difference between rise and increase

rise - ( өсөх, дээшлэх, нэмэгдэх) [intransitive](үүнийг чи "өссөн, дээшилсэн" гэсэн утгаар хэрэглэж болно - тоо ширхэгийн талаас авч үзээгүй гэдгийг анхаар)
1)   (+ adverb/preposition)
        to come or go upward; to reach a higher level or position

            - Smoke was rising from the chimney.

            - The river has risen (by) several feet.

2)   (+ adverb/preposition)

            (formal) to get up from a lying, sitting, or kneeling position

                 - They rose from the table.

                 - She rose to her feet.

     3)   of sun/ moon

           when the sun, moon, etc.rises, it appears above the horizon

                 - The sun rises in the east.

      4)  to increase in amount or number

                 - rising fuel bills

                 - The price of gas rose.

                 - Unemployment rose (by) 3%.

       5)  (+ adverb/preposition)

        to become more successful, important, powerful, etc.

             - a rising young politician

             - He rose to the rank of general.

increase - (өсөх, өсгөх, олшруулах, нэмэгдүүлэх, ихсэх) [intransitive, transitive] ( чи зөвхөн үүнийг ямар нэг юм "олон болсон, олширсон" гэсэн утгаар хэрэглэнэ - тоо ширхэгийн хувьд)
to become or to make something greater in amount, number, value, etc.
increase (from A) (to B)
   The population has increased from 1.2 million to 1.8 million.
   The price of oil increased.
increase in something
   Oil increased in price.
increase by something
   The rate of inflation increased by 2%.
increase something (from A) (to B)
   We need to increase productivity.
increase something (by something)
   They increased the price by 50%.

difference between rise and increase

• Explanation:
  As I see it, rise would involve a difference in levels whereas increase is used when quantities are involved. Usually the two are interchangeable, except:
  1. in geographical phenomena: The level of the sea has risen; the sun has risen above the horizon.
  2. standards (taken as a kind of level): The degree of interest in politics should rise as the US Elections draw near (cf. Interest in politics should rise/increase as...)
  The rule is that "increase" can normally be replaced with "rise" but the converse is not always true.

• Explanation:
  I don't have a comprehensive answer. Generally, things we think of as levels rise. So temperatures rise (although "increase" is possible), presumably because we think of the level of mercury (or whatever) in the thermometer. Things we think of as quantities increase, the number of people caught speeding has increased.
  
  In most cases, although one verb may be preferable, the other is at least possible.