A New Technique to Solve Transportation Problems Using De-Pythagorean Value in Generalized Interval Valued Pythagorean Environment

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:

• 1.

  The information is collateral to a certain interval.

• 2.

  Non-appearance of the concept of membership function.

Considering (Zadeh, 1965) Fuzzy number, we can notify:

• 1.

  Prominent of the conviction of inclusion of the elements.

• 2.

  Existence of the utility of membership function.

Noting (Atanassov, 1986) in case of Intuitionistic fuzzy number, we can understand:

• 1.

  Launching the concept of inclusion and exclusion of the elements.

• 2.

  Availability of the utility of membership and non-membership functions.

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:

• 1.

  Augmentation part of Institutionistic Fuzzy number and its membership function.

• 2.

  Alteration of membership functions in a logical way.

1.2 Basic Idea for Taking Parametric Interval Number

The interval numbers are constituted in two ways:

• 1.

  Writing in simple interval. E.g., , which means that all the information

• 2.

  Composing in parametric form. E.g., , , which means all the information is where .

Now a basic question arises why we have taken the second representation? The answer for the following question is that we can cover all the points between and by applying the second representation. According to our requirements, we can insert a particular value of and find the result. When we insert we find the lowest value of the resultant interval and if we write we find the highest value of the resultant interval.