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Granulation of ecological networks under fuzzy soft environment

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Abstract

The main idea of this work is the exploration of granular structures by applying the hybrid models of fuzzy soft sets and fuzzy soft graphs to discuss the indiscernibility partition of set of universe. The information granulation is examined by applying fuzzy soft theory, and the corresponding behavior of granules is reviewed. This article proposes a novel technique of formation of granular structures using fuzzy soft graphs and defines the fuzzy soft granules. Two degree-based models are introduced to explore the abstraction of these granular structure. Then, we use these two degree-based models to granulate the certain relationships between different species in an ecological system. Further, we develop and implement some algorithms of our proposed models to granulate the underconsideration networks. Finally, a comprehensive comparison of our proposed model with other existing techniques is presented to prove the applicability and effectiveness of fuzzy soft granulation.

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References

  • Akram M, Luqman A (2020) Fuzzy hypergraphs and related extensions. Stud Fuzziness Soft Comput. https://doi.org/10.1007/978-981-15-2403-5

    Article  MATH  Google Scholar 

  • Akram M, Zafar F (2020) Hybrid soft computing models applied to graph theory. Stud Fuzziness Soft Comput. https://doi.org/10.1007/978-3-030-16020-3

    Article  MATH  Google Scholar 

  • Akram M, Adeel A, Alcantud JCR (2018) Fuzzy \(N\)-soft sets: a novel model with applications. J Intell Fuzzy Syst 35(4):4757–4771

    Google Scholar 

  • Akram M, Adeel A, Alcantud JCR (2019a) Group decision-making methods based on hesitant \(N\)-soft sets. Expert Syst Appl 115:95–105

    Google Scholar 

  • Akram M, Adeel A, Alcantud JCR (2019b) Hesitant fuzzy \(N\)-soft sets: a new model with applications in decision-making. J Intell Fuzzy Syst 36(6):6113–6127

    Google Scholar 

  • Akram M, Ilyas F, Garg H (2020) Multi-criteria group decision making based on ELECTRE I method in pythagorean fuzzy information. Soft Comput 24:3425–3453

    Google Scholar 

  • Ali MI (2012) Another view on reduction of parameters in soft sets. Appl Soft Comput 12(6):1814–1821

    Google Scholar 

  • Ali SH (2013) Novel approach for generating the key of stream cipher system using random forest data mining algorithm. In: 2013 6th international conference on developments in E-systems engineering. IEEE, New York, pp 259–269

  • Ali MI, Feng F, Liu XY, Min WK, Shabir M (2009) On some new operations in soft set theory. Comput Math Appl 57(9):1547–1553

    MathSciNet  MATH  Google Scholar 

  • Al-Janabi S, Alkaim AF (2019) A nifty collaborative analysis to predicting a novel tool (DRFLLS) for missing values estimation. J Soft Comput. https://doi.org/10.1007/s00500-019-03972-x

    Article  Google Scholar 

  • Al-Janabi S, Patel A, Fatlawi H, Kalajdzic K, Al Shourbaji I (2014) Empirical rapid and accurate prediction model for data mining tasks in cloud computing environments. In: 2014 international congress on technology, communication and knowledge (ICTCK). IEEE, New York, pp 1–8

  • Al-Janabi S, Mohammad M, Al-Sultan A (2019) A new method for prediction of air pollution based on intelligent computation. Soft Comput. https://doi.org/10.1007/s00500-019-04495-1

    Article  Google Scholar 

  • Alkaim AF, Al-Janabi S (2019) Multi objectives optimization to gas flaring reduction from oil production. In: International conference on big data and networks technologies. Springer, Cham, pp 117–139

  • Berge C (1973) Graphs and hypergraphs. North-Holland Publishing Company, Amsterdam

    MATH  Google Scholar 

  • Bianchi FM, Livi L, Rizzi A, Sadeghian A (2014) A Granular computing approach to the design of optimized graph classifcation systems. Soft Comput 18:393–412

    Google Scholar 

  • Bisi C, Chiaselotti G, Ciucci D, Gentile T, Infusino FG (2017) Micro and macro models of granular computing induced by the indiscernibility relation. Inf Sci 388:247–273

    MathSciNet  Google Scholar 

  • Chen G, Zhong N (2011) Granular structures in graphs. In: International conference on rough sets and knowledge technology. Springer, Berlin, pp 649–658

  • Chen G, Zhong N, Yao Y (2008) A hypergraph model of granular computing. In: IEEE international conference on granular computing, pp 130–135

  • Chiaselotti G, Ciucci D, Gentile T (2016) Simple graphs in granular computing. Inf Sci 340:279–304

    MathSciNet  MATH  Google Scholar 

  • Feng F, Jun YB, Liu XY, Li LF (2010a) An adjustable approach to fuzzy soft set based decision making. J Comput Appl Math 234:10–20

    MathSciNet  MATH  Google Scholar 

  • Feng F, Li CX, Davvaz B, Irfan AM (2010b) Soft sets combined with fuzzy sets and rough sets: a tentative approach. Soft Comput 14:899–911

    MATH  Google Scholar 

  • Feng F, Fujita H, Ali MI, Yager RR, Liu X (2019) Another view on generalized intuitionistic fuzzy soft sets and related multiattribute decision making methods. IEEE Trans Fuzzy Syst 27(3):474–488

    Google Scholar 

  • Gong Z, Wang Q (2017) On the connection of fuzzy hypergraph with fuzzy information system. J Intell Fuzzy Syst 33(3):1665–1676

    MATH  Google Scholar 

  • Gu K, Wang L, Yin B (2019) Social community detection and message propagation scheme based on personal willingness in social network. Soft Comput 23(15):6267–6285

    Google Scholar 

  • Guan X, Li Y, Feng F (2013) A new order relation on fuzzy soft sets and its application. Soft Comput 17(1):63–70

    MATH  Google Scholar 

  • Kalajdzic K, Ali SH, Patel A (2015) Rapid lossless compression of short text messages. Comput Stand Interfaces 37:53–59

    Google Scholar 

  • Kaur C, Kumar R (2019) A fuzzy hierarchy-based pattern matching technique for melody classification. Soft Comput 2(1):7375–7392

    Google Scholar 

  • Khameneh ZA, Kiliçman A (2019) Multi-attribute decision-making based on soft set theory: a systematic review. Soft Comput 23(16):6899–6920

    Google Scholar 

  • Lin TY (1997) Granular computing. In: Announcement of the BISC special interest group on granular computing

  • Luqman A, Akram M, Koam AN (2019a) An \(m\)-polar fuzzy hypergraph model of granular computing. Symmetry 11(4):483

    Google Scholar 

  • Luqman A, Akram M, Koam AN (2019b) Granulation of hypernetwork models under the q-rung picture fuzzy environment. Mathematics 7(6):496

    Google Scholar 

  • Maji PK, Roy AR, Biswas R (2001) Fuzzy soft sets. J Fuzzy Math 9(3):589–602

    MathSciNet  MATH  Google Scholar 

  • Maji PK, Biswas R, Roy AR (2003) Soft set theory. Comput Math Appl 45(4–5):555–562

    MathSciNet  MATH  Google Scholar 

  • Molodtsov DA (1999) Soft set theory-first results. Comput Math Appl 37:19–31

    MathSciNet  MATH  Google Scholar 

  • Molodtsov DA (2004) The theory of soft sets. URSS Publishers, Moscow (in Russian)

    Google Scholar 

  • Mordeson JN, Nair PS (1998) Fuzzy graphs and fuzzy hypergraphs, 2nd edn. Physica Verlag, Heidelberg

    MATH  Google Scholar 

  • Patel A, Al-Janabi S, AlShourbaji I, Pedersen J (2015) A novel methodology towards a trusted environment in mashup web applications. Comput Secur 49:107–122

    Google Scholar 

  • Pawlak Z (1991) Rough sets. Theoretical aspects of reasoning about data. Kluwer Academic Publisher, London

    MATH  Google Scholar 

  • Radha K, Kumaravel N (2013) The degree of an edge in Cartesian product and composition of two fuzzy graphs. Int J Appl Math Stat Sci 2(2):65–78

    Google Scholar 

  • Rosenfeld A (1975) Fuzzy graphs. In fuzzy sets and their applications to cognitive and decision processes. Academic Press, New York, pp 77–95

    Google Scholar 

  • Roy AR, Maji PK (2007) A fuzzy soft set theoretic approach to decision making problems. J Comput Appl Math 203:412–418

    MATH  Google Scholar 

  • Singh PK, Kumar AC, Li J (2016) Knowledge representation using interval-valued fuzzy formal concept lattice. Soft Comput 20(4):1485–1502

    MATH  Google Scholar 

  • Song Y, Li G (2019) Handling group decision-making model with incomplete hesitant fuzzy preference relations and its application in medical decision. Soft Comput 23(15):6657–6666

    MATH  Google Scholar 

  • Stell JG (1999) Granulation for graphs. In: International conference on spatial information theory. Springer, Berlin, pp 417–432

  • Stell JG (2010) Relational granularity for hypergraphs. In: International conference on rough sets and current trends in computing. Springer, Berlin, pp 267–276

  • Wang Q, Gong Z (2018) An application of fuzzy hypergraphs and hypergraphs in granular computing. Inf Sci 429:296–314

    MathSciNet  Google Scholar 

  • William-West TO, Singh D (2018) Information granulation for rough fuzzy hypergraphs. Granul Comput 3(1):75–92

    Google Scholar 

  • Yang J, Wang G, Zhang Q (2018) Knowledge distance measure in multigranulation spaces of fuzzy equivalence relation. Inf Sci 448:18–35

    MathSciNet  Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353

    MATH  Google Scholar 

  • Zadeh LA (1979) Fuzzy sets and information granularity. In: Gupta N, Ragade R, Yager R (eds) Advances in fuzzy set theory and applications. North-Holland, Amsterdam, pp 3–18

    Google Scholar 

  • Zadeh LA (1997) Towards a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic. Fuzzy Sets Syst 19:111–127

    MathSciNet  MATH  Google Scholar 

  • Zhan J, Akram M, Sitara M (2018) Novel decision-making method based on bipolar neutrosophic information. Soft Comput 23(20):9955–9977

    Google Scholar 

  • Zhang H, Li Q (2019) Intuitionistic fuzzy filter theory on residuated lattices. Soft Comput 23(16):6777–6783

    MATH  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Mathematics, University of the Punjab, New Campus, Lahore, 4590, Pakistan

    Muhammad Akram & Anam Luqman

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  1. Muhammad Akram
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  2. Anam Luqman
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Correspondence to Muhammad Akram.

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Communicated by A. Di Nola.

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Akram, M., Luqman, A. Granulation of ecological networks under fuzzy soft environment. Soft Comput 24, 11867–11892 (2020). https://doi.org/10.1007/s00500-020-05083-4

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