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Bridging the Gap Between probabilistic and fuzzy Entropy

IEEE TRANSACTIONS ON fuzzy SYSTEMS 2020年第9期28卷 2175-2184页

作者： Aggarwal, Manish IIM Ahmedabad Ahmadabad 380015 Gujarat India

The real-world decision making often involves a comparison of uncertain systems or alternatives based on fuzzy evaluations. The concept of fuzzy entropy is quite useful in such situations. However, fuzzy entropy and the conventional probabilistic entropy differ in their semantics. This article critically examines the existing fuzzy entropy functions and redefine them to bring them closer to the probabilistic entropy. More specifically, new variants of the extant Luca and Termini, and Pal and Pal fuzzy entropy functions are proposed. The proposed fuzzy entropy functions are extended for the probabilistic-fuzzy uncertainty, commonly observed in the real world. A real application is included to demonstrate the usefulness of the proposed entropy functions in decision making applications.

关键词： Entropy Uncertainty fuzzy sets probabilistic logic Decision making Measurement uncertainty Additives Decision making fuzzy entropy probabilistic-fuzzy subjective uncertainty uncertainty

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On fuzzy entropy functions based on human attitude

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JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY 2024年第8期75卷 1510-1523页

作者： Aggarwal, Manish IIT Jodhpur Sch AI & Data Sci Jodhpur India IIT Jodhpur Digital Humanities Res Grp Jodhpur India

A fuzzy entropy function is useful to quantify the underlying vagueness. However, unlike probability, uncertainty due to vagueness is essentially perceived by a human agent in his/her cognition. This paper presents new fuzzy entropy functions that yields fuzzy entropy specific to the agent's attitudinal tendency. Besides, the proposed functions correspond to the conventional entropy functions in the probabilistic domain, making them amenable to represent probabilistic-fuzzy (prob-fuzzy) uncertainty easily. To demonstrate this ability, the proposed functions are also extended to the prob-fuzzy domain. A case-study is included to show the usefulness of the proposed fuzzy and prob-fuzzy entropy functions.

关键词： Uncertainty fuzzy entropy decision-making probabilistic-fuzzy attitude

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On Agent-Specific fuzzy Entropy Functions

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IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS 2023年第1期53卷 2-11页

作者： Aggarwal, Manish IIT Jodhpur Sch Artificial Intelligence & Data Sci Jheepasani 342030 India

The concern of this article is to introduce versatile fuzzy and probabilistic-fuzzy entropy functions that could quantify the overall ambiguity of a system as perceived by the agent. The central principle behind the proposed functions is: besides the underlying ambiguity, an agent's inherent outlook toward ambiguity casts a great influence on the perceived entropy. The proposed functions also consider the tendency to exxaggerate/downplay the ambiguity. More specifically, the proposed entropy functions take as argument the perceived ambiguity value, rather than the actual membership grade. Besides, the relationship between the perceived membership grade and ambiguity is closely modeled to compute the overall entropy. The variants of the proposed functions for the probabilistic-fuzzy domain are also presented. A real case study is included to demonstrate the significance of the work.

关键词： Entropy Uncertainty probabilistic logic fuzzy sets Random variables Faces Uncertain systems Attitudinal character decision-making fuzzy entropy probabilistic-fuzzy subjective uncertainty uncertainty

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Assessing Potential of Organizations with fuzzy Entropy

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Operations Research Forum 2023年第1期4卷 11页

作者： Aggarwal, Manish Krishankumar, R. Ravichandran, K.S. Senapati, T. Yager, R.R. School of Artificial Intelligence and Data Science IIT Jodhpur Jodhpur India Digital Humanities IIT Jodhpur Jodhpur India Department of Computer Science and Engineering Amrita School of Computing Amrita Vishwa Vidyapeetham Coimbatore India Department of Mathematics Amrita School of Physical Sciences Amrita Vishwa Vidyapeetham Coimbatore India School of Mathematics and Statistics Southwest University Chongqing Beibei 400715 China Machine Intelligence Institute Iona College New Rochelle 10801 NY United States

Assessing the performance of organizations in the near future has been a challenging problem because of the factors of subjective assessment of the uncertainty. To cater to such applications, a novel form of fuzzy entropy is proposed to unify the concepts of fuzzy entropy and the conventional Shannon’s entropy. The proposed entropy provides a direct and convenient framework to quantify the uncertainty associated with a firm in the near future. It is also shown that the proposed form is amenable in extending the fuzzy entropy functions to the probabilistic-fuzzy domain. Thus, the proposed form of fuzzy entropy finds a special significance in the human decision-making problems. A case study illustrates the applicability of the proposed functions in assessment of future performance of a firm. © 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

关键词： Attitudinal character Entropy fuzzy logic probabilistic-fuzzy Uncertainty

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An entropy framework for randomness and fuzziness

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EXPERT SYSTEMS WITH APPLICATIONS 2024年 243卷

作者： Aggarwal, Manish Indian Inst Technol Sch Artificial Intelligence & Data Sci Jodhpur India Indian Inst Technol Jodhpur Digital Humanities Jodhpur India

In the real world, it is common to observe both randomness and fuzziness concurrently. Accordingly, event/system/decision has multiple possibilities. Thus, in order to compare multiple uncertain options, measure of overall uncertainty is often desired. This is the topic of this paper. A versatile and intuitive framework that could quantify concurrent probabilistic, fuzzy, and prob-fuzzy uncertainties is proposed. Based on the same, new entropy functions are developed to quantify the prob-fuzzy uncertainty. The proposed entropy functions are inspired from the popular entropy functions such as Shannon's entropy. The properties of entropy functions are rigorously analysed. A real case-study in the agriculture and environment domain included to demonstrate the usefulness of the work.

关键词： fuzzy entropy Uncertainty Decision-making Attitudinal character probabilistic-fuzzy

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Redefining fuzzy entropy with a general framework

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EXPERT SYSTEMS WITH APPLICATIONS 2021年 164卷 113671-113671页

作者： Aggarwal, Manish IIT Jodhpur Jodhpur Rajasthan India

A general entropy framework is proposed, which could lead to intuitive, interpretable and comparable entropy functions in both probabilistic or fuzzy domain, alike. Based on the proposed general entropy framework, the existing fuzzy entropy functions are redefined. The proposed entropy functions are also extended to the probabilistic-fuzzy domain. The usefulness of the work is shown in a real world case study. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： fuzzy entropy Uncertainty Decision-making Subjective uncertainty probabilistic-fuzzy

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