Pansystems-based fuzzy systems relations and clustering

Purpose - Melting universality, quantification and relative computability into a meta-synthesis, pansystems theory develops an investigation on W-fuzziness and 0*-fuzziness connected with generalized conceptions such as derivative, equation, variational principle and OR. The purpose of this paper is to unify various mathematical structures, fuzziness categories, definitions of systems are unified within a general framework.Design methodology approach - The paper includes topics: pansystems approach to fuzzy systems and relations, pansystems variational principle and Zadeh's extension principle, pansystems clustering and its fuzzy embodiment, pansystems topology and approximation to fuzziness, relative unification of fuzziness and roughness.Findings - Zadeh extension principle about fuzziness transmission can be considered as a specific model of pansystems extremum principle, and so the more modes can be developed. Based on them a further investigation is present on pansystems clustering, which is a W-fuzzy clustering, an extension or sublation of traditional one and fuzzy one.Originality value - Pansystems clustering embodies mutuality of many logoi of different subbraches with classification-styled OR, including related interpromotions of the principles among knowledge rediscovery, data mining, mathematical reasoning and the investigations of fuzzy systems. W-fuzziness and 0*-fuzziness realize a relative unification for many logoi and principles.