Paraconsistent Many-Valued Similarity Modelling
Abdulai, Inusah (2026)
Tampere University
2026
Tieto- ja sähkötekniikan tohtoriohjelma - Doctoral Programme in Computing and Electrical Engineering
Informaatioteknologian ja viestinnän tiedekunta - Faculty of Information Technology and Communication Sciences
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Väitöspäivä
2026-04-10
Julkaisun pysyvä osoite on
https://urn.fi/URN:ISBN: 978-952-03-4469-6
https://urn.fi/URN:ISBN: 978-952-03-4469-6
Tiivistelmä
Decision science is a broad subject that encompasses all aspects of our lives. It equips us with the basic decision-making tools that enable us to make more rational, ethical, and productive decisions. This study focuses on the Multi-Attribute Decision- Making (MADM) branch of decision science. Over the years, a series of single and hybrid models have been developed to solve various Multi-attribute decision-making problems.
However, relatively little research has been done in the literature to address decision-making problems defined by the availability of vague and partially conflicting data. Hence, a decision-making model has been developed in this thesis to solve problems of this kind.
In addition, to bolster the performance of the popular PROMETHEE method, we have addressed the PROMETHEE II approach that has been identified as one of the major drawbacks of the PROMETHEE methodology.
Further, most existing methods can be considered complicated or cumbersome, an thus users may find it difficult to keep track of the calculations relating to large size decision problems. Therefore, in this thesis, a technique has been advanced to deal with such large size decision debacles.
Furthermore, a new method has been introduced to address outranking problems that are characterised by the presence of imprecise and conflicting information in situations where two or more decision-makers are involved. The objective is to derive a decision that represents the decision of the whole group (group decision-making).
Having also acknowledged the flaws of generating weights of criteria and other parameters by intuition, an easy and more accurate approach of calculating weights has been proposed to relieve decision-makers of the burden of having to determine these weights intuitively.
Last but not least, a unique model has been introduced to solve multi-attribute decision-making problems in both fuzzy and non-fuzzy environments.
In general, four models have been developed through the amalgamation of paraconsistent logic, Pavelka fuzzy logic, and fuzzy similarity relations. A fifth model, on the other hand, is mainly dependent on the Borda rule.
To test the efficiency of the developed models, a number of data sets including energy and mobile telecommunication data sets from Ghana have been analysed, and the results of these new methods have been compared with those of popular methods such as PROMETHEE, ELECTRE II, and TOPSIS.
In fact, our new approaches have the edge over these methods when it comes to certain considerations such as efficiency in relation to the size of the decision problem and the range of problems each method can solve. Actually, the efficiency of the novel models lies in the fact that they employ easier and simpler calculation procedures than the normal methods. This enables users to keep track of the progress of the calculation process without losing focus and sense of direction, especially when dealing with large-size decision problems (decision problems with numerous criteria and a great many options). Moreover, due to the flexibility and or adaptability of our models, they can be used to solve outranking decision-making problems in both classical and non-classical fields. However, the same cannot be said for the normal techniques mentioned above. Also, Unlike the above usual techniques, the novel approaches can address multi-attribute decision-making problems with incomplete and inconsistent values in their data sets. In effect, the new models are less laborious, save time, are more flexible, less prone to calculation errors, and therefore generate more accurate results than these traditional methods.
However, these novel techniques are not without drawbacks. One of the drawbacks is the rank reversal problem. That is, the ranking order of a given set of alternatives may be reversed when a new alternative is added to the already existing set of alternatives. Another drawback is that our advanced models cannot be used to solve outranking problems that have a set of sub-criteria associated with the main set of criteria. Finally, extremely large-size decision problems (assume a problem with 150 options and 100 criteria) would be too costly in terms of time, energy, and other efforts needed to get these models to solve such problems.
Furthermore, with the energy data from Ghana, the motive was to establish the six energy sources to form the energy basket for the country. Eventually, the six were identified as hydro power, solar energy, wind energy, biomass, natural gas, and oil.
In terms of mobile telecommunication, the objective was to identify the best mobile network operator among five mobile operators in the Accra region of Ghana. These five operators for the sake of confidentiality were denoted by α1 , α2 , α3 , α4 , and α5 , and in the end, α2 was adjudged the best mobile network by all the methods and α3 as the worst one.
However, relatively little research has been done in the literature to address decision-making problems defined by the availability of vague and partially conflicting data. Hence, a decision-making model has been developed in this thesis to solve problems of this kind.
In addition, to bolster the performance of the popular PROMETHEE method, we have addressed the PROMETHEE II approach that has been identified as one of the major drawbacks of the PROMETHEE methodology.
Further, most existing methods can be considered complicated or cumbersome, an thus users may find it difficult to keep track of the calculations relating to large size decision problems. Therefore, in this thesis, a technique has been advanced to deal with such large size decision debacles.
Furthermore, a new method has been introduced to address outranking problems that are characterised by the presence of imprecise and conflicting information in situations where two or more decision-makers are involved. The objective is to derive a decision that represents the decision of the whole group (group decision-making).
Having also acknowledged the flaws of generating weights of criteria and other parameters by intuition, an easy and more accurate approach of calculating weights has been proposed to relieve decision-makers of the burden of having to determine these weights intuitively.
Last but not least, a unique model has been introduced to solve multi-attribute decision-making problems in both fuzzy and non-fuzzy environments.
In general, four models have been developed through the amalgamation of paraconsistent logic, Pavelka fuzzy logic, and fuzzy similarity relations. A fifth model, on the other hand, is mainly dependent on the Borda rule.
To test the efficiency of the developed models, a number of data sets including energy and mobile telecommunication data sets from Ghana have been analysed, and the results of these new methods have been compared with those of popular methods such as PROMETHEE, ELECTRE II, and TOPSIS.
In fact, our new approaches have the edge over these methods when it comes to certain considerations such as efficiency in relation to the size of the decision problem and the range of problems each method can solve. Actually, the efficiency of the novel models lies in the fact that they employ easier and simpler calculation procedures than the normal methods. This enables users to keep track of the progress of the calculation process without losing focus and sense of direction, especially when dealing with large-size decision problems (decision problems with numerous criteria and a great many options). Moreover, due to the flexibility and or adaptability of our models, they can be used to solve outranking decision-making problems in both classical and non-classical fields. However, the same cannot be said for the normal techniques mentioned above. Also, Unlike the above usual techniques, the novel approaches can address multi-attribute decision-making problems with incomplete and inconsistent values in their data sets. In effect, the new models are less laborious, save time, are more flexible, less prone to calculation errors, and therefore generate more accurate results than these traditional methods.
However, these novel techniques are not without drawbacks. One of the drawbacks is the rank reversal problem. That is, the ranking order of a given set of alternatives may be reversed when a new alternative is added to the already existing set of alternatives. Another drawback is that our advanced models cannot be used to solve outranking problems that have a set of sub-criteria associated with the main set of criteria. Finally, extremely large-size decision problems (assume a problem with 150 options and 100 criteria) would be too costly in terms of time, energy, and other efforts needed to get these models to solve such problems.
Furthermore, with the energy data from Ghana, the motive was to establish the six energy sources to form the energy basket for the country. Eventually, the six were identified as hydro power, solar energy, wind energy, biomass, natural gas, and oil.
In terms of mobile telecommunication, the objective was to identify the best mobile network operator among five mobile operators in the Accra region of Ghana. These five operators for the sake of confidentiality were denoted by α1 , α2 , α3 , α4 , and α5 , and in the end, α2 was adjudged the best mobile network by all the methods and α3 as the worst one.
Kokoelmat
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