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In this paper the authors introduce the "Theory of α-Sustainable Development" which is developed using fuzzy set theory. The existing concept and definition of "Sustainable Development" is correct and well understood by the world, but is not very precisely defined. In our "Theory of α-Sustainable Development" we say that every development (D) is a sustainable development up to certain extent depending upon the fuzzy measure 'α' of the amount of sustainability of D. We propose double categorization of every hybrid-pillar (HP) Development for better evaluation: Categorization in Type-1 and Categorization in Type-2. For a single-pillar development D the value of the fuzzy measure α is a non-negative number in [0,1], and the same is also true for a hybrid pillar (2P or 3P) development D while categorizing under Type-2. However, while categorizing the HP-Developments under Type-1, the value of α is an ordered pair (α 1 , α 2) where α 1 and α 2 are in [0,1]. Every development D is graded to be qualified as one of the five categories of sustainable development: SSD, GSD, PSD, WSD and NSD. In 'Theory of α-Sustainable Development' the existing core notion of 'Sustainable Development' is neither compromised nor diluted. The theory initially discusses about 'single-pillar Sustainable Development' and then about 'multi-pillar Sustainable Development' (also called by Hybrid Pillar Sustainable Development). The notion of 'α-Sustainable Development' will be very much useful to the corresponding regulatory bodies to improve the practices of dealing a development D with the existing notion of Yes-No type of sustainable development. Mathematically, the core aim of this paper is to grade a development D in the continuous range [0,1] instead of the existing notion of grading in the discrete range {0, 1}. This work deals only with those type of developments which are completely constructed, not about reviewing the interim progress of them. The "Theory of α-Sustainable Development" is an open proposal to the 2030 Agenda meeting, and will surely enrich the policy of ESD for educating the present and future generation people and thus to retain the sustainability of our planet as a whole. [ABSTRACT FROM AUTHOR]