Jianhua Jin

Robustness of fuzzy reasoning via logically equivalence measure

Abstract In this paper, we discuss robustness of fuzzy reasoning. After proposing the definition of perturbation of fuzzy sets based on some logic-oriented equivalence measure, we present robustness results for various fuzzy logic connectives, fuzzy implication operators, inference rules and fuzzy reasoning machines, and discuss the relations between the robustness of fuzzy reasoning and that of fuzzy conjunction and implication operators. The robustness results are presented in terms of δ -equalities of fuzzy sets based on some logic-oriented equivalence measure, and the maximum of δ (which ensures the corresponding δ -equality holds) is derived.

Algebraic properties of L-fuzzy finite automata

Fuzzy automata theory on lattice-ordered monoids was introduced by Li and Pedrycz. Dropping the distributive laws, fuzzy finite automata (L-FFAs for short) based on a more generalized structure L, named a po-monoid, are presented and investigated from the view of algebra in this paper. The notions of (strong) successor and source operators, fuzzy successor and source operators which are shown to be closure operators on certain conditions are introduced and discussed in detail. Using the weak primary submachines, a unique decomposition theorem of a fuzzy finite automaton based on a lattice-ordered monoid is obtained. Taking L as a quantale, fuzzy subsystems are proved to be the same as fuzzy submachines of an L-FFA. In particular, intrinsic connections between algebraic properties of L and properties of some operators of an L-FFA are discovered. It is shown that the join-preserving property of fuzzy successor and source operators can be fully characterized by the right and left distributive laws respectively, and the idempotence of successor operator can be characterized equivalently by the nonexistence of zero divisors when L is a lattice-ordered monoid.

Refractured Well Selection for Multicriteria Group Decision Making by Integrating Fuzzy AHP with Fuzzy TOPSIS Based on Interval-Typed Fuzzy Numbers

Multicriteria group decision making (MCGDM) research has rapidly been developed and become a hot topic for solving complex decision problems. Because of incomplete or non-obtainable information, the refractured well-selection problem often exists in complex and vague conditions that the relative importance of the criteria and the impacts of the alternatives on these criteria are difficult to determine precisely. This paper presents a new model for MCGDM by integrating fuzzy analytic hierarchy process (AHP) with fuzzy TOPSIS based on interval-typed fuzzy numbers, to help group decision makers for well-selection during refracturing treatment. The fuzzy AHP is used to analyze the structure of the selection problem and to determine weights of the criteria with triangular fuzzy numbers, and fuzzy TOPSIS with interval-typed triangular fuzzy numbers is proposed to determine final ranking for all the alternatives. Furthermore, the algorithm allows finding the best alternatives. The feasibility of the proposed methodology is also demonstrated by the application of refractured well-selection problem and the method will provide a more effective decision-making tool for MCGDM problems.

A new portfolio selection model with interval-typed random variables and the empirical analysis

This paper proposes a new portfolio selection model, where the goal is to maximize the expected portfolio return and meanwhile minimize the risks of all the assets. The average return of every asset is considered as an interval number, and the risk of every asset is treated by probabilistic measure. An algorithm for solving the portfolio selection problem is given. Then a Pareto-maximal solution could be obtained under order relations between interval numbers. Finally, the empirical analysis is presented to show the feasibility and robustness of the model.

Weighted Automata Over Valuation Monoids with Input and Multi-output Characteristics

Weighted automata are significant modelling notions of discrete dynamic systems. This paper aims to study weighted automata over valuation monoids with input and multi-output characteristics, whose truth values involve a wide range of algebraic structures such as semirings and strong bimonoids. In particular, if these domains are Cauchy double unital valuation monoids, it is pointed out that weighted sequential-like automata and weighted generalized Moore automata are equivalent in the sense of the same input and multi-output behaviors.

Possibility Interval-Valued Multi-fuzzy Soft Sets and Theirs Applications

The notions of interval-valued multi-fuzzy soft set and possibility interval-valued multi-fuzzy soft set are proposed in this paper. Several interesting algebraic properties of them are then investigated. In particular, both interval-valued multi-fuzzy soft set and possibility interval-valued multi-fuzzy soft set with union and intersection operators turn out to be distributive lattices. Finally, possibility interval-valued multi-fuzzy soft sets are applied to decision making and an illustrated example is given.

The algebraic characterizations for a formal power series over complete strong bimonoids

On the basis of run semantics and breadth-first algebraic semantics, the algebraic characterizations for a classes of formal power series over complete strong bimonoids are investigated in this paper. As recognizers, weighted pushdown automata with final states (WPDAs for short) and empty stack (WPDAs

On Robustness of Min-Implication Fuzzy Relation Equation

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