A logical reasoning based decision making method for handling qualitative knowledge

Abstract Successful decision-making analysis needs to take both advantages of human analysts and computers, and human knowledge is usually expressed in a qualitative way. Computer based approaches are good at handling quantitative data, while it is still challenging on how to well structure qualitative knowledge and incorporate them as part of decision analytics. This paper develops a logical reasoning based decision-making framework for handling qualitative human knowledge. In this framework, an algebraic structure is adopted for modelling qualitative human knowledge in a systematic way, and a logic based approximate reasoning method is then proposed for inferring the final decision based on the structured qualitative knowledge. By taking a non-classical logic as its formal foundation, the proposed logical reasoning based decision making method is able to model and infer with qualitative human knowledge directly without numerical approximation in a strict way.

[1]  Marc Roubens,et al.  Fuzzy sets and decision analysis , 1997, Fuzzy Sets Syst..

[2]  Jerry M. Mendel,et al.  Computing with words and its relationships with fuzzistics , 2007, Inf. Sci..

[3]  Juan Carlos Augusto,et al.  A linguistic multi-criteria decision making approach based on logical reasoning , 2014, Inf. Sci..

[4]  Jun Liu,et al.  Lattice-Valued Logic - An Alternative Approach to Treat Fuzziness and Incomparability , 2003, Studies in Fuzziness and Soft Computing.

[5]  Lattice Order Group Decision Making with Interval Probability Based on Prospect Theory , 2015 .

[6]  Van-Nam Huynh,et al.  An algebraic approach to linguistic hedges in Zadeh's fuzzy logic , 2002, Fuzzy Sets Syst..

[7]  Oscar Cordón,et al.  A model of fuzzy linguistic IRS based on multi-granular linguistic information , 2003, Int. J. Approx. Reason..

[8]  Wenyi Wang,et al.  Fuzzy Multi-Objective Lattice Order Decision Approach for Preference Ranking in Conflict Analysis , 2016, Int. J. Comput. Intell. Syst..

[9]  Luis Martínez,et al.  Sensory evaluation based on linguistic decision analysis , 2007 .

[10]  Jun Liu,et al.  An axiomatizable logical foundation for lattice-ordered qualitative linguistic approach for reasoning with words , 2014, Inf. Sci..

[11]  Lotfi A. Zadeh,et al.  The concept of a linguistic variable and its application to approximate reasoning - II , 1975, Inf. Sci..

[12]  Francisco Herrera,et al.  A model based on linguistic 2-tuples for dealing with multigranular hierarchical linguistic contexts in multi-expert decision-making , 2001, IEEE Trans. Syst. Man Cybern. Part B.

[13]  Jun Liu,et al.  A lattice-valued linguistic-based decision making method , 2005, 2005 IEEE International Conference on Granular Computing.

[14]  Witold Pedrycz,et al.  Fuzzy logic-based generalized decision theory with imperfect information , 2012, Inf. Sci..

[15]  Yiming Cao,et al.  A method of multimedia teaching evaluation based on fuzzy linguistic concept lattice , 2019, Multimedia Tools and Applications.

[16]  Núria Agell,et al.  Ranking multi-attribute alternatives on the basis of linguistic labels in group decisions , 2012, Inf. Sci..

[17]  Gerhard X. Ritter,et al.  Computational Intelligence Based on Lattice Theory , 2007, Studies in Computational Intelligence.

[18]  Lotfi A. Zadeh,et al.  The concept of a linguistic variable and its application to approximate reasoning-III , 1975, Inf. Sci..

[19]  Witold Pedrycz,et al.  Modeling with linguistic entities and linguistic descriptors: a perspective of granular computing , 2017, Soft Comput..

[20]  Jerry M. Mendel,et al.  Type-2 Fuzzy Sets as Well as Computing with Words , 2019, IEEE Computational Intelligence Magazine.

[21]  Jun Liu,et al.  Non-Clausal Multi-ary α-Generalized Resolution Calculus for a Finite Lattice-Valued Logic , 2018, Int. J. Comput. Intell. Syst..

[22]  Dan Meng,et al.  On weighted unbalanced linguistic aggregation operators in group decision making , 2013, Inf. Sci..

[23]  Jianming Zhan,et al.  Rough soft lattice implication algebras and corresponding decision making methods , 2017, Int. J. Mach. Learn. Cybern..

[24]  Francisco Herrera,et al.  Linguistic decision analysis: steps for solving decision problems under linguistic information , 2000, Fuzzy Sets Syst..

[25]  Francisco Herrera,et al.  An overview on the 2-tuple linguistic model for computing with words in decision making: Extensions, applications and challenges , 2012, Inf. Sci..

[26]  Owen R. Cote,et al.  Rational choice and security studies : Stephen Walt and his critics , 2000 .

[27]  Hernán Astudillo,et al.  An architecture based on computing with words to support runtime reconfiguration decisions of service-based systems , 2018, Int. J. Comput. Intell. Syst..

[28]  Francisco Herrera,et al.  The 2-Tuple Linguistic Computational Model. Advantages of Its Linguistic Description, Accuracy and Consistency , 2001, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[29]  N. C. Ho,et al.  Extended hedge algebras and their application to fuzzy logic , 1992 .

[30]  Lotfi A. Zadeh,et al.  From Computing with Numbers to Computing with Words - from Manipulation of Measurements to Manipulation of Perceptions , 2005, Logic, Thought and Action.

[31]  Luis Martínez-López,et al.  Computing with Words in Risk Assessment , 2010, Int. J. Comput. Intell. Syst..

[32]  S. K. Das,et al.  A logical reasoning with preference , 1995, Decis. Support Syst..

[33]  David A. Plaisted,et al.  History and Prospects for First-Order Automated Deduction , 2015, CADE.

[34]  Francisco Herrera,et al.  A group decision making model dealing with comparative linguistic expressions based on hesitant fuzzy linguistic term sets , 2013, Inf. Sci..

[35]  Salem Benferhat,et al.  Reasoning with multiple-source information in a possibilistic logic framework , 2006, Inf. Fusion.

[36]  Luis Martínez-López,et al.  Some Views on Information Fusion and Logic Based Approaches in Decision Making under Uncertainty , 2010, J. Univers. Comput. Sci..

[37]  G. Priest An introduction to non-classical logic , 2001 .

[38]  Ling Wei,et al.  Attributes reduction and rules acquisition in an lattice-valued information system with fuzzy decision , 2017, Int. J. Mach. Learn. Cybern..

[39]  Behnam Malakooti,et al.  Ranking and screening multiple criteria alternatives with partial information and use of ordinal and cardinal strength of preferences , 2000, IEEE Trans. Syst. Man Cybern. Part A.

[40]  Francisco Herrera,et al.  Computing with Words in Decision support Systems: An overview on Models and Applications , 2010, Int. J. Comput. Intell. Syst..

[41]  José L. Verdegay,et al.  On aggregation operations of linguistic labels , 1993, Int. J. Intell. Syst..

[42]  Jun Liu,et al.  Weak Completeness of Resolution in a Linguistic Truth-Valued Propositional Logic , 2007, IFSA.

[43]  Francisco Herrera,et al.  Computing with words in decision making: foundations, trends and prospects , 2009, Fuzzy Optim. Decis. Mak..

[44]  N. C. Ho,et al.  Hedge algebras: an algebraic approach to structure of sets of linguistic truth values , 1990 .

[45]  Juan Carlos Augusto,et al.  Ordering based decision making - A survey , 2013, Inf. Fusion.

[46]  Odile Papini,et al.  Reasoning with partially ordered information in a possibilistic logic framework , 2004, Fuzzy Sets Syst..

[47]  Rosa M. Rodríguez,et al.  Computing With Comparative Linguistic Expressions and Symbolic Translation for Decision Making: ELICIT Information , 2020, IEEE Transactions on Fuzzy Systems.

[48]  Nguyen Cat Ho,et al.  Fuzziness measure on complete hedge algebras and quantifying semantics of terms in linear hedge algebras , 2007, Fuzzy Sets Syst..

[49]  Didier Dubois,et al.  From Semantic to Syntactic Approaches to Information Combination in Possibilistic Logic , 1998 .

[50]  Jun Liu,et al.  Determination of α-resolution in lattice-valued first-order logic LF(X) , 2011, Inf. Sci..

[51]  Jun Ma,et al.  Linguistic Truth-Valued Lattice Implication Algebra and Its Properties , 2006, The Proceedings of the Multiconference on "Computational Engineering in Systems Applications".

[52]  Paul P. Wang Computing with Words , 2001 .

[53]  L. A. ZADEH,et al.  The concept of a linguistic variable and its application to approximate reasoning - I , 1975, Inf. Sci..

[54]  Luis Martínez-López,et al.  AN EXTENDED HIERARCHICAL LINGUISTIC MODEL FOR DECISION‐MAKING PROBLEMS , 2011, Comput. Intell..

[55]  Juan Carlos Augusto,et al.  Parameterized Uncertain Reasoning Approach Based on a Lattice-Valued Logic , 2011, ECSQARU.