Paraconsistent Many-Valued Similarity Modelling: Optimal Decision on Telecommunication Operators in the Greater Accra Region of Ghana

Abstract

Decision science is a broad discipline that covers all spheres of life. It equips us with indispensable decision-making tools for the management of our homes and families, theology, politics, economics and education in a more logical and ethical manner. The aspect of this broad field under the focus of this study is the multi-attribute decision-making strand. Over the years, numerous single and hybrid methods have been developed to resolve multi-attribute decision-making problems in the areas of choice making and ranking of a finite set of decision alternatives. However, the major drawback of these existing methods is the difficulty in staying focus and keeping track of the calculations when the decision-makers are dealing with large size decision problems. As a result, in this study, we advance a model for addressing choice and ranking problems in both fuzzy and non-fuzzy environments. The advanced tool (model) originated from three combined sources as paraconsistent logic, Pavelka style fuzzy sentential logic and the concept of many-valued similarities. To corroborate the efficacy or otherwise of the novel model, it has been applied to two data sets - one from Ghana on the performance of five mobile phone operators with respect to four criteria and the other too on five car brands in relation to four attributes. In each of these two cases, we were to rank the decision alternatives in the corresponding data set from the best to the worst. Further, we ranked the elements of each of these two data sets using three normal multi-attribute decision-making methods - Preference Ranking Organisation MeTHod for Enrichment Evaluation (PROMETHEE I and II); Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) and Elimination and Choice Translating Reality II (ELECTRE II) - and then juxtaposed the rankings of our new method with those of these usual methods. From this juxtaposition, we realised that our model and the three traditional methods had almost the same rankings and selected one of the networks as the best performing mobile phone operator and another one as the worst performing network. On the second data set, all the four methods unanimously settled on civic car as the best brand and ford as the worst one. Moreover, the novel model proposed here has been found to be more resilient and capable of dealing with large size decision-making problems with relative ease than each of the three usual approaches mentioned herein.