﻿ Dr. Ryszard Janicki's Publications in Approximate Reasoning, Rough Sets, Ranking and Pairwise Comparisons

APPROXIMATE REASONING, ROUGH SETS, RANKING AND PAIRWISE COMPARISONS

When dealing with big data approximate reasoning is a necessity as obtaining exact results or analyzing all data is often not feasible.

Consider the following problem: we have a set of data that have been obtained in an empirical manner. From the nature of the problem we know that the set should have some structure and desired properties, for example, it should be partially ordered, but because the data are empirical it is not. In general case this might be just an arbitrary set without the desired structure and properties. What is the “best” approximation that has the desired structure and properties and how it can be computed? In general, we cannot assume the existence of any obvious numerical metric which is a substantial theoretical and practical obstacle.

While ‘Rough Sets’ (Pawlak 1982) handle lower and upper approximations very well, ‘optimal’ and ‘structural’ (i.e. having desired special properties) approximations are much less developed. While some frameworks for structural (Yao 1996, Janicki 2010) and optimal (Janicki-Lenarcic 2016) Rough Sets approximations exist, they are far from being universal and satisfactory. Usually, it is not clear how ‘optimal’ approximation should be defined (Janicki 2018), and what kind of ‘similarity’ should be chosen (Tversky 1977). It also turns out that even for very simple similarity measures and rather simple desired properties the problems often may become NP-complete, so some second level of approximation might be needed (Janicki 2018).

Current research involves two orthogonal approaches. The first is to develop a family of abstract metrics that can be used for various classes of sets, relational structures, and properties. The second approach is to simulate the concept of a metric by a sequence of ‘lower’ and ‘upper’ approximations that preserve the desired properties (in both the standard theory of relations and rough sets settings). In both cases finding some efficient algorithms and supporting software is a long term ultimate goal.

There are plenty of potential applications of approximate reasoning (in a sense described above) in Knowledge Engineering, Classification Theory, Clustering, etc.

One obvious important application and a good testbed is pairwise comparisons based non-numerical ranking (Janicki 2009, which provided the main motivation for this general problem).

Most of the ranking theories either assumes some numerical (quantitative) metrics or uses rather very specific assumptions. The pairwise comparisons method is based on the observation that it is much easier to rank the importance of two objects than it is to rank the importance of several objects. While non-numerical (or qualitative) ranking was informally used for a very long time, its strict formalization started with (Janicki-Koczkodaj 1996). A comprehensive theory of non-numerical pairwise comparisons based ranking where the binary relationship between objects is characterized by five relations interpreted as ‘indifference’, ‘slightly in favour’, ‘in favor’, ‘strongly better’ and ‘extremely better’ (including a thorough analysis of consistency), was provided by (Janicki 2009, Janicki-Zhai 2012).

A combined version of pairwise comparisons that involves both quantitative and qualitative techniques has been proposed by (Janicki-Soudkhah 2015, Janicki 2018a) and applied in areas not typical for using pairwise comparisons paradigm, namely software evaluation, and data classification.

Current research involves a formal relationship between qualitative and quantitative models, especially between concepts of consistency in both models, and a thorough study of the role of consistency scales. The combined model could be a good alternative for the popular numerical pairwise comparisons based technique called Analytical Hierarchy Process (Saaty 1977).

# Approximate Reasoning, Rough Sets, Ranking and Pairwise Comparisons

2022

1.  R. Janicki, Similarity for Multisets and Heterogenous Sets, IPMU’2022 (19th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems), Communications in Computer  and Information Science 1601, Springer 2022, 332-344, https://doi.org/10.1007/978-3-031-08971-8_28

2.  R. Janicki, M. Mahmoud, On Multiplicative, Additive and Qualitative Pairwise Comparisons, Proc. of 17th Conference on Computer Science and Intelligent Systems FedCSIS 2022, Sofia, Bulgaria, Sept. 4-7 2022, pp. 247-251.

2019

3.    X. Xie, X. Qin, Q. Zhou, Y. Zhou, T. Zhang, R. Janicki, W. Zhao, A novel test-cost-sensitive attribute reduction approach using the binary bat algorithm, Knowledge Based Systems,  doi.org/10.1016/j.knosys.2019.104938

4.  X. Xie, R. Janicki, X. Qin, W. Zhao, G. Huang, Local search for attribute reduction, IJCRS’2019 (International Joint Conference on Rough Sets), Lecture Notes in Artificial Intelligence 11499, Springer 2019, 102-117

2018

5.   R. Janicki, Approximations of Arbitrary Relations by Partial Orders, International Journal of Approximate Reasoning, 98 (2018) 177-195.

6.  R. Janicki, Finding Consistent Weights Assignments with Combined Pairwise Comparisons, International Journal of Management and Decision Making, 17, 3 (2018) 322-247

2017

7.  R. Janicki, Yet Another Kind of Rough Sets Induced by Coverings, Proc. of IJCRS’2017 (International Joint Conference on Rough Sets), Lecture Notes in Artificial Intelligence 10313, Springer 2017, 140-153.

2016

8.  R. Janicki, A. Lenarcic, Optimal Approximations with Rough Sets and Similarities in Measure Spaces, International Journal of Approximate Reasoning, 71 (2016) 1-14.

9.   R. Janicki, On Optimal Approximations of Arbitrary Relations by Partial Orders, Proc. of IJCRS’2016 (International Joint Conference on Rough Sets), Lecture Notes in Artificial Intelligence 9920, Springer 2016, 107-119.

10.   A. D. Bogobowicz, R. Janicki, On Approximation of Relations by Generalized Closures

2015

11.  R. Janicki, M. H. Soudkhah, On Classification with Pairwise Comparisons, Support Vector Machines and Feature Domain Overlapping 58, 3 (2015).

12.  R. Janicki, On Qualitative and Quantitative Pairwise Comparisons, Proc. of ICAT’15 (International Conference on Advanced Technology & Sciences), Antalya, Turkey, August 4-7, 2015, pp. 21-28.

13.  A. Mirdad, R. Janicki, Applications of Mixed Pairwise Comparisons, Proc. of ICAI’2015 (International Conference on Artificial Intelligence), Las Vegas, Nevada, USA, July 27-30, 2015, pp. 414-420, CSREA Press

2013

14.  R. Janicki, Property-Driven Rough Sets Approximations of Relations, In A. Skowron, Z. Suraj (eds.), Rough Sets and Intelligent Systems - Professor Zdzisław Pawlak in Memoriam (Series: Intelligence Systems Reference Laboratory Vol. 42), pp. 333-357, Springer 2013.

15.  R. Janicki, A. Lenarcic, Optimal Approximations with Rough Sets, Proc. of RSKT’2013 (7th Int. Conf. on Rough Sets and Knowledge Technology), Lecture Notes in Artificial Intelligence 8171, Springer 2013, 87-98.

16.  M. H. Soudkhah, R. Janicki, Weighted Features Classification with Pairwise Comparisons, Support Vector Machines and Feature Domain Overlapping, 22nd IEEE WETICE (Workshops on Enabling Technologies: Infrastructure for Collaborative Enterprises) Conference, 4th Track on Cooperative Knowledge Discovery & Data Mining, Hammamet, Tunisia 2013, pp. 172-177, IEEE Publ.

17.  A. Bogobowicz, R. Janicki, On pairwise comparisons based internal and external measures for  software evaluation, 22nd IEEE WETICE (Workshops on Enabling Technologies: Infrastructure for Collaborative Enterprises) Conference, 1st Track on Validating Software for Critical Systems, Hammamet, Tunisia 2013, pp. 371-376, IEEE Publ.

2012

18.  R. Janicki, Y. Zhai, On a Pairwise Comparison Based Consistent Non-Numerical Ranking, Logic Journal of IGPL 20, 4 (2012), 667-676.

19.  R. Janicki, Y. Zhai, Rank Reversals and Testing of Pairwise Comparisons Based Non-Numerical Rankings, Proc. of 10th Int. FLINS Conf. On Uncertainty Modeling in Knowledge Engineering and Decision Making, Istanbul, Turkey 2012, pp.374-381.

2011

20.  R. Janicki, Y. Zhai, Remarks on Pairwise Comparison Numerical and Non-Numerical Rankings, Proc. of RSKT’2011 (Rough Sets and Knowledge Technology), Lecture Notes in Artificial Intelligence 6954, Springer 2011, 290-300.

21.  R. Janicki, Y. Zhai, On Testing Pairwise Comparisons Based Non-Numerical Rankings, Proc. of ICAAA’2011 (International Conference on Applied Analysis and Algebra), pp. 45-49, Istanbul, Turkey 2011.

2010

22.  R. Janicki, Approximation of Arbitrary Binary Relations by Partial Orders. Classical and Rough Set Models, Transactions on Rough Sets 13 (2010), 17-38.

23.  R. Janicki, Y. Zhai, On a Consistency Driven Pairwise Comparison Based Non-numerical Ranking, Proc. of CMMSE’2010 (Computational and Mathematical Methods in Science and Engineering), Vol. 2, pp. 566-576, Almeria, Spain, 2010.

2009

24.  R. Janicki, Pairwise Comparisons Based Non-Numerical Ranking, Fundamenta Informaticae 94 (2009), 1-21.

25.  P. Adamic, V. Babiy, R. Janicki, T. Kakiashvili, W. W. Koczkodaj, R. Tadeusiewicz, Pairwaise Comparisons and Visual Perceptions of Equal Area Polygons, Perceptual and Motor Skills, 108, 1 (2009), 37-42.

26.  R. Janicki, On Rough Sets with Structures and Properties, 12th RSFDGrC’2009 (Rough Sets, Fuzzy Sets, Data Mining and Granular Computing), Lecture Notes in Artificial Intelligence 5958, Springer 2009, 109-116.

2008

27.  R. Janicki, Some Remarks on Approximations of Arbitrary Binary Relations by Partial Orders, Proc. of RSCTC’2008 (Rough Sets and Current Trends in Computing), Lecture Notes in Artificial Intelligence 5306, Springer 2008, 81-91.

28.  R. Janicki, Ranking with Partial Orders and Pairwise Comparisons, Proc. of RSKT’2008 (Rough Sets and Knowledge Technology), Lecture Notes in Artificial Intelligence 5009, Springer 2008, 442-451.

29.  R. Janicki, W. W. Koczkodaj, V. Babiy, Pairwise Comparisons and Ranking, ICSS’08 (Int. Conference on Social Sciences), Izmir, Turkey 2008.

2007

30.  R. Janicki, Pairwise Comparisons, Incomparability and Partial Orders, ICEIS’2007 ( 9th Int. Conference on Enterprise Information Systems), Volume 2 (Artificial Intelligence and Decision Support Systems), pp. 297-302, Funchal, Portugal 2007.

1998

31.  R. Janicki, W. Koczkodaj, "A Weak Order Solution to a Group Ranking and Consistency-Driven Pairwise Comparisons", Applied Mathematics and Computation, 94 (1998), 227-241.

1997

32.  R. Janicki, "Pairwise Comparisons Revisited", 6th Symposium on Intelligent Information Systems, Zakopane, Poland, 1997, 47-52.

1996

33.  R. Janicki, W. Koczkodaj, "A Weak Order Approach to Group Ranking", Computers and Mathematics with Applications, 32, 2 (1996), 51-59.

34.  R. Janicki, W. Koczkodaj, "Consistency-Driven Approach to Knowledge Acquisition for Expert Systems", Proceedings of CESA'96 (Computational Engineering in System Applications), Lille, France, 1996, 87-96.

1994

35.  R. Janicki, "On Non-Numerical Ranking", Proceedings of the 3rd International Workshop on Rough Sets and Soft Computing (RSSC'94), San Jose, California, 1994, 190-197.

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