic fuzzy ordered weighted geometric (FIFOWG) operator and fuzzy number intuitionistic fuzzy hybrid geometric (FIFHG) operator; Xu et al [12][13][14][15] extended these two operators to accommodate the situations where the input arguments are linguistic variables or uncertain linguistic variables, for example, Xu 12 proposed the linguistic weighted geometric averaging (LWGA) operator, linguistic ordered weighted geometric averaging (LOWGA) operator and linguistic hybrid geometric averaging (LHGA) operator, Wei 13 proposed the extended 2-tuple weighted geometric (ET-WG) operator and extended 2-tuple ordered weighted geometric (ET-OWG) operator, Xu 14 proposed the uncertain linguistic weighted geometric mean (ULWGM) operator and uncertain linguistic ordered weighted geometric (ULOWG) operator, Wei …”