1.1 Theory of Vagueness
In the light of recent events, fiascos of different domains cannot be solved by our usual perception of crisp numbers, because the sets of information acquired are very much associated with the theory of uncertainty. The postulate of impreciseness executes a crucial role in the field of modeling sciences and engineering problem but there lingers a note of inquisition as to how to expound the concept of ambiguity in our mathematical modeling. Diverse Researchers from all the four corners of the planet have manifested multifarious outlooks for defining them, furnishing us with their recommendations and perspectives to employ the theory of uncertainty. We are equipped with copious literary evidences in order to allocate some basic uncertainty parameters assuming that there is no unique rearrangement of the parameter of uncertainty. It can be streamlined adhering to the whims of decision makers deciphering the puzzles of quandary and can be distinguished as well as portraying different applications. Our basic manifesto is to represent some points of information regarding the parameter of uncertainty showing their difference from other concepts assisting the notion of ambiguity utilizing some technical terms, schematics and illustrations. In this paper we advise the mathematicians to affirm the uncertainty parameter as parametric interval valued Neutrosophic number.
The elementary proofs of dissimilarity between some uncertain parameter are as follows.
Having taken Interval number, we can observe:
Considering (Zadeh, 1965) Fuzzy number, we can notify:
Noting (Atanassov, 1986) in case of Intuitionistic fuzzy number, we can understand:
Observing (Smarandache, 1998) Taking into account Neutrosophic fuzzy number:
- 1.
Establishing the concept of truth, falsehood and indefinite nature of the elements.
- 2.
Existence of manipulating inclusion function for truth, falsehood and inconclusiveness.
Surveying (Yager & Abbasov, 2013) Analysis of Pythagorean fuzzy number: