Linguistic truth-valued lattice-valued propositional logic system ℓP(X) based on linguistic truth-valued lattice implication algebra

Lai, Jiajun; Xu, Yang

doi:10.1016/j.ins.2010.01.021

Cited by 20 publications

(10 citation statements)

References 32 publications

(32 reference statements)

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“…They [15,113] also extended the possibilistic logic by defining new combination rules to aggregate multiple-source information, which provides a coherent way to represent and reason uncertain information from different sources. Inspired from hedge algebra and by analyzing semantic heredity of linguistic hedges, based on the extensive work on lattice implication algebras and the corresponding logic systems [114], Xu, et al proposed linguistic truth-valued lattice implication algebra [115,116], as simply shown in Fig. 3, for modelling ordinal linguistic information, and discussed the corresponding logic system [116,117] and the approximate reasoning approaches based on it [118,119].…”

Section: Logic Based Decision Makingmentioning

confidence: 99%

“…Inspired from hedge algebra and by analyzing semantic heredity of linguistic hedges, based on the extensive work on lattice implication algebras and the corresponding logic systems [114], Xu, et al proposed linguistic truth-valued lattice implication algebra [115,116], as simply shown in Fig. 3, for modelling ordinal linguistic information, and discussed the corresponding logic system [116,117] and the approximate reasoning approaches based on it [118,119]. Liu et al [19] laid some basic ideas on lattice valued decision making, especially with linguistic information, along with some lattice structures for representing the ordinal linguistic information involved in decision making procedure.…”

Section: Logic Based Decision Makingmentioning

confidence: 99%

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Ordering based decision making – A survey

et al. 2013

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A B S T R A C TDecision making is the crucial step in many real applications such as organization management, financial planning, products evaluation and recommendation. Rational decision making is to select an alternative from a set of different ones which has the best utility (i.e., maximally satisfies given criteria, objectives, or preferences). In many cases, decision making is to order alternatives and select one or a few among the top of the ranking. Orderings provide a natural and effective way for representing indeterminate situations which are pervasive in commonsense reasoning. Ordering based decision making is then to find the suitable method for evaluating candidates or ranking alternatives based on provided ordinal information and criteria, and this in many cases is to rank alternatives based on qualitative ordering information. In this paper, we discuss the importance and research aspects of ordering based decision making, and review the existing ordering based decision making theories and methods providing future research directions.

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Section: Logic Based Decision Makingmentioning

confidence: 99%

Section: Logic Based Decision Makingmentioning

confidence: 99%

Ordering based decision making – A survey

et al. 2013

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“…Nguyen et al [17], [18] presented linguistic logics with truth-valued domain based on linear symmetrical hedge algebra. Lai and Xu [15] presented a linguistic truth-valued lattice-valued propositional logic system, called lP(X)P(X), whose truth value domain is a lattice implication algebra. Liu et al [16] proposed an automated reasoning algorithm based on the linguistic valued Lukasiewicz propositional logic with truth-value in Łukasiewicz linguistic valued algebras.…”

Section: Introductionmentioning

confidence: 99%

Resolution Method in Linguistic Propositional Logic

Nguyen¹,

Tran²

2016

ijacsa

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Abstract-In the present paper, the resolution method for a linguistic propositional logic with truth value in a logical algebra -refined hedge algebra, is focused. The preliminaries of refined hedge algebra are given first. Then the syntax and semantic of linguistic propositional are defined. Finally, a resolution method which based on resolution principle in two-valued logic is established. Accordingly, the research in this paper will be helpful support for the application of intelligent reasoning system based on linguistic-valued logic which includes incomparable information.

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“…Automated reasoning in linguistic logic has been attracting many researchers. Many works presented resolution algorithms in linguistic logics with truth value domain based on the implication lattice algebraic structures [2,3,15,16,19] or based on hedge algebra [4,8,10,11]. Along the line of these research directions, we study automated reasoning based on resolution for linguistic propositional logic with truth value domain is taken from linear symmetrical hedge algebra.…”

Section: Introductionmentioning

confidence: 99%

Resolution in Linguistic Propositional Logic Based on Linear Symmetrical Hedge Algebra

Nguyen

Doan

et al. 2014

Advances in Intelligent Systems and Computing

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Abstract. The paper introduces a propositional linguistic logic that serves as the basis for automated uncertain reasoning with linguistic information. First, we build a linguistic logic system with truth value domain based on a linear symmetrical hedge algebra. Then, we consider Gödel's t-norm and t-conorm to define the logical connectives for our logic. Next, we present a resolution inference rule, in which two clauses having contradictory linguistic truth values can be resolved. We also give the concept of reliability in order to capture the approximative nature of the resolution inference rule. Finally, we propose a resolution procedure with the maximal reliability.

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Linguistic truth-valued lattice-valued propositional logic system ℓP(X) based on linguistic truth-valued lattice implication algebra

Cited by 20 publications

References 32 publications

Ordering based decision making – A survey

Ordering based decision making – A survey

Resolution Method in Linguistic Propositional Logic

Resolution in Linguistic Propositional Logic Based on Linear Symmetrical Hedge Algebra

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