The Pseudo-Pascal Triangle of Maximum Deng Entropy

PPascal triangle (known as Yang Hui Triangle in Chinese) is an important model in mathematics while the entropy has been heavily studied in physics or as uncertainty measure in information science. How to construct the the connection between Pascal triangle and uncertainty measure is an interesting topic. One of the most used entropy, Tasllis entropy, has been modelled with Pascal triangle. But the relationship of the other entropy functions with Pascal triangle is still an open issue. Dempster-Shafer evidence theory takes the advantage to deal with uncertainty than probability theory since the probability distribution is generalized as basic probability assignment, which is more efficient to model and handle uncertain information. Given a basic probability assignment, its corresponding uncertainty measure can be determined by Deng entropy, which is the generalization of Shannon entropy. In this paper, a Pseudo-Pascal triangle based the maximum Deng entropy is constructed. Similar to the Pascal triangle modelling of Tasllis entropy, this work provides the a possible way of Deng entropy in physics and information theory

Criteria Uncertainty in Multiple Criteria Decision Analysis of Sustainable Manufacturing Systems

Multiple Criteria Decision Analysis (MCDA) is a discipline used by decision makers to evaluate conflicting features when choosing among alternatives. MCDA methods are applied in the field of sustainable manufacturing to weigh the importance of traditional criteria when compared to sustainability indicators. However, a recurring issue in MCDA is the uncertainty in the assessments of alternatives. In this project, a novel framework to deal with uncertainty in MCDA has been developed. It uses scenario planning to get optimistic and pessimistic assessments for the different alternatives. Then, assigning probabilities to the scenarios and applying COPRAS-N, an introduced modification of COPRAS-G, 11 weighted scenarios are calculated. Finally, the relative significance and ranking of each alternative are graphed according to the weighted scenarios so that their evolution and the different situations are represented. With the presented approach, internal and external uncertainties can be dealt with at the same time. The final decision is made by analysing the graphics and results and, if necessary, looking at the concepts of expected scenario and average performance introduced in this project. The framework has been applied to 3 case studies with a focus on sustainability found in the literature. The results show that providing a final ranking of alternatives without considering other likely scenarios may lead to wrong decisions. In fact, in Case study 1, the choice of the best alternative would have changed if the developed framework had been applied. Representing all the scenarios has proved to ensure the final decision and enable to evaluate all the possible outcomes, solving in this way the uncertainty.Objectius de Desenvolupament Sostenible::9 - Indústria, Innovació i Infraestructur

AN INTERVAL TYPE 2 FUZZY EVIDENTIAL REASONING APPROACH TO PERSONNEL RECRUITMENT

Recruitment process is a procedure of selecting an ideal candidate amongst different applicants who suit the qualifications required by the given institution in the best way. Due to the multi criteria nature of the recruitment process, it involves contradictory, numerous and incommensurable criteria that are based on quantitative and qualitative measurements. Quantitative criteria evaluation are not always dependent on the judgement of the expert, they are expressed in either monetary terms or engineering measurements, meanwhile qualitative criteria evaluation depend on the subjective judgement of the decision maker, human evaluation which is often characterized with subjectivity and uncertainties in decision making. Given the uncertain, ambiguous, and vague nature of recruitment process there is need for an applicable methodology that could resolve various inherent uncertainties of human evaluation during the decision making process. This work thus proposes an interval type 2 fuzzy evidential reasoning approach to recruitment process. The approach is in three phases; in the first phase in order to capture word uncertainty an interval type 2(IT2) fuzzy set Hao and Mendel Approach (HMA) is proposed to model the qualification requirement for recruitment process. This approach will cater for both intra and inter uncertainty in decision makers’judgments and demonstrates agreements by all subjects (decision makers) for the regular overlap of subject data intervals and the manner in which data intervals are collectively classified into their respective footprint of uncertainty. In the second phase the Intervaltype 2 fuzzy Analytical hierarchical process was employed as the weighting model to determine the weight of each criterion gotten from the decision makers. In the third phase the interval type 2 fuzzy was hybridized with the ranking evidential reasoning algorithm to evaluate each applicant to determine their final score in order to choose the most ideal candidate for recruitment.The implementation tool for phase two and three is Java programming language. Application of this proposed approach in recruitment process will resolve both intra and inter uncertainty in decision maker’s judgement and give room for consistent ranking even in place of incomplete requirement

State of Art of Plithogeny Multi Criteria Decision Making Methods

Plithogenic sets coined by Smarandache in the year 2018 has unveiled new research opportunities in the field of Multi criteria decision making (MCDM). The contributions and developments of new decision making approaches based on plithogeny is gaining high momentum presently. The theoretical conceptualization of different phenomenon with plithogenic sets are also applied in designing optimal solutions to the decision making problems. This review paper presents the applications of plithogenic MCDM from the year 2018 to till date in almost all the spheres of decision making scenario. The literature works of the researchers presented in this paper will certainly portray the compatibility and flexibility of plithogenic sets, operators and other decision making tools. Though the time span considered for counting on the plithogeny based works is short, the applications of plithogenic sets are growing many in number and also plithogeny based theories are amplifying in a speedy manner. This has motivated the authors to investigate on the proliferation of plithogeny applications in decision making. This review paper has focused on the dimensions of different fields to which plithogeny is applied, new plithogeny based theories, extension of plithogeny, plithogenic based operators and measures. In addition to it the data on the publications of plithogeny based articles and interests of researchers are also presented as a part of this review work. The overall impact of plithogeny in the arena of decision making science and on the researchers of the same field is well sketched in this paper with the intention and hope of inspiring plithogenic researchers