Hedge algebras: an algebraic approach to structure of sets of linguistic truth values
Fuzzy Sets and Systems
Algebraic structures in fuzzy logic
Fuzzy Sets and Systems
Extended hedge algebras and their application to fuzzy logic
Fuzzy Sets and Systems
Fuzzy logic of Lukasiewicz logic: a clarification
Fuzzy Sets and Systems
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
An algebraic approach to linguistic hedges in Zadeh's fuzzy logic
Fuzzy Sets and Systems - Data bases and approximate reasoning
Information Sciences—Informatics and Computer Science: An International Journal
The Algebraic Properties of Linguistic Value "Truth" and Its Reasoning
IFSA '07 Proceedings of the 12th international Fuzzy Systems Association world congress on Foundations of Fuzzy Logic and Soft Computing
A linguistic truth-valued reasoning approach in decision making with incomparable information
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology - Fuzzy theory and technology with applications
Linguistic Values-based Intelligent Information Processing: Theory, Methods, and Applications
Linguistic Values-based Intelligent Information Processing: Theory, Methods, and Applications
Which logic is the real fuzzy logic?
Fuzzy Sets and Systems
Are fuzzy sets a reasonable tool for modeling vague phenomena?
Fuzzy Sets and Systems
IEEE Transactions on Fuzzy Systems
Information Sciences: an International Journal
A linguistic aggregation operator with three kinds of weights for nuclear safeguards evaluation
Knowledge-Based Systems
A linguistic truth-valued uncertainty reasoning model based on lattice-valued logic
FSKD'05 Proceedings of the Second international conference on Fuzzy Systems and Knowledge Discovery - Volume Part I
On compatibilities of α-lock resolution method in linguistic truth-valued lattice-valued logic
Soft Computing - A Fusion of Foundations, Methodologies and Applications
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Fuzzy logic = computing with words
IEEE Transactions on Fuzzy Systems
A 2-tuple fuzzy linguistic representation model for computing with words
IEEE Transactions on Fuzzy Systems
A new version of 2-tuple fuzzy linguistic representation model for computing with words
IEEE Transactions on Fuzzy Systems
A View of Averaging Aggregation Operators
IEEE Transactions on Fuzzy Systems
A Fuzzy Linguistic Methodology to Deal With Unbalanced Linguistic Term Sets
IEEE Transactions on Fuzzy Systems
Information Sciences: an International Journal
A dynamic consensus scheme based on a nonreciprocal fuzzy preference relation modeling
Information Sciences: an International Journal
Information Sciences: an International Journal
Information Sciences: an International Journal
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It is commonsense that people do express, think, reason, and make decision directly using linguistic terms in natural language rather than using numerical quantification. How to establish the formalized approach imitating the common way of human being's to manipulate directly linguistic terms without numerical approximation to provide the rational decision is still an open research area. Investigations on the algebraic structure of linguistic term set for varied decision making applications (especially in social science) still lack a formalism for development of strict linguistic valued logic system as a theoretical foundation and its approximate reasoning scheme in practice. To attain this goal we characterize and construct a typical structure of commonly used linguistic term sets in natural language by a lattice-ordered algebra structure - lattice implication algebra (LIA), where Lukasiewicz implication algebra, as a special case of LIA, plays a substantial role. By using Lukasiewicz logic's axiomatizability in terms of Pavelka type fuzzy logic, we propose a new axiomatizable lattice ordered qualitative linguistic truth-valued logic system based on LIA to place an important foundation for further establishing formal linguistic truth-valued logic based approximate reasoning and decision making with applications. This proposed logic system has a distinct feature of handling comparable or incomparable linguistic terms directly without numerical quantification, will be especially beneficial for perception-based decision making processes. It attempts to enhance the quantitative theory of decision science with qualitative, algebraic and logic-oriented approaches to achieve reasoning with words.