Multicriteria decision making based on bi-direction Choquet integrals

Abstract To deal with multicriteria decision making (MCDM) problems with interaction criteria, the Choquet integral (CI) is one of effective tools. This paper first proposes the reverse Choquet integral (RCI), which defines the importance of the ordered elements in an opposite principle to the CI. To show the principle of the RCI, we offer its concrete expression in view of the Mobius representation by which one can clearly see the difference and the relationship between the CI and the RCI. Then, we propose the “bi-direction Choquet integral” (BDCI), which is a convex combination of the CI and the RCI. To get the interactions of ordered coalitions comprehensively, this paper further proposes the generalized Shapley bi-direction Choquet integral (GSBDCI). Furthermore, the hybrid generalized Shapley bi-direction Choquet integral (HGSBDCI) is proposed, which defines the importance of ordered positions and the criteria with interactions simultaneously. With respect to these types of CIs, their exponent forms are also discussed. Finally, we use an application case to show the utilization of the proposed new CIs for MCDM. The proposed new Choquet integrals provide us a very useful way to deal with MCDM problems.

[1]  Saleem Abdullah,et al.  Multiattribute group decision making based on interval-valued Pythagorean fuzzy Einstein geometric aggregation operators , 2019, Granular Computing.

[2]  Tasawar Hayat,et al.  Numerical solutions of fuzzy differential equations using reproducing kernel Hilbert space method , 2015, Soft Computing.

[3]  Wen-Shing Lee,et al.  Evaluating and ranking energy performance of office buildings using fuzzy measure and fuzzy integral , 2010 .

[4]  Zhiming Zhang,et al.  Maclaurin symmetric means of dual hesitant fuzzy information and their use in multi-criteria decision making , 2019, Granular Computing.

[5]  Zeshui Xu,et al.  Computation of generalized linguistic term sets based on fuzzy logical algebras for multi-attribute decision making , 2020, Granular Computing.

[6]  Chunqiao Tan,et al.  Barriers analysis for reverse logistics in Thailand’s palm oil industry using fuzzy multi-criteria decision-making method for prioritizing the solutions , 2020, Granular Computing.

[7]  M. Sugeno,et al.  A theory of fuzzy measures: Representations, the Choquet integral, and null sets , 1991 .

[8]  Gabriella Pasi,et al.  A Multi-Criteria Decision Making approach based on the Choquet integral for assessing the credibility of User-Generated Content , 2019, Inf. Sci..

[9]  Michio Sugeno,et al.  A study on subjective evaluations of printed color images , 1991, Int. J. Approx. Reason..

[10]  Jean-Luc Marichal,et al.  The influence of variables on pseudo-Boolean functions with applications to game theory and multicriteria decision making , 2000, Discret. Appl. Math..

[11]  Li Wang,et al.  An extension approach of TOPSIS method with OWAD operator for multiple criteria decision-making , 2018, Granular Computing.

[12]  Marek Reformat,et al.  Choquet based TOPSIS and TODIM for dynamic and heterogeneous decision making with criteria interaction , 2017, Inf. Sci..

[13]  D. S. Hooda,et al.  Extension of intuitionistic fuzzy TODIM technique for multi-criteria decision making method based on shapley weighted divergence measure , 2019 .

[14]  Mohammed Al-Smadi,et al.  Fuzzy conformable fractional differential equations: novel extended approach and new numerical solutions , 2020, Soft Comput..

[15]  G. Choquet.  Theory of capacities , 1954 .

[16]  Mohamed Benrejeb,et al.  Choquet integral for criteria aggregation in the flexible job-shop scheduling problems , 2008, Math. Comput. Simul..

[17]  Asad Ali,et al.  New approach to multiple attribute group decision-making based on Pythagorean fuzzy Einstein hybrid geometric operator , 2019, Granular Computing.

[18]  Michio Sugeno,et al.  Choquet integral with respect to a symmetric fuzzy measure of a function on the real line , 2016, Ann. Oper. Res..

[19]  M. Grabisch.  Fuzzy integral in multicriteria decision making , 1995 .

[20]  Michel Grabisch,et al.  A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid , 2010, Ann. Oper. Res..

[21]  Shyi-Ming Chen,et al.  Multiattribute decision making based on novel score function of intuitionistic fuzzy values and modified VIKOR method , 2019, Inf. Sci..

[22]  M. Sugeno,et al.  An interpretation of fuzzy measures and the Choquet integral as an integral with respect to a fuzzy , 1989 .

[23]  Michel Grabisch,et al.  A discrete Choquet integral for ordered systems , 2011, Fuzzy Sets Syst..

[24]  Michel Grabisch,et al.  K-order Additive Discrete Fuzzy Measures and Their Representation , 1997, Fuzzy Sets Syst..

[25]  Saleem Abdullah,et al.  Some induced aggregation operators based on interval-valued Pythagorean fuzzy numbers , 2019 .

[26]  Alain Chateauneuf,et al.  Some Characterizations of Lower Probabilities and Other Monotone Capacities through the use of Möbius Inversion , 1989, Classic Works of the Dempster-Shafer Theory of Belief Functions.

[27]  Harish Garg,et al.  Improved possibility degree method for ranking intuitionistic fuzzy numbers and their application in multiattribute decision-making , 2018, Granular Computing.

[28]  Muhammad Sajjad Ali Khan,et al.  An extension of VIKOR method for multi-attribute decision-making under Pythagorean hesitant fuzzy setting , 2018, Granular Computing.

[29]  Fanyong Meng,et al.  Interval‐Valued Intuitionistic Fuzzy Multiattribute Group Decision Making Based on Cross Entropy Measure and Choquet Integral , 2013, Int. J. Intell. Syst..

[30]  Zhao Na.  The Generalized WOWA Operator and Its Application , 2012 .

[31]  Kannan Govindan,et al.  Developing a green city assessment system using cognitive maps and the Choquet Integral , 2019, Journal of Cleaner Production.

[32]  Behzad Moshiri,et al.  A GIS-based multi-criteria analysis model for earthquake vulnerability assessment using Choquet integral and game theory , 2017, Natural Hazards.

[33]  Jean-Luc Marichal,et al.  An axiomatic approach of the discrete Choquet integral as a tool to aggregate interacting criteria , 2000, IEEE Trans. Fuzzy Syst..

[34]  Fanyong Meng,et al.  Linguistic intuitionistic fuzzy Hamacher aggregation operators and their application to group decision making , 2018, Granular Computing.

[35]  László Lovász,et al.  Submodular functions and convexity , 1982, ISMP.

[36]  Marjan S. Jalali,et al.  Enhancing the decision-making virtuous cycle of ethical banking practices using the Choquet integral , 2018, Journal of Business Research.

[37]  Tasawar Hayat,et al.  Application of reproducing kernel algorithm for solving second-order, two-point fuzzy boundary value problems , 2017, Soft Comput..

[38]  D. Schmeidler.  Integral representation without additivity , 1986 .

[39]  José Rui Figueira,et al.  On the Choquet multiple criteria preference aggregation model: Theoretical and practical insights from a real-world application , 2018, Eur. J. Oper. Res..

[40]  V. Torra.  The weighted OWA operator , 1997, International Journal of Intelligent Systems.

[41]  Arthur P. Dempster,et al.  Upper and Lower Probabilities Induced by a Multivalued Mapping , 1967, Classic Works of the Dempster-Shafer Theory of Belief Functions.

[42]  Shyamal Kumar Mondal,et al.  Trapezoidal interval type-2 fuzzy soft stochastic set and its application in stochastic multi-criteria decision-making , 2018, Granular Computing.

[43]  Jian-Zhang Wu,et al.  Compromise principle based methods of identifying capacities in the framework of multicriteria decision analysis , 2014, Fuzzy Sets Syst..

[44]  Arunodaya Raj Mishra,et al.  Multiple-criteria decision-making for service quality selection based on Shapley COPRAS method under hesitant fuzzy sets , 2018, Granular Computing.

[45]  Shyi-Ming Chen,et al.  Interval-valued intuitionistic fuzzy multiple attribute decision making based on nonlinear programming methodology and TOPSIS method , 2020, Inf. Sci..

[46]  Tufan Demirel,et al.  Location selection for underground natural gas storage using Choquet integral , 2017 .