Date of Submission


Date of Award


Institute Name (Publisher)

Indian Statistical Institute

Document Type

Doctoral Thesis

Degree Name

Doctor of Philosophy

Subject Name

Computer Science


Electronics and Communication Sciences Unit (ECSU-Kolkata)


Ray, Kumar Sankar (ECSU-Kolkata; ISI)

Abstract (Summary of the Work)

Many years of research in Artificial Intelligence, Cognitive Science and allied area reveal that the cognitive process of human reasoning deals with imprecise premises. As cognitive process of human reasoning is mainly concerned with the individual's perception, it is liable to be imprecise in nature. Precise traditional two-valued logic and/or multi-valued logics are not effective in handling such reasoning processes. This motivated Zadeh (109) to investigate how these impreciseness in human rea- soning could be modeled through some computable entities. In this regard, Zadeh has shown how such imprecise linguistic terms could be expressed through fuzzy sets over universes of discourse, how linguistic variables could be handled and how deductive processes could be modeled for reasoning with imprecise concepts. These researches together with research on the calculus of linguistic variables (111] resulted in a general theory of approximate reasoning. The main motivation of the theory of approximate reasoning is apparently the desire to build up a quantitative framework that will allow us to derive an approx- imate conclusion from imprecise knowledge. Approximate reasoning is somewhat structured yet flexible and more importantly, reliable. The basic principles of the theory of approximate reasoning have been formulated by Zadeh (110, 113, 114). Since then, different forms of approximate reasoning have been studied by many researchers (35, 37, 38, 39). A collection of imprecise knowledge given by human experts gives a fuzzy system. The task of a fuzzy system is to exploit the expert's knowledge and model the world with it. A fuzzy system reasons with its knowledge. Reasoning with impre- cise knowledge is one of the main problems in the design of fuzzy systems. It has been extremely difficult for traditional mathematical models to capture such inex- act reasoning in all its power and flexibility. Reasoning with imprecise data also shows that there is much flexibility in the reasoning of a cognitive agent. Different patterns of approximate reasoning in human beings indicate a need for similarity matching, in situations where there is no directly applicable knowledge, to come up with a plausible conclusion. In such cases, the confidence in a conclusion may be determined, based on a degree of similarity. In order to capture this, we also need corresponding flexibility in our model. Specifically, we need means to han- dle graded information on the one hand and the concept of similarity on the other hand. Conventional approximate reasoning does not consider the concept of similar- ity measure in deriving a consequence. Existing similarity based reasoning methods modify the consequence of a rule, based on a measure of similarity and therefore, the consequence becomes independent of the conditionals. To satisfy both the require- ments simultaneously, we need to integrate conventional approximate reasoning and similarity based reasoning for an adequate theory of similarity based approximate reasoning.In the present thesis, we attempt to use the concept of similarity between prototypes of fuzzy sets in approximate reasoning methodology. This is why the title of the thesis is 'Similarity based approximate reasoning'. New similarity measures are proposed and existing phenomenon of similarity based reasoning and approximate reasoning methods are combined. We attempt to account for different patterns of human reasoning through the proposed similarity based approximate reasoning mechanism.


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Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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