Abstract
The Triple I method for the model of intuitionistic fuzzy modus tollens (IFMT) satisfies the local reductivity instead of the reductivity. In order to improve the quality of the Triple I method for lack of reductivity, the paper is intended to present a new approximate reasoning method for IFMT problem. First, the concept of intuitionistic fuzzy difference operator is proposed and its properties on the lattice structure of intuitionistic fuzzy sets are studied. Then, the dual Triple I method for FMT based on residual fuzzy difference operator is presented and the dual Triple I method is generated for IFMT. Moreover, a decomposition method of IFMT is provided. Furthermore, the reductivity of methods is investigated. Finally,α-dual Triple I method of IFMT is proposed.
Highlights
The real world is too complicated to be described precisely and it is full of uncertainty
We introduce the concepts of the intuitionistic fuzzy difference operators and coadjoint pair and provide the unified form of the residual intuitionistic fuzzy difference operators adjoint to intuitionistic t-conorms derived from the left-continuous t-norms
Taking into account 0∗ being the smallest element of L∗ in the Triple D Principle of intuitionistic fuzzy modus tollens (IFMT), we propose the α-Triple D principle as follows: A∗(x) should be the biggest intuitionistic fuzzy set on X satisfying (A∗ (x) ⊖L∗ B∗ (y)) ⊖L∗ (A (x) ⊖L∗ B (y)) ≤ α under the order of L∗ where α ∈ L∗
Summary
The real world is too complicated to be described precisely and it is full of uncertainty. For trying to provide a logic foundation for fuzzy reasoning, Wang proposed the full implication Triple I method (Triple I method for short). The intuitionistic fuzzy sets introduced by Atanassov [17] is a pair of fuzzy sets, namely, a membership and a nonmembership function, which represent positive and negative aspects of the given information. It constitutes an appropriate knowledge representation framework. In order to construct the theoretical foundation of intuitionistic fuzzy reasoning, Cornelis et al [24,25,26] have made fruitful pioneering work They presented the intuitionistic fuzzy t-norms and t-conorms [25]. We denote by FSs(X), IFSs(X) the set of all fuzzy sets in X and the set of all intuitionistic fuzzy sets, respectively
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