Aggarwal, Manish

In the real world, it is common to observe both randomness and fuzziness concurrently. Accordingly, an event/system/decision has multiple possibilities. Thus, in order to compare multiple uncertain options, a 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 the entropy functions are rigorously analysed. A real case-study in the agriculture and environment domain is included to demonstrate the usefulness of the work.

The pervasiveness of the Internet coupled with the advantages of cloud have almost made cloud services a necessity for organizations and individuals alike. However, it is a complex decision to choose a cloud vendor because of the large number of criteria and alternatives. Furthermore, the criteria in the case of cloud vendor selection are often interactive (synergic or opposing). To address this need, an approach is presented in this paper to select the most suitable cloud vendor while considering the nuances of human decision making, such as interactive criteria, and varying behavioural characteristics of the decision-makers (DMs). To this end, the recent Choquet logit models are deployed and generalized to add to their modelling abilities. Specifically, the following choice models are developed: generalized Choquet logit, generalized attitudinal Choquet logit, generalized Choquet mixed logit, and generalized attitudinal Choquet mixed logit models. The proposed generalized logit models have the Choquet logit, and the attitudinal Choquet logit models as their special cases. Thus the contributions of this work are two-fold: first an approach is developed to select suitable cloud vendor considering the human nuances and the actual practical aspects of the problem, and secondly a new class of powerful choice models is developed which may be useful in aiding any complex human decision-making, in which the cognitive power of the DM proves to be limited. The method is designed to consider the real nuances of the human decision making such as varying attitudes and varying degree of criteria interaction. The effectiveness of the proposed models in cloud vendor selection is tested through a real world case study from the Indian state of Tamil Nadu. In the case-study, there are 9 cloud vendors in the fray and 4 experts with different attitudes and different suggestions for the best cloud vendor. An approach is developed to solve this problem and a final ranking of the cloud vendors is determined considering experts suggestions. Apart from finding the best cloud vendor, the case study also helps in studying the role of an expert's attitudinal tendency on his preferences. Thus, concomitantly, the proposed approach also guides how to choose the best alternative based on the opinions of different experts with different attitudinal tendencies, without necessitating a forced consensus.

In this paper, new entropy functions are formulated based on an agent's perceived uncertainty that inevitably affects the agent's choice. The role of the decision-maker's (DM's) attitude is emphasized as one of the key determinants of such an entropy function. More specifically, new attitude-based variants of Shannon's, Pal & Pal, and Aggarwal's probabilistic entropies are introduced. The extant fuzzy entropies are also extended to consider the agent's specific attitude. The proposed entropy functions provide a wide range of entropy values with the conventional entropy functions as their special cases. The special cases of the proposed entropies are examined. The wide applicability of the proposed entropy functions in multi criteria decision making is highlighted. A case-study is included to showcase the usefulness of the proposed entropy functions in the real world. � 2021

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.