Neutrosophic MCDM Problems

A B B  C M 0.5 0.3 0.2 α·m 0.4 0.24 0.16 (1- α)·m(A) 0.1 0.06 0.04

Lost mass of m(A) of 0.1 is going half-half to A  B and to

A  C; Lost mass of B of 0.06 is going half-half to A  B and to

B  C; Lost mass of B  C of 0.04 is going to A  B  C. The result:

A B B  C A  B A  C A  B  C 0.4 0.24 0.16 0.05 0.05 0.04 0.03 0.03

DSm Reliability 0.4 0.24 0.19 0.08 0.05 0.04 DST Reliability 0.4 0.24 0 0 0 0.36 DSmRel is more specific than DSTRel.

Neutrosophic MCDM Problems

Kajal Chatterjee Presently I am working on MCDM problems in uncertain domains. Few papers are published by mine and few are under processing (in fuzzy, rough, grey); neutrosophic set is good area. I have read many papers of yours and others jointly working with you. I have few queries for you:

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I want to apply neutrosophic set and its extensions in

MCDM problems. I have studied Interval valued neutrosophic set (NS), intuitionistic NS, Bipolar NS, fuzzy rough NS etc... But can you suggest me the latest one you have find out, to be applied here. I have published papers and few are in pipeline on areas of Multi-Criteria Decision Making (MCDM) methods like TOPSIS, VIKOR, COPRAS which are used in uncertain domain (fuzzy, rough, Grey sets and number). But studying deeply and seeing the flexibility in Neutrosophic set, I think it can be applied for decision making. MCDM mainly applies in two part: 1st part is criteria weight selection, and 2nd part is ranking the alternatives based on the criteria weights. There are many papers based on the above scenarios. 1. In crisp mode: AHP for criteria weights, and VIKOR for ranking alternatives. 2. In Fuzzy mode: fuzzy AHP for criteria weight, and fuzzy VIKOR for ranking alternatives. Similarly, uncertain numbers like Type-2 fuzzy, intuitionistic fuzzy, interval-valued fuzzy, multi-fuzzy are applied for the above in place of fuzzy numbers. 3. Similarly, Grey numbers, rough numbers are also applied. But each has its own advantage and disadvantage.

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4. There are also hybrid uncertain numbers: rough fuzzy number, or fuzzy rough number, or interval valued fuzzy rough number in decision making. 5. Here, we want to apply from among one of your methods: interval-valued neutrosophic set, intuitionistic neutrosophic set, bipolar neutrosophic set etc. 6. But few works in MCDM are already done based on above methods. So, as a creator and originator of neutrosophic set, I want from you some recent works you have done, in current year, which can be applied in our paper. Florentin Smarandache 1. I will go through my α-discounting method, an alternative to AHP and will try to apply it in uncertain domain. Only one paper "Fuzzy α-discounting method for multi-criteria decision-making" by Atilla Karaman and Metin Dagdeviren, has been developed where uncertain fuzzy number is applied. 2. Then we develop Neutrosophic EDAS methodology (a new MCDM method) for alternative ranking. 3. Finding a suitable case study, we will apply the above

Neutrosophic α-discounting-EDAS MCDM methodology (which will be new in this field). 4. A comparative analysis will be done for α-discounting, fuzzy α-discounting and Neutrosophic α-discounting for the ranking of criteria weights.

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