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Ma L, Ali Z, Yin S. Implementation of Learning Management Systems (LMS) in higher education systems through bipolar complex hesitant fuzzy Aczel-Alsina power aggregation operators: A case review for China. PLoS One 2024; 19:e0300317. [PMID: 38574096 PMCID: PMC10994378 DOI: 10.1371/journal.pone.0300317] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2023] [Accepted: 02/27/2024] [Indexed: 04/06/2024] Open
Abstract
A learning management system (LMS) is a web-based application or software platform computed to facilitate the development, tracking, management, reporting, and delivery of education and training programs. Many valuable and dominant factors are working behind the Learning Management System (LMS), but no one can find which factor is most important and valuable for LMS during COVID-19 among the following five alternatives, called Improved Accessibility, Blended Learning, Collaboration and Communications, Assessment and Evaluation, and Administrative Efficiency. For this, first, we derive the techniques of bipolar complex hesitant fuzzy (BCHF) sets, and then we evaluate some flexible operational laws, called Algebraic operational laws and Aczel-Alsina operational laws. Secondly, using the above techniques, we elaborate the technique of BCHF Aczel-Alsina power averaging (BCHFAAPA), BCHF Aczel-Alsina power weighted averaging (BCHFAAPWA), BCHF Aczel-Alsina power geometric (BCHFAAPG), and BCHF Aczel-Alsina power weighted geometric (BCHFAAPWG) operators. Some basic properties are also investigated for each proposed operator. Further, to evaluate the problem concerning LMS, we compute the multi-attribute decision-making (MADM) techniques for invented operators. Finally, we select some prevailing operators and try to compare their ranking results with our proposed results to enhance the worth and capability of the invented theory.
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Affiliation(s)
- Lijun Ma
- College of Land and Resources, Hebei Agricultural University, Baoding, China
| | - Zeeshan Ali
- Department of Mathematics and Statistics, Riphah International University, Islamabad, Pakistan
| | - Shi Yin
- College of Economics and Management, Hebei Agriculture University, Baoding, China
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Musa SY. N-bipolar hypersoft sets: Enhancing decision-making algorithms. PLoS One 2024; 19:e0296396. [PMID: 38227603 PMCID: PMC10791010 DOI: 10.1371/journal.pone.0296396] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/14/2023] [Accepted: 12/12/2023] [Indexed: 01/18/2024] Open
Abstract
This paper introduces N-bipolar hypersoft (N-BHS) sets, a versatile extension of bipolar hypersoft (BHS) sets designed to effectively manage evaluations encompassing both binary and non-binary data, thereby exhibiting heightened versatility. The major contributions of this framework are twofold: Firstly, the N-BHS set introduces a parameterized representation of the universe, providing a nuanced and finite granularity in perceiving attributes, thereby distinguishing itself from conventional binary BHS sets and continuous fuzzy BHS sets. Secondly, this model signifies a new area of research aimed at overcoming limitations inherent in the N-bipolar soft set when handling multi-argument approximate functions. Through the strategic partitioning of attributes into distinct subattribute values using disjoint sets, the N-BHS set emerges as a powerful tool for effectively addressing uncertainty-related problems. In pursuit of these objectives, the paper outlines various algebraic definitions, including incomplete N-BHS sets, efficient N-BHS sets, normalized N-BHS sets, equivalence under normalization, N-BHS complements, and BHS sets derived from a threshold, exemplified through illustrative examples. Additionally, the article explores set-theoretic operations within the N-BHS sets framework, such as relative null/whole N-BHS sets, N-BHS subsets, and two distinct approaches to N-BHS extended/restricted union and intersection. Finally, it proposes and compares decision-making methodologies regarding N-BHS sets, including a comprehensive comparison with relevant existing models.
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Affiliation(s)
- Sagvan Y. Musa
- Department of Mathematics, Faculty of Education, University of Zakho, Zakho, Iraq
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Lv Z, Li J, He G. Hazard Assessment of Concrete Dam Cracks Based on Variable Fuzzy Sets and the Modified Analytic Hierarchy Process. ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING 2023. [DOI: 10.1007/s13369-023-07668-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/06/2023]
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Shi X, Ali Z, Mahmood T, Liu P. Power Aggregation Operators of Interval-Valued Atanassov-Intuitionistic Fuzzy Sets Based on Aczel–Alsina t-Norm and t-Conorm and Their Applications in Decision Making. INT J COMPUT INT SYS 2023; 16:43. [PMCID: PMC10043541 DOI: 10.1007/s44196-023-00208-7] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/30/2023] Open
Abstract
Aczel–Alsina t-norm and t-conorm are important t-norm and t-conorm, and they are extended from algebraic t-norm and t-conorm. Obviously, Aczel–Alsina t-norm and t-conorm are more general than some existing t-norm and t-conorm. Furthermore, the power aggregation (PA) operator is also a very famous and valuable operator which can consider the power relation between any two input parameters. In addition, Interval-valued Atanassov-intuitionistic fuzzy set (IVA-IFS) can easily express uncertain information. In order to fully use their advantages, in this analysis, we extend the PA operators based on Aczel–Alsina t-norm and t-conorm to IVA-IFS and propose the interval-valued Atanassov-intuitionistic fuzzy Aczel–Alsina power averaging (IVA-IFAAPA), interval-valued Atanassov-intuitionistic fuzzy Aczel–Alsina power ordered averaging (IVA-IFAAPOA), interval-valued Atanassov-intuitionistic fuzzy Aczel–Alsina power geometric (IVA-IFAAPG) and interval-valued Atanassov-intuitionistic fuzzy Aczel–Alsina power ordered geometric (IVA-IFAAPOG) operators. Moreover, we discuss the properties of the presented operators such as idempotency, monotonicity, and boundedness. In addition, a multi-attribute decision-making (MADM) procedure is proposed to process the IVA-IF information. Finally, a practical example is used to show the effectiveness and superiority of the proposed method by comparing it with some existing operators.
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Affiliation(s)
- Xinming Shi
- School of Business Administration, Shandong Women’s University, Jinan, 250300 Shandong People’s Republic of China
| | - Zeeshan Ali
- Department of Mathematics and Statistics, International Islamic University Islamabad, Islamabad, Pakistan
- Department of Mathematical Modeling, Statistics and Bioinformatics, KERMIT, Ghent University, Coupure Links 653, Ghent, Belgium
| | - Tahir Mahmood
- Department of Mathematics and Statistics, International Islamic University Islamabad, Islamabad, Pakistan
| | - Peide Liu
- School of Business Administration, Shandong Women’s University, Jinan, 250300 Shandong People’s Republic of China
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Ali G, Farooq A, Al-Shamiri MMA. Novel multiple criteria decision-making analysis under m-polar fuzzy aggregation operators with application. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2023; 20:3566-3593. [PMID: 36899593 DOI: 10.3934/mbe.2023166] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/18/2023]
Abstract
Aggregation is a very efficient indispensable tool in which several input values are transformed into a single output value that further supports dealing with different decision-making situations. Additionally, note that the theory of m-polar fuzzy (mF) sets is proposed to tackle multipolar information in decision-making problems. To date, several aggregation tools have been widely investigated to tackle multiple criteria decision-making (MCDM) problems in an m-polar fuzzy environment, including m-polar fuzzy Dombi and Hamacher aggregation operators (AOs). However, the aggregation tool to deal with m-polar information under Yager's operations (that is, Yager's t-norm and t-conorm) is missing in the literature. Due to these reasons, this study is devoted to investigating some novel averaging and geometric AOs in an mF information environment through the use of Yager's operations. Our proposed AOs are named as the mF Yager weighted averaging (mFYWA) operator, mF Yager ordered weighted averaging operator, mF Yager hybrid averaging operator, mF Yager weighted geometric (mFYWG) operator, mF Yager ordered weighted geometric operator and mF Yager hybrid geometric operator. The initiated averaging and geometric AOs are explained via illustrative examples and some of their basic properties, including boundedness, monotonicity, idempotency and commutativity are also studied. Further, to deal with different MCDM situations containing mF information, an innovative algorithm for MCDM is established under the under the condition of mFYWA and mFYWG operators. After that, a real-life application (that is, selecting a suitable site for an oil refinery) is explored under the conditions of developed AOs. Moreover, the initiated mF Yager AOs are compared with existing mF Hamacher and Dombi AOs through a numerical example. Finally, the effectiveness and reliability of the presented AOs are checked with the help of some existing validity tests.
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Affiliation(s)
- Ghous Ali
- Department of Mathematics, Division of Science and Technology, University of Education, Lahore, Pakistan
| | - Adeel Farooq
- Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Pakistan
| | - Mohammed M Ali Al-Shamiri
- Department of Mathematics, Faculty of Science and Arts, Mahayl Assir, King Khalid University, Abha, Saudi Arabia
- Department of Mathematics and Computer, Faculty of Science, Ibb University, Ibb, Yemen
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Adeel A, Akram M, Çaǧman N. Decision-making analysis based on hesitant fuzzy N-soft ELECTRE-I approach. Soft comput 2022. [DOI: 10.1007/s00500-022-06981-5] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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Feng X, Shi H, Wei C. Evaluation of employee green behavior ability based on a fuzzy BWM-VIKOR approach. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2022. [DOI: 10.3233/jifs-212660] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Abstract
As a core resource of the company, employees play a major role to implement green management related behaviors in enterprises. Management department is also working hard to improve the ability of employees to perform these green behaviors for the company’s sustainable development capabilities. This study is the first effort that evaluation of effect factors of employee green behavior ability (EGBA) by intuitionistic fuzzy number-best worst method (IFN-BWM). To reach the study objective, a total of four criteria and twenty-seven sub-criteria for evaluation of EGBA are collected from the existing literatures. Subsequently, the PFN-VIKOR methodology (Pythagorean Fuzzy Number-Visekriterijumska Optimizacija I Kom-promisno Resenje) is proposed to rank EGBA levels. The results of this study show that employee self-efficacy and employee initiative in learning relevant green knowledge are important factors to enhance EGBA. Moreover, findings confirm that extended fuzzy semantic values and novel algorithm can accurately measure the decision makers’ mind and improve the accuracy of evaluation. This study also provides a framework for managers to evaluate their employee’ green behavior ability.
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Affiliation(s)
- Xiangqian Feng
- School of Business, Nanjing Normal University, Nanjing, P.R. China
| | - Hui Shi
- School of Business, Nanjing Normal University, Nanjing, P.R. China
| | - Cuiping Wei
- College of Mathematical Sciences, Yangzhou University, Yangzhou, P.R. China
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Wei D, Rong Y, Garg H. An extended WASPAS approach for teaching quality evaluation based on pythagorean fuzzy reducible weighted Maclaurin symmetric mean. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2022. [DOI: 10.3233/jifs-210821] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
Teaching quality evaluation (TQE) can not only improve teachers’ teaching skills, but also provide an important reference for school teaching management departments to formulate teaching reform measures and strengthen teaching management. TQE is a process of grading and ranking a given teachers based on the comprehensive consideration of multiple evaluation criteria by expert. The Maclaurin symmetric mean (MSM), as a powerful aggregation function, can capture the correlation among multiple input data more efficient. Although multitude weighted MSM operators have been developed to handle the Pythagorean fuzzy decision issues, these above operators do not possess the idempotency and reducibility during the procedure of information fusion. To conquer these defects, we present the Pythagorean fuzzy reducible weighted MSM (PFRWMSM) operator and Pythagorean fuzzy reducible weighted geometric MSM (PFRWGMSM) operator to fuse Pythagorean fuzzy assessment information. Meanwhile, several worthwhile properties and especial cases of the developed operators are explored at length. Afterwards, we develop a novel Pythagorean fuzzy entropy based upon knowledge measure to ascertain the weights of attribute. Furthermore, an extended weighted aggregated sum product assessment (WASPAS) method is developed by combining the PFRWMSM operator, PFRWGMSM operator and entropy to settle the decision problems of unknown weight information. The efficiency of the proffered method is demonstrated by a teaching quality evaluation issue, as well as the discussion of sensitivity analysis for decision outcomes. Consequently, a comparative study of the presented method with the extant Pythagorean fuzzy approaches is conducted to display the superiority of the propounded approach.
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Affiliation(s)
- Dongmei Wei
- School of Computer and Software Engineering, Xihua University, Chengdu, Sichuan, P.R. China
| | - Yuan Rong
- School of Management, Shanghai University, Baoshan District, Shanghai, P.R. China
| | - Harish Garg
- School of Computer and Software Engineering, Xihua University, Chengdu, Sichuan, P.R. China
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Abstract
With the rapid growth of population, the global impact of solar technology is increasing by the day due to its advantages over other power production technologies. Demand for solar panel systems is soaring, thus provoking the arrival of many new manufacturers. Sale dealers or suppliers face an uncertain problem to choose the most adequate technological solution. To effectively address such kind of issues, in this paper we propose the Fermatean fuzzy soft expert set model by combining Fermatean fuzzy sets and soft expert sets. We describe this hybrid model with numerical examples. From a theoretical standpoint, we demonstrate some essential properties and define operations for this setting. They comprise the definitions of complement, union and intersection, the OR operation and the AND operation. Concerning practice in this new environment, we provide an algorithm for multi-criteria group decision making whose productiveness and authenticity is dutifully tested. We explore a practical application of this approach (that is, the selection of a suitable brand of solar panel system). Lastly, we give a comparison of our model with certain related mathematical tools, including fuzzy and intuitionistic fuzzy soft expert set models.
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Affiliation(s)
- Muhammad Akram
- Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan
| | - Ghous Ali
- Department of Mathematics, Division of Science and Technology, University of Education, Lahore, Pakistan
| | | | - Aneesa Riaz
- Department of Mathematics, Division of Science and Technology, University of Education, Lahore, Pakistan
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Lin S, Zhu W. How subjective information with AI for digital revolution. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2021. [DOI: 10.3233/jifs-211624] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
This paper summarizes the relationship of subjective information with artificial intelligence (AI) technology and points out how the role of subjective information and its position in AI. Eventually, the characteristic of digital era is the “softening of the theories and hardening of the experiences”. Subjective information is widely used in digital revolution for transforming the qualitative estimations into quasi-quantitative solutions, such as the empirical methods in decision making for quantitative management, etc., it will be the transferor for realizing it. The theoretical formulation of how subjective information is digitized through “Fuzzy-AI Model” for digital revolution is presented in this paper; it has becoming a universal problem solver of utilizing AI technology for quantizing the degree uncertainties in decision-making and fuzzy estimation. Besides, the “Big Data” searching will heavily depend on the completeness of its source information, yet “subjective information” approach can directly predict human thinking or the internal law of complicated objective events into an explicit digital form, for the completeness of source information to make the correct and comprehensive “Big Data” prediction possible. Practical case studies are presented.
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Affiliation(s)
- Shaopei Lin
- Institute of Engineering Management, Shanghai Jiao Tong University, Shanghai, PRC
| | - Wei Zhu
- College of Transportation Engineering, Tongji University, Shanghai, PRC
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Akram M, Ali G, Peng X, Ul Abidin MZ. Hybrid group decision-making technique under spherical fuzzy N-soft expert sets. Artif Intell Rev 2021. [DOI: 10.1007/s10462-021-10103-2] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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12
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Akram M, Ahmad U, Rukhsar. Threshold graphs under picture Dombi fuzzy information. GRANULAR COMPUTING 2021. [DOI: 10.1007/s41066-021-00291-1] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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Tchier F, Ali G, Gulzar M, Pamučar D, Ghorai G. A New Group Decision-Making Technique under Picture Fuzzy Soft Expert Information. ENTROPY 2021; 23:e23091176. [PMID: 34573801 PMCID: PMC8467849 DOI: 10.3390/e23091176] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/29/2021] [Revised: 08/30/2021] [Accepted: 08/31/2021] [Indexed: 11/16/2022]
Abstract
As an extension of intuitionistic fuzzy sets, the theory of picture fuzzy sets not only deals with the degrees of rejection and acceptance but also considers the degree of refusal during a decision-making process; therefore, by incorporating this competency of picture fuzzy sets, the goal of this study is to propose a novel hybrid model called picture fuzzy soft expert sets by combining picture fuzzy sets with soft expert sets for dealing with uncertainties in different real-world group decision-making problems. The proposed hybrid model is a more generalized form of intuitionistic fuzzy soft expert sets. Some novel desirable properties of the proposed model, namely, subset, equality, complement, union and intersection, are investigated together with their corresponding examples. Two well-known operations AND and OR are also studied for the developed model. Further, a decision-making method supporting by an algorithmic format under the proposed approach is presented. Moreover, an illustrative application is provided for its better demonstration, which is subjected to the selection of a suitable company of virtual reality devices. Finally, a comparison of the initiated method is explored with some existing models, including intuitionistic fuzzy soft expert sets.
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Affiliation(s)
- Fairouz Tchier
- Department of Mathematics, King Saud University, P.O. Box 22452, Riyadh 11495, Saudi Arabia;
| | - Ghous Ali
- Department of Mathematics, Division of Science and Technology, University of Education, Lahore 54770, Pakistan;
| | - Muhammad Gulzar
- Department of Mathematics, Government College University Faisalabad, Faisalabad 38000, Pakistan;
| | - Dragan Pamučar
- Department of Logistics, Military Academy, University of Defence in Belgrade, 11000 Belgrade, Serbia
- Correspondence:
| | - Ganesh Ghorai
- Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore 721102, India;
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Abstract
In many real-life problems, decision-making is reckoned as a powerful tool to manipulate the data involving imprecise and vague information. To fix the mathematical problems containing more generalized datasets, an emerging model called q-rung orthopair fuzzy soft sets offers a comprehensive framework for a number of multi-attribute decision-making (MADM) situations but this model is not capable to deal effectively with situations having bipolar soft data. In this research study, a novel hybrid model under the name of q-rung orthopair fuzzy bipolar soft set (q-ROFBSS, henceforth), an efficient bipolar soft generalization of q-rung orthopair fuzzy set model, is introduced and illustrated by an example. The proposed model is successfully tested for several significant operations like subset, complement, extended union and intersection, restricted union and intersection, the ‘AND’ operation and the ‘OR’ operation. The De Morgan’s laws are also verified for q-ROFBSSs regarding above-mentioned operations. Ultimately, two applications are investigated by using the proposed framework. In first real-life application, the selection of land for cropping the carrots and the lettuces is studied, while in second practical application, the selection of an eligible student for a scholarship is discussed. At last, a comparison of the initiated model with certain existing models, including Pythagorean and Fermatean fuzzy bipolar soft set models is provided.
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Akram M, Ali G, Alcantud JCR. Parameter reduction analysis under interval-valued m-polar fuzzy soft information. Artif Intell Rev 2021. [DOI: 10.1007/s10462-021-10027-x] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
Abstract
AbstractThis paper formalizes a novel model that is able to use both interval representations, parameterizations, partial memberships and multi-polarity. These are differing modalities of uncertain knowledge that are supported by many models in the literature. The new structure that embraces all these features simultaneously is called interval-valued multi-polar fuzzy soft set (IVmFSS, for short). An enhanced combination of interval-valued m-polar fuzzy (IVmF) sets and soft sets produces this model. As such, the theory of IVmFSSs constitutes both an interval-valued multipolar-fuzzy generalization of soft set theory; a multipolar generalization of interval-valued fuzzy soft set theory; and an interval-valued generalization of multi-polar fuzzy set theory. Some fundamental operations for IVmFSSs, including intersection, union, complement, “OR”, “AND”, are explored and investigated through examples. An algorithm is developed to solve decision-making problems having data in interval-valued m-polar fuzzy soft form. It is applied to two numerical examples. In addition, three parameter reduction approaches and their algorithmic formulation are proposed for IVmFSSs. They are respectively called parameter reduction based on optimal choice, rank based parameter reduction, and normal parameter reduction. Moreover, these outcomes are compared with existing interval-valued fuzzy methods; relatedly, a comparative analysis among reduction approaches is investigated. Two real case studies for the selection of best site for an airport construction and best rotavator are studied.
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