Noncommutative Logic Systems with Applications in Management and Engineering
Keywords:
fuzzy logic, fuzzy logic system, noncommutative logic, modeling, control, ethics, psychology, decision makingAbstract
Zadeh's (min-max, standard) fuzzy logic and various other logics are commutative, but natural language has nuances suggesting the premises are not equal, with premises contributing to the conclusion according to their prominency. Therefore, we suggest variants of salience-based, noncommutative and non-associative fuzzy logic (prominence logic) that may better model natural language and reasoning when using linguistic variables. Noncommutative fuzzy logics have several theoretical and applicative motivations to be used as models for human inference and decision making processes. Among others, asymmetric relations in economy and management, such as buyer-seller, provider-user, and employer-employee are noncommutative relations and induce noncommutative logic operations between premises or conclusions. A class of noncommutative fuzzy logic operators is introduced and fuzzy logic systems based on the corresponding noncommutative logics are described and analyzed. The prominence of the operators in the noncommutative operations is conventionally assumed to be determined by their precedence. Specific versions of noncommutative logics in the class of the salience-based, noncommutative logics are discussed. We show how fuzzy logic systems may be built based on these types of logics. Compared with classic fuzzy systems, the noncommutative fuzzy logic systems have improved performances in modeling problems, including the modeling of economic and social processes, and offer more flexibility in approximation and control. Applications discussed include management and engineering problems and issues in the field of firms’ ethics or ethics of AI algorithms.References
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[42] Zadeh, L.A. (2003). Toward a perception-based theory of probabilistic reasoning. In: Melo-Pinto P., Teodorescu H.N., Fukuda T. (Eds.), Systematic Organisation of Information in Fuzzy Systems. IOS Press, Amsterdam, 2003. https://doi.org/10.1016/B978-044451379-3/50001-7
[43] Zhu, C.; Jin, L.S.; Mesiar, R; Yager, R.R. (2020). Using preference leveled evaluation functions to construct fuzzy measures in decision making and evaluation. International Journal of General Systems 49 (2), 161-173, 2020. https://doi.org/10.1080/03081079.2019.1668384
[44] [Online] https://www.process.st/value-statement/
[2] Anderson, J.E. (1979). A theoretical foundation for the gravity equation. The American Economic Review, 69(1): 106-116, 1979.
[3] Brown, W.; Yoshioka, C.F.; Munoz, P. (2004). Organizational mission as a core dimension in employee retention. Journal of Park & Recreation Administration. 22 (2), 28-43, 2004.
[4] Castro, J.L. (1995). Fuzzy logic controllers are universal approximators. IEEE Transactions On Systems, Man, and Cybernetics, 25(4), 629-635, 1995. https://doi.org/10.1109/21.370193
[5] Ciungu, L.C. (2013). Non-commutative Multiple-Valued Logic Algebras. Springer Science & Business Media, 2013. https://doi.org/10.1007/978-3-319-01589-7
[6] Clarke, H.D.; Kornberg, A.; McIntyre, C.; Bauer-Kaase P.; Kaase, M. (1999). The effect of economic priorities on the measurement of value change: new experimental evidence. The American Political Science Review, 93 (3), 637-647, 1999. https://doi.org/10.2307/2585579
[7] Cloutier, O.; Felusiak, L.; Hill, C.; Pemberton-Jones, E.J. (2015). The importance of developing strategies for employee retention. Journal of Leadership, Accountability and Ethics, 12(2), 119-129, 2015.
[8] Di Nola A.; Georgescu G.; Iorgulescu A. (2002). Pseudo-BL algebras: Part I. Mult. Val. Logic, 8 (2002) 673-716. Part II, Mult. Val. Logic 8, 717-750, 2002.
[9] Dong L. (2015). Public value management: integration of value and instrumental rationalities. In: Public Administration Theories. Palgrave Macmillan, New York, 225-248, 2015. https://doi.org/10.1057/9781137536426_10
[10] Fletcher, R.; Frey, D.; Teodorescu, M.; Gandhi, A.; Nakeshimana, A. (2020). RES.EC-001 Exploring Fairness in Machine Learning for International Development. Massachusetts Institute of Technology: MIT OpenCourseWare, https://ocw.mit.edu, 2020.
[11] Girard, J.-Y. (1993). On the unity of logic. Annals of Pure and Applied Logic 59, 201-217, 1993. https://doi.org/10.1016/0168-0072(93)90093-S
[12] Hajek, P. (2003). Fuzzy logics with noncommutative conjuctions, Journal of Logic and Computation, 13(4), 469-479, 2003. https://doi.org/10.1093/logcom/13.4.469
[13] Hajek, P. (2006). What is mathematical fuzzy logic. Fuzzy Sets and Systems, 157, 597-603, 2006. https://doi.org/10.1016/j.fss.2005.10.004
[14] Hillman, A.J.; Keim, G.D. (2001). Shareholder value, stakeholder management, and social issues: What's the bottom line? Strategic Management Journal, 22, 125-139, 2001. https://doi.org/10.1002/1097-0266(200101)22:23.0.CO;2-H
[15] Hsini, M.; Irzi, N.; Kefi, K. (2020). On a fractional problem with variable exponent. Proceedings of The Romanian Academy Series A, 21(2), 105-114, 2020.
[16] Klement, E.P.; Mesiar R.; Pap, E. (2004). Triangular norms. Position paper II: General constructions and parameterized families. Fuzzy Sets and Systems, 145, 411-438, 2004. https://doi.org/10.1016/S0165-0114(03)00327-0
[17] Klir, G.J. (2003). Uncertainty-basd information. In: Melo-Pinto P., Teodorescu H.N., Fukuda T. (Eds.), Systematic Organisation of Information in Fuzzy Systems. IOS Press, Amsterdam, 2003. https://doi.org/10.1016/B0-12-227240-4/00188-X
[18] Lewer, J.J.; Van den Berg, H. (2008). A gravity model of immigration. Economics Letters, 99 (1), 164-167, 2008. https://doi.org/10.1016/j.econlet.2007.06.019
[19] Madan D.B. (2006). Equilibrium asset pricing: with non-Gaussian factors and exponential utilities. Quantitative Finance, 6(6), 455-463, 2006. https://doi.org/10.1080/14697680600804437
[20] Mellics, P.-A. (2004). A topological correctness criterion for non-commutative logic. In: Ehrhard T.; Girard J-Y.; Ruet P.; Scott, P., Linear Logic in Computer Science, Cambridge University Press, London Mathematical Society, Lecture Note Series 316. hal-00154204, 283-323, 2004.
[21] Mesiar, R. (2001). Triangular norms - An overview. In B. Reusch et al. (eds.), Computational Intelligence in Theory and Practice. Springer, Berlin Heidelberg, 2001. https://doi.org/10.1007/978-3-7908-1831-4_3
[22] Mineev, M.; Putinar, M.; Teodorescu, R. Random matrices in 2D, Laplacian growth and operator theory. https://arxiv.org/pdf/0805.0049.pdf.
[23] O'Flynn, J. (2007). From New Public Management to Public Value: Paradigmatic change and managerial implications. Australian Journal of Public Administration, 66(3), 353-366, 2007. https://doi.org/10.1111/j.1467-8500.2007.00545.x
[24] Ouyang, W.; Yu, C.W.; Huang, P.; Chang, H. (2017). Non-commutative path planning for tours with diversified attractions, 2017 Sixth International Conference on Future Generation Communication Technologies (FGCT), Dublin, 1-5, 2017. https://doi.org/10.1109/FGCT.2017.8103733
[25] Sagiv, L.; Schwartz, S.H. (1995). Value priorities and readiness for out-group social contact. Journal of Personality and Social Psychology, 69(3), 437-448, 1995. https://doi.org/10.1037/0022-3514.69.3.437
[26] Schwartz, S. (1996). Value priorities and behavior: Applying a theory of integrated value systems. In C. Seligman, J.M. Olson, M.P. Zanna (Eds.), The Ontario symposium on personality and social psychology, Lawrence Erlbaum Associates, Inc., 8, 1-24, 1996.
[27] Sheridan, J.E. (1992). Organizational culture and employee retention. The Academy of Management Journal, 35(5), 1036-1056, 1992. https://doi.org/10.2307/256539
[28] Stout, L.N. (2010). Categorical approaches to non-commutative fuzzy logic. Fuzzy Sets and Systems, 161, 2462-2478, 2010. https://doi.org/10.1016/j.fss.2010.03.001
[29] Su, Z. et al. (2020). Hesitant fuzzy DeGroot opinion dynamics model and its application in multiattribute decision making. International Journal of Computers Communications & Control, 15(4), 3888, 2020. https://doi.org/10.15837/ijccc.2020.4.3888
[30] Tarafdar, M.; Teodorescu, M.; Tanriverdi, H.; Robert, L.; Morse L. (2020). Seeking ethical use of AI algorithms: Challenges and mitigations. ICIS 2020, 2020/9/27.
[31] Teodorescu, H.-N.; Kandel, A.; Schneider, M. (1999). Fuzzy modeling and dynamics. Fuzzy Sets and Systems, 106 (1), 1-3, 1999. https://doi.org/10.1016/S0165-0114(98)00352-2
[32] Teodorescu, H.-N.L. (2011). On the meaning of approximate reasoning. An unassuming subsidiary to Lotfi Zadeh's paper dedicated to the memory of Grigore Moisil. International Journal of Computers Communications & Control, 6(3), 577-580, 2011. https://doi.org/10.15837/ijccc.2011.3.2136
[33] Teodorescu, H.-N. (2012). Taylor and bi-local piecewise approximations with neuro-fuzzy systems. Studies in Informatics and Control, 21 (4), 367-376, 2012. https://doi.org/10.24846/v21i4y201202
[34] Teodorescu, H.-N. (2018). Perspectives in Fuzzy Logic and Fuzzy Systems, Romanian Journal of Information Science and Technology, 20 (4), 324-327, 2018.
[35] Teodorescu, M.H. (2017). Machine Learning Methods for Strategy Research. Report number 18-011, Harvard Business School Research Paper Series, 2017/7/31, https://hbswk.hbs.edu/item/machine-learning-methods-for-strategy-research. https://doi.org/10.2139/ssrn.3012524
[36] Teodorescu, M.H.; Morse, L.; Awwad, Y.; Kane, J. (2020). A framework for fairer Machine Learning in organizations. Academy of Management Proceedings, 1, 16889, 2020. https://doi.org/10.5465/AMBPP.2020.16889abstract
[37] Teodorescu, M.H., Khanna, T. (2019). Context in knowledge flows: Host country versus headquarters as sources for the MNC subsidiary. Academy of Management Proceedings, 1, 18238, 2019. https://doi.org/10.5465/AMBPP.2019.18238abstract
[38] Vansteenwegen, P.; Souffriau, W.; Berghe, G.V.; Van Oudheusden, D. (2011). The City Trip Planner: An expert system for tourists. Expert Systems with Applications, 38, 6540-6546, 2011. https://doi.org/10.1016/j.eswa.2010.11.085
[39] Yager, R.R. (2003). Organizing information using a hierarchical fuzzy model. In: Melo-Pinto P., Teodorescu H.N., Fukuda T. (Eds.), Systematic Organisation of Information in Fuzzy Systems. IOS Press, Amsterdam, 2003.
[40] Yager, R.R. (2020). Some fuzzy measure modeled multi-criteria formulations. International Journal of General Systems 49 (2), 222-233, 2020. https://doi.org/10.1080/03081079.2020.1713115
[41] Yu, C.W.; Cheng, R. H.; Wu, T.; Chang, H. (2015). Non-commutative path planning strategy, Proc. 2015 8th International Conference on Ubi-Media Computing (UMEDIA), Colombo, 33-37, 2015. https://doi.org/10.1109/UMEDIA.2015.7297424
[42] Zadeh, L.A. (2003). Toward a perception-based theory of probabilistic reasoning. In: Melo-Pinto P., Teodorescu H.N., Fukuda T. (Eds.), Systematic Organisation of Information in Fuzzy Systems. IOS Press, Amsterdam, 2003. https://doi.org/10.1016/B978-044451379-3/50001-7
[43] Zhu, C.; Jin, L.S.; Mesiar, R; Yager, R.R. (2020). Using preference leveled evaluation functions to construct fuzzy measures in decision making and evaluation. International Journal of General Systems 49 (2), 161-173, 2020. https://doi.org/10.1080/03081079.2019.1668384
[44] [Online] https://www.process.st/value-statement/
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