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An Approach for Decision Making with Linguistic Intuitionistic Fuzzy Interval Value
Li Zou, Yunhui Gao, Qingkun Liu and Xin Liu

In the reality, people use linguistic value rather than numerical information to express their evaluations or preferences in decision making problems. To deal with both positive and negative information, we propose a linguistic decision making approach based on linguistic intuitionistic fuzzy interval pair. The fuzzy logical algebra is an important tool to deal with fuzzy information. As a prelinear residuated structure, triangle algebras are used to develop a logic that formally characterizes tautologies (true formulas) in interval valued residuated lattices. In this paper, based on 2n-element linguistic truth-valued lattice implication algebra 𝓛𝓘2n = (LI2n,⋃,∩,→, ((hn, t), (hn, f )), ((h1, t), (h1, f))), we discuss the 6-element linguistic truth-valued intuitionistic fuzzy lattice triangular algebra structure,transforming it into the linguistic truth-valued intuitionistic fuzzy interval value by using two unary operations μ and ν of triangular algebra, defining the transformation function [μ ⦿ ν] and comparing the interval values by using scoring functions. Then combine the interval values with lingusitic generalized ordered weighted averaging operator(referred to as LGOWA) and apply it to decision-making. The illustration example shows that the proposed approach more effective for decision making under a fuzzy environment with both positive and negative linguistic truth values.

Keywords: Lattice implication algebra, linguistic truth-valued intuitionisitic fuzzy lattice, linguistic intuitionistic fuzzy interval value, LGOWA operator

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